@article {43269,
	title = {Algebraic multigrid methods for metric-perturbed coupled problems},
	journal = {SIAM J. Sci. Comput.},
	year = {2023},
	publisher = {SIAM},
	abstract = {We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers based on aggregation-based algebraic multigrid methods with custom smoothers that preserve the coupling information on each coarse level. We prove that with the proper choice of subspace splitting we obtain uniform convergence in discretization and physical parameters in the two-level setting. Additionally, we show parameter robustness and scalability with regards to number of the degrees of freedom of the system on several numerical examples related to the biophysical processes in the brain, namely the electric signalling in excitable tissue modeled by bidomain, EMI and reduced EMI equations.},
	url = {https://arxiv.org/abs/2305.06073},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@article {42993,
	title = {Estimates for the astrocyte endfoot sheath permeability of the extra-cellular pathway},
	journal = {Fluids and Barriers of the CNS},
	volume = {20},
	year = {2023},
	publisher = {biorxiv},
	author = {Koch, Timo and Vinje, Vegard and Mardal, Kent-Andre}
}
@article {43292,
	title = {Exploring New Electroencephalogram Parameters in Electroconvulsive Therapy},
	journal = {The Journal of ECT},
	year = {2023},
	month = {Jan-01-2023},
	publisher = { Wolters Kluwer Health},
	issn = {1095-0680},
	doi = {10.1097/YCT.0000000000000930},
	url = {https://journals.lww.com/10.1097/YCT.0000000000000930https://journals.lww.com/10.1097/YCT.0000000000000930},
	author = {Jakob Emil {Schreiner} and Kessler, Ute and Ketil Joachim {Oedegaard} and Mardal, Kent-Andre and Oltedal, Leif}
}
@article {43096,
	title = {Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation},
	journal = {Fluids and Barriers of the Central Nervous System},
	year = {2023},
	month = {08/2023},
	publisher = {Springer Nature},
	abstract = {Human brain homeostasis requires carefully regulated transport of nutrients and waste, but its governing mechanisms are hard to quantify. By combining multi-modal gMRI data over 48 hours with high-fidelity inverse computational modelling, we here identify several potential transport mechanisms that best explain the clinical observations. Our findings support the combined roles of local, vascular and glymphatic-type clearance pathways within human brain tissue with tissue flow velocities on the order of $\mu$m/min, local clearance rates at the order of 10**(-3)/min, and\&nbsp;enhanced diffusion by a factor 3.5, in sleeping and sleep-deprived subjects. Reduced advection fully explains reduced tracer clearance after sleep-deprivation, supporting the role of sleep and sleep deprivation on human brain clearance.},
	doi = {https://doi.org/10.1101/2023.01.01.522190},
	author = {Vinje, Vegard and Zapf, Bastian and Ringstad, Geir and Per Kristian {Eide} and Marie E. {Rognes} and Mardal, Kent-Andre}
}
@inproceedings {42935,
	title = {Rational approximation preconditioners for multiphysics problems},
	journal = {Numerical Methods and Applications (NMA 2022)},
	volume = {13858},
	year = {2023},
	month = {05/2023},
	pages = {100-113},
	publisher = { Springer},
	edition = {Lecture Notes in Computer Science},
	address = {Cham},
	abstract = {We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations.},
	keywords = {Multiphysics, preconditioning, Rational approximation},
	isbn = {978-3-031-32412-3},
	doi = {10.1007/978-3-031-32412-3_9},
	url = {https://doi.org/10.1007/978-3-031-32412-3_9},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}},
	editor = {Georgiev, Ivan and Datcheva, Maria and Georgiev, Krassimir and Nikolov, Geno}
}
@article {43163,
	title = {Sleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport},
	journal = {Nature Communications},
	year = {2023},
	month = {Jan-12-2023},
	publisher = {Nature},
	doi = {10.1038/s41467-023-36643-5},
	url = {https://www.nature.com/articles/s41467-023-36643-5https://www.nature.com/articles/s41467-023-36643-5.pdfhttps://www.nature.com/articles/s41467-023-36643-5.pdfhttps://www.nature.com/articles/s41467-023-36643-5},
	author = {Bojarskaite, Laura and Vallet, Alexandra and Daniel M. {Bj{\o}rnstad} and Kristin M. Gullest {Binder} and Cunen, C{\'e}line and Heuser, Kjell and Kuchta, Miroslav and Mardal, Kent-Andre and Enger, Rune}
}
@article {28368,
	title = {Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion},
	journal = {SIAM J. of Numerical Analysis},
	volume = {61},
	year = {2023},
	publisher = {arXiv},
	url = {https://arxiv.org/pdf/2109.15006.pdf},
	author = {Gomez-Vargas, Bryan and Mardal, Kent-Andre and Ruiz-Baier, Ricardo and Vinje, Vegard}
}
@article {paper45,
	title = {CSF circulation and dispersion yield rapid clearance from intracranial compartments},
	journal = {Frontiers in Bioengineering and Biotechnology},
	volume = {12},
	year = {2022},
	month = {09/2022},
	publisher = {Frontiers},
	doi = {https://doi.org/10.3389/fbioe.2022.932469},
	url = {https://www.frontiersin.org/articles/10.3389/fbioe.2022.932469/full},
	author = {Hornkj{\o}l, Martin and Lars Magnus {Valnes} and Geir A. {Ringstad} and Marie E. {Rognes} and Per Kristian {Eide} and Mardal, Kent-Andre and Vinje, Vegard}
}
@article {42973,
	title = {Encoder{\textendash}decoder neural networks for predicting future},
	journal = {Journal of Biophotonics},
	volume = {15},
	year = {2022},
	month = {06/2022},
	pages = {e202200097},
	publisher = {Wiley},
	issn = {1864-063X},
	doi = {10.1002/jbio.v15.910.1002/jbio.202200097},
	author = {Kuchta, Miroslav and Sileshi Gizachew {Wubshet} and Nils Kristian {Afseth} and Mardal, Kent-Andre and Kristian Hovde {Liland}}
}
@misc {42968,
	title = {Fractional Laplacians and Hybridized DG},
	howpublished = {Simula{\textquoteright}s Workshop on computational mechanics models on domains of heterogeneous dimensionality, Split, Croatia},
	year = {2022},
	author = {Kuchta, Miroslav and Budisa, Ana and Hu, Xiaozhe and Ludmil Tomov {Zikatanov} and Mardal, Kent-Andre}
}
@misc {42965,
	title = {Fractional operators in coupled multiphysics problems with implicit coupling},
	howpublished = {Numerical Solution of Fractional Differential Equations and Applications  NSFDE\&A{\textquoteright}22},
	year = {2022},
	author = {Kuchta, Miroslav and Wietse M {Boon} and Karl Erik {Holter} and Hornkj{\o}l, Martin and Koch, Timo and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {42655,
	title = {The glymphatic system: Current understanding and modeling},
	journal = {iScience},
	year = {2022},
	month = {08/2022},
	publisher = {Cell Press},
	address = {iScience},
	issn = {25890042},
	doi = {10.1016/j.isci.2022.104987},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S2589004222012597},
	author = {Bohr, Tomas and Poul G. {Hjorth} and Sebastian C. {Holst} and Hrab{\v e}tov{\'a}, Sabina and Kiviniemi, Vesa and Lilius, Tuomas and Lundgaard, Iben and Mardal, Kent-Andre and Erik A. {Martens} and Mori, Yuki and N{\"a}gerl, Valentin and Nicholson, Charles and Tannenbaum, Allen and John H. {Thomas} and Tithof, Jeffrey and Benveniste, Helene and Jeffrey J. {Iliff} and Douglas H. {Kelley} and Nedergaard, Maiken}
}
@article {42936,
	title = {HAZniCS {\textendash} Software Components for Multiphysics Problems},
	journal = {ACM Transactions on Mathematical Software},
	year = {2022},
	publisher = {ACM},
	abstract = {We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus of the paper is on the design and implementation of a pool of robust and efficient solver algorithms which tackle issues related to the complex interfacial coupling of the physical problems often encountered in applications in brain biomechanics. The robustness and efficiency of the numerical algorithms and methods is shown in several numerical examples, namely the Darcy-Stokes equations that model flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue.},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@article {42756,
	title = {Investigating molecular transport in the human brain from MRI with physics-informed neural networks},
	journal = {Scientific Reports},
	volume = {12},
	year = {2022},
	month = {Jan-12-2022},
	pages = {15475},
	publisher = {Springer Nature},
	doi = {10.1038/s41598-022-19157-w},
	url = {https://www.nature.com/articles/s41598-022-19157-w},
	author = {Zapf, Bastian and Haubner, Johannes and Kuchta, Miroslav and Ringstad, Geir and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@book {27753,
	title = {Mathematical modeling of the human brain: from magnetic resonance images to finite element simulation},
	series = {Simula SpringerBriefs on Computing},
	volume = {10},
	year = {2022},
	pages = {118},
	publisher = {Springer},
	organization = {Springer},
	address = {Cham},
	author = {Mardal, Kent-Andre and Marie E. {Rognes} and Travis B. {Thompson} and Lars Magnus {Valnes}}
}
@misc {43225,
	title = {Modeling fluid flow in perivascular networks},
	howpublished = {ECCOMAS22, Oslo (Norway)},
	year = {2022},
	doi = {https://doi.org/10.5281/zenodo.7848945},
	author = {Daversin-Catty, C{\'e}cile and Vinje, Vegard and Gjerde, Ingeborg and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@misc {42967,
	title = {Parameter-robust Methods for Biot-Stokes and Darcy-Stokes Interfacial Coupling without Lagrange Multipliers},
	howpublished = {15th World Congress on Computation Mechanics},
	year = {2022},
	author = {Kuchta, Miroslav and Wietse M {Boon} and Hornkj{\o}l, Martin and Koch, Timo and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {42567,
	title = {Parameter-robust methods for the Biot{\textendash}Stokes interfacial coupling without Lagrange multipliers},
	journal = {Journal of Computational Physics},
	volume = {467},
	year = {2022},
	month = {Jan-10-2022},
	pages = {111464},
	publisher = { Elsevier},
	issn = {00219991},
	doi = {10.1016/j.jcp.2022.111464},
	author = {Wietse M. {Boon} and Hornkj{\o}l, Martin and Kuchta, Miroslav and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@misc {42966,
	title = {Parameter-robust monolithic solvers for coupled Biot/Darcy-Stokes models},
	howpublished = {27th International Domain Decomposition Conference, DD27},
	year = {2022},
	author = {Kuchta, Miroslav and Wietse M {Boon} and Koch, Timo and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@misc {42964,
	title = {Parameter-robust monolithic solvers for Stokes-Darcy/Biot systems},
	howpublished = {The 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Oslo, Norway},
	year = {2022},
	author = {Kuchta, Miroslav and Wietse M {Boon} and Karl Erik {Holter} and Hornkj{\o}l, Martin and Koch, Timo and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {hong2021robust,
	title = {Robust approximation of generalized Biot-Brinkman problems},
	journal = {Journal on Scientific Computing},
	volume = {93},
	year = {2022},
	month = {11/2022},
	pages = {77},
	publisher = {Springer},
	url = {https://arxiv.org/abs/2112.13618},
	author = {Hong, Q. and Kraus, J. and Kuchta, Miroslav and Lymbery, M. and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {42757,
	title = {Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form},
	journal = {SIAM Journal on Scientific Computing},
	volume = {4426},
	year = {2022},
	month = {Jan-08-2022},
	pages = {B1148 - B1174},
	publisher = {SIAM},
	issn = {1064-8275},
	doi = {10.1137/21M1452974},
	url = {https://epubs.siam.org/doi/10.1137/21M1452974},
	author = {Wietse M. {Boon} and Koch, Timo and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {28467,
	title = {Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {60},
	year = {2022},
	month = {Jan-02-2022},
	pages = {195 - 221},
	publisher = {SIAM },
	issn = {0036-1429},
	doi = {10.1137/21M139147X},
	url = {https://epubs.siam.org/doi/10.1137/21M139147Xhttps://epubs.siam.org/doi/pdf/10.1137/21M139147X},
	author = {Mardal, Kent-Andre and Sogn, Jarle and Takacs, Stefan}
}
@article {42566,
	title = {Simulating epileptic seizures using the bidomain model},
	journal = {Scientific Reports},
	volume = {12},
	year = {2022},
	month = {Jan-12-2022},
	publisher = { Springer nature},
	doi = {10.1038/s41598-022-12101-y},
	url = {https://www.nature.com/articles/s41598-022-12101-yhttps://www.nature.com/articles/s41598-022-12101-y.pdfhttps://www.nature.com/articles/s41598-022-12101-y.pdfhttps://www.nature.com/articles/s41598-022-12101-y},
	author = {Schreiner, Jakob and Mardal, Kent-Andre}
}
@article {bojarskaite2022sleep,
	title = {Sleep cycle-dependent vascular dynamics enhance perivascular cerebrospinal fluid flow and solute transport},
	journal = {bioRxiv},
	year = {2022},
	publisher = {BioArxiv},
	author = {Bojarskaite, Laura and Daniel Marelius {Bj{\o}rnstad} and Vallet, Alexandra and Kristin M Gullesta {Binder} and Cunen, C{\'e}line and Heuser, Kjell and Kuchta, Miroslav and Mardal, Kent-Andre and Enger, Rune}
}
@article {paper35,
	title = {Accurate discretization of poroelasticity without Darcy stability {\textendash} Stokes-Biot revisited},
	journal = {BIT Numerical Mathematics},
	volume = {61},
	year = {2021},
	pages = {941-976},
	publisher = {Springer},
	doi = {https://doi.org/10.1007/s10543-021-00849-0},
	author = {Mardal, Kent-Andre and Marie E. {Rognes} and Thompson, Travis}
}
@article {kuchta2020analysis,
	title = {Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {59},
	year = {2021},
	pages = {558{\textendash}582},
	publisher = {SIAM},
	doi = {https://doi.org/10.1137/20M1329664},
	author = {Kuchta, Miroslav and Laurino, Federica and Mardal, Kent-Andre and Zunino, Paolo}
}
@inbook {27254,
	title = {A cell-based model for ionic electrodiffusion in excitable tissue},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	number = {7},
	year = {2021},
	pages = {14-27},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	url = {https://www.springer.com/gp/book/9783030611569},
	author = {Ada Johanne {Ellingsrud} and Daversin-Catty, C{\'e}cile and Marie E. {Rognes}},
	editor = {Mardal, Kent-Andre and Marie E. {Rognes} and Tveito, Aslak}
}
@inbook {27507,
	title = {Derivation of a Cell-Based Mathematical Model of Excitable Cells},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	pages = {1-13},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	chapter = {1},
	address = {Cham},
	abstract = {Excitable cells are of vital importance in biology, and mathematical models have contributed significantly to understand their basic mechanisms. However, classical models of excitable cells are based on severe assumptions that may limit the accuracy of the simulation results. Here, we derive a more detailed approach to modeling that has recently been applied to study the electrical properties of both neurons and cardiomyocytes. The model is derived from first principles and opens up possibilities for studying detailed properties of excitable cells. We refer to the model as the EMI model because both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model, in contrast to classical spatial models of excitable cells. Later chapters of the present text will focus on numerical methods and software for solving the model. Also, in the next chapter, the model will be extended to account for ionic concentrations in the intracellular and extracellular spaces.},
	isbn = {978-3-030-61157-6},
	issn = {2512-1677},
	doi = {10.1007/978-3-030-61157-6_1},
	url = {https://link.springer.com/content/pdf/10.1007\%2F978-3-030-61157-6_1.pdf},
	author = {Karoline Horgmo {J{\ae}ger} and Tveito, Aslak},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {28208,
	title = {Direction and magnitude of cerebrospinal fluid flow vary substantially across central nervous system diseases},
	journal = {Fluids and Barriers of the CNS},
	volume = {18},
	year = {2021},
	month = {Jan-12-2021},
	publisher = {Springer},
	doi = {10.1186/s12987-021-00251-6},
	url = {https://fluidsbarrierscns.biomedcentral.com/articles/10.1186/s12987-021-00251-6},
	author = {Per Kristian {Eide} and Lars Magnus {Valnes} and Erika Kristina {Lindstr{\o}m} and Mardal, Kent-Andre and Ringstad, Geir}
}
@inbook {27586,
	title = {Improving Neural Simulations with the EMI Model},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	year = {2021},
	pages = {87{\textendash}98},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {Mathematical modeling of neurons is an essential tool to investigate neuronal activity alongside with experimental approaches. However, the conventional modeling framework to simulate neuronal dynamics and extracellular potentials makes several assumptions that might need to be revisited for some applications. In this chapter we apply the EMI model to investigate the ephaptic effect and the effect of the extracellular probes on the measured potential. Finally, we introduce reduced EMI models, which provide a more computationally efficient framework for simulating neurons with complex morphologies.},
	isbn = {978-3-030-61157-6},
	doi = {10.1007/978-3-030-61157-6_7},
	url = {https://doi.org/10.1007/978-3-030-61157-6_7},
	author = {Alessio Paolo {Buccino} and Kuchta, Miroslav and Schreiner, Jakob and Mardal, Kent-Andre},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@inbook {27585,
	title = {Iterative Solvers for EMI Models},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	year = {2021},
	pages = {70{\textendash}86},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {This chapter deals with iterative solution algorithms for the four EMI formulations derived in (17, Chapter 5). Order optimal monolithic solvers robust with respect to material parameters, the number of degrees of freedom of discretization as well as the time-stepping parameter are presented and compared in terms of computational cost. Domain decomposition solver for the single-dimensional primal formulation is discussed.},
	isbn = {978-3-030-61157-6},
	doi = {10.1007/978-3-030-61157-6_6},
	url = {https://doi.org/10.1007/978-3-030-61157-6_6},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@inbook {27570,
	title = {Modeling Cardiac Mechanics on a Sub-Cellular Scale},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	month = {11/2020},
	pages = {28-43},
	publisher = { Springer International Publishing},
	organization = { Springer International Publishing},
	edition = {1},
	chapter = {3},
	address = {Cham},
	abstract = {We aim to extend existing models of single-cell mechanics to the EMI framework, to define spatially resolved mechanical models of cardiac myocytes embedded in a passive extracellular space. The models introduced here will be pure mechanics models employing fairly simple constitutive laws for active and passive mechanics. Future extensions of the models may include a coupling to the electrophysiology and electro-diffusion models described in the other chapters, to study the impact of spatially heterogeneous ion concentrations on the cell and tissue mechanics.},
	author = {Telle, {\r A}shild and Wall, Samuel and Sundnes, Joakim},
	editor = {Tveito, Aslak and Marie E. {Rognes} and Mardal, Kent-Andre}
}
@book {27752,
	title = {Modeling Excitable Tissue: The EMI Framework},
	year = {2021},
	publisher = {Springer},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@misc {43224,
	title = {Modeling fluid flow in perivascular networks},
	howpublished = {Oslo glymphatics symposium, Oslo (Norway)},
	year = {2021},
	doi = {https://doi.org/10.5281/zenodo.7848945},
	author = {Daversin-Catty, C{\'e}cile and Gjerde, Ingeborg and Mardal, Kent-Andre and Marie E. {Rognes} and Vinje, Vegard}
}
@inbook {27497,
	title = {Operator Splitting and Finite Difference Schemes for Solving the EMI Model},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	volume = {7},
	year = {2021},
	pages = {44 - 55},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	chapter = {4},
	address = {Cham},
	abstract = {We want to be able to perform accurate simulations of a large number of cardiac cells based on mathematical models where each individual cell is represented in the model. This implies that the computational mesh has to have a typical resolution of a few {\textmu}m leading to huge computational challenges. In this paper we use a certain operator splitting of the coupled equations and showthat this leads to systems that can be solved in parallel. This opens up for the possibility of simulating large numbers of coupled cardiac cells.},
	isbn = {978-3-030-61156-9},
	issn = {2512-1677},
	doi = {10.1007/978-3-030-61157-6_4},
	url = {http://link.springer.com/content/pdf/10.1007/978-3-030-61157-6_4},
	author = {Karoline Horgmo {J{\ae}ger} and Kristian Gregorius {Hustad} and Cai, Xing and Tveito, Aslak},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {paper33,
	title = {Parameter robust preconditioning by congruence for multiple-network poroelasticity},
	journal = {SIAM Journal of Scientific Computing},
	volume = {43},
	year = {2021},
	pages = {B984{\textendash}B1007},
	publisher = {SIAM},
	doi = {https://doi.org/10.1137/20M1326751},
	author = {Piersanti, Eleonora and Jeonghun J. {Lee} and Mardal, Kent-Andre and Marie E. {Rognes} and Thompson, Travis}
}
@inproceedings {paper42,
	title = {Parameter robust preconditioning for multi-compartmental Darcy equations},
	journal = {Numerical Mathematics and Advanced Applications ENUMATH 2019},
	volume = {139},
	year = {2021},
	pages = {794{\textendash}797},
	publisher = {Springer International Publishing},
	edition = {1},
	doi = {10.1007/978-3-030-55874-1},
	author = {Piersanti, Eleonora and Marie E. {Rognes} and Mardal, Kent-Andre}
}
@article {28207,
	title = {Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot{\textquoteright}s Equations Utilizing Total Pressure},
	journal = {SIAM Journal on Scientific Computing},
	volume = {43},
	year = {2021},
	month = {Jan-01-2021},
	pages = {B961 - B983},
	publisher = {SIAM},
	issn = {1064-8275},
	doi = {10.1137/20M1379708},
	url = {https://epubs.siam.org/doi/10.1137/20M1379708https://epubs.siam.org/doi/pdf/10.1137/20M1379708},
	author = {Wietse M. {Boon} and Kuchta, Miroslav and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {27807,
	title = {Sleep deprivation impairs molecular clearance from the human brain},
	journal = {Brain},
	volume = {144},
	year = {2021},
	month = {04/2021},
	pages = {863-874},
	publisher = {Oxford Academic},
	address = {Brain},
	abstract = {It remains an enigma why human beings spend one-third of their life asleep. Experimental data suggest that sleep is required for clearance of waste products from brain metabolism. This has, however, never been verified in humans. The primary aim of the present study was to examine in vivo whether one night of total sleep deprivation affects molecular clearance from the human brain. Secondarily, we examined whether clearance was affected by subsequent sleep. Multiphase MRI with standardized T1 sequences was performed up to 48 h after intrathecal administration of the contrast agent gadobutrol (0.5 ml of 1 mmol/ml), which served as a tracer molecule. Using FreeSurfer software, we quantified tracer enrichment within 85 brain regions as percentage change from baseline of normalized T1 signals. The cerebral tracer enrichment was compared between two cohorts of individuals; one cohort (n = 7) underwent total sleep deprivation from Day 1 to Day 2 (sleep deprivation group) while an age and gender-matched control group (n = 17; sleep group) was allowed free sleep from Day 1 to Day 2. From Day 2 to 3 all individuals were allowed free sleep. The tracer enriched the brains of the two groups similarly. Sleep deprivation was the sole intervention. One night of sleep deprivation impaired clearance of the tracer substance from most brain regions, including the cerebral cortex, white matter and limbic structures, as demonstrated on the morning of Day 2 after intervention (sleep deprivation/sleep). Moreover, the impaired cerebral clearance in the sleep deprivation group was not compensated by subsequent sleep from Day 2 to 3. The present results provide in vivo evidence that one night of total sleep deprivation impairs molecular clearance from the human brain, and that humans do not catch up on lost sleep.},
	doi = {https://doi.org/10.1093/brain/awaa443},
	author = {Per Kristian {Eide} and Vinje, Vegard and Are Hugo {Pripp} and Mardal, Kent-Andre and Geir Andre {Ringstad}}
}
@inbook {27588,
	title = {Solving the EMI Equations using Finite Element Methods},
	booktitle = {Modeling Excitable Tissue: The EMI Framework},
	year = {2021},
	pages = {56{\textendash}69},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {This chapter discusses 2 X 2 symmetric variational formulations and associated finite element methods for the EMI equations. We demonstrate that the presented methods converge at expected rates, and compare the approaches in terms of approximation of the transmembrane potential. Overall, the choice of which formulation to employ for solving EMI models becomes largely a matter of desired accuracy and available computational resources.},
	isbn = {978-3-030-61157-6},
	doi = {10.1007/978-3-030-61157-6_5},
	url = {https://doi.org/10.1007/978-3-030-61157-6_5},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Marie E. {Rognes}},
	editor = {Tveito, Aslak and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {28209,
	title = {Variations in the cerebrospinal fluid dynamics of the American alligator (Alligator mississippiensis)},
	journal = {Fluids and Barriers of the CNS},
	volume = {18},
	year = {2021},
	month = {Jan-12-2021},
	publisher = {Springer},
	doi = {10.1186/s12987-021-00248-1},
	url = {https://fluidsbarrierscns.biomedcentral.com/articles/10.1186/s12987-021-00248-1},
	author = {Bruce A. {Young} and Adams, James and Jonathan M. {Beary} and Mardal, Kent-Andre and Schneider, Robert and Kondrashova, Tatyana}
}
@article {27656,
	title = {Apparent diffusion coefficient estimates based on 24 hours tracer movement support glymphatic transport in human cerebral cortex},
	journal = {Scientific Reports},
	volume = {10},
	year = {2020},
	month = {Jan-12-2020},
	publisher = {Nature},
	doi = {10.1038/s41598-020-66042-5},
	url = {http://www.nature.com/articles/s41598-020-66042-5http://www.nature.com/articles/s41598-020-66042-5.pdfhttp://www.nature.com/articles/s41598-020-66042-5.pdfhttp://www.nature.com/articles/s41598-020-66042-5},
	author = {Lars Magnus {Valnes} and Mitusch, Sebastian and Ringstad, Geir and Per Kristian {Eide} and Simon W {Funke} and Mardal, Kent-Andre}
}
@article {erhardt2020dynamics,
	title = {Dynamics of a neuron{\textendash}glia system: the occurrence of seizures and the influence of electroconvulsive stimuli: A mathematical and numerical study},
	journal = {Journal of computational neuroscience},
	volume = {48},
	number = {2},
	year = {2020},
	pages = {229-251},
	publisher = {Springer},
	author = {Andr{\'e} H {Erhardt} and Mardal, Kent-Andre and Schreiner, Jakob}
}
@article {26683,
	title = {Intracranial pressure elevation alters CSF clearance pathways},
	journal = {Fluids and Barriers of the CNS},
	volume = {17},
	number = {29},
	year = {2020},
	month = {04/2020},
	publisher = {Springer Nature BMC},
	keywords = {brain mechanics, Cerebrospinal Fluid, Intracranial pressure},
	doi = {https://doi.org/10.1186/s12987-020-00189-1},
	author = {Vinje, Vegard and Eklund, Anders and Mardal, Kent-Andre and Marie E. {Rognes} and St{\o}verud, Karen-Helene}
}
@article {27722,
	title = {The mechanisms behind perivascular fluid flow},
	journal = {PLOS ONE},
	volume = {15},
	number = {12},
	year = {2020},
	pages = {1-20},
	publisher = {Public Library of Science},
	abstract = {Flow of cerebrospinal fluid (CSF) in perivascular spaces (PVS) is one of the key concepts involved in theories concerning clearance from the brain. Experimental studies have demonstrated both net and oscillatory movement of microspheres in PVS (Mestre et al. (2018), Bedussi et al. (2018)). The oscillatory particle movement has a clear cardiac component, while the mechanisms involved in net movement remain disputed. Using computational fluid dynamics, we computed the CSF velocity and pressure in a PVS surrounding a cerebral artery subject to different forces, representing arterial wall expansion, systemic CSF pressure changes and rigid motions of the artery. The arterial wall expansion generated velocity amplitudes of 60{\textendash}260\&nbsp;μm/s, which is in the upper range of previously observed values. In the absence of a static pressure gradient, predicted net flow velocities were small (\&lt;0.5\&nbsp;μm/s), though reaching up to 7\&nbsp;μm/s for non-physiological PVS lengths. In realistic geometries, a static systemic pressure increase of physiologically plausible magnitude was sufficient to induce net flow velocities of 20{\textendash}30\&nbsp;μm/s. Moreover, rigid motions of the artery added to the complexity of flow patterns in the PVS. Our study demonstrates that the combination of arterial wall expansion, rigid motions and a static CSF pressure gradient generates net and oscillatory PVS flow, quantitatively comparable with experimental findings. The static CSF pressure gradient required for net flow is small, suggesting that its origin is yet to be determined.},
	doi = {10.1371/journal.pone.0244442},
	url = {https://doi.org/10.1371/journal.pone.0244442},
	author = {Daversin-Catty, C{\'e}cile and Vinje, Vegard and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {baerland2020observation,
	title = {An observation on the uniform preconditioners for the mixed Darcy problem},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {36},
	number = {6},
	year = {2020},
	pages = {1718{\textendash}1734},
	publisher = { Wiley},
	author = {B{\ae}rland, Trygve and Kuchta, Miroslav and Mardal, Kent-Andre and Thompson, Travis}
}
@article {boon2020robust,
	title = {Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot{\textquoteright}s equations utilizing total pressure},
	journal = {arXiv preprint arXiv:2011.05236},
	year = {2020},
	publisher = {SIAM},
	author = {Wietse M {Boon} and Kuchta, Miroslav and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {HOLTER2020,
	title = {Robust preconditioning for coupled Stokes{\textendash}Darcy problems with the Darcy problem in primal form},
	journal = {Computers \& Mathematics with Applications},
	year = {2020},
	publisher = {Elsevier},
	issn = {0898-1221},
	doi = {https://doi.org/10.1016/j.camwa.2020.08.021},
	url = {http://www.sciencedirect.com/science/article/pii/S0898122120303291},
	author = {Karl Erik {Holter} and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {holter2020robust,
	title = {Robust preconditioning of monolithically coupled multiphysics problems},
	journal = {arXiv preprint arXiv:2001.05527},
	year = {2020},
	publisher = {SIAM},
	author = {Karl Erik {Holter} and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {27161,
	title = {Slope limiting the velocity field in a discontinuous Galerkin divergence-free two-phase flow solver},
	journal = {Computers \& Fluids},
	volume = {196},
	year = {2020},
	month = {Jan-01-2020},
	pages = {104322},
	publisher = {Elsevier},
	issn = {00457930},
	doi = {10.1016/j.compfluid.2019.104322},
	author = {Landet, Tormod and Mardal, Kent-Andre and Mortensen, Mikael}
}
@article {26757,
	title = {Delayed clearance of cerebrospinal fluid tracer from choroid plexus in idiopathic normal pressure hydrocephalus},
	journal = {Journal of Cerebral Blood Flow \& Metabolism},
	volume = {2530},
	year = {2019},
	month = {Jul-09-2019},
	pages = {0271678X1987479},
	publisher = {SAGE journals},
	address = {Journal of Cerebral Blood Flow and Metabolism},
	issn = {0271-678X},
	doi = {10.1177/0271678X19874790},
	url = {http://journals.sagepub.com/doi/10.1177/0271678X19874790http://journals.sagepub.com/doi/pdf/10.1177/0271678X19874790http://journals.sagepub.com/doi/pdf/10.1177/0271678X19874790http://journals.sagepub.com/doi/full-xml/10.1177/0271678X19874790},
	author = {Per Kristian {Eide} and Lars Magnus {Valnes} and Are Hugo {Pripp} and Mardal, Kent-Andre and Ringstad, Geir}
}
@article {Buccino_2019,
	title = {How does the presence of neural probes affect extracellular potentials?},
	journal = {Journal of Neural Engineering},
	volume = {16},
	number = {2},
	year = {2019},
	month = {feb},
	pages = {026030},
	publisher = {IOP} Publishing},
	abstract = {{Objective. Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them. Approach. We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes{\textquoteright} presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials. Main results. Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation. Significance. Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.},
	doi = {10.1088/1741-2552/ab03a1},
	url = {https://doi.org/10.1088\%2F1741-2552\%2Fab03a1},
	author = {Alessio Paolo {Buccino} and Kuchta, Miroslav and Karoline Horgmo {J{\ae}ger} and Torbj{\o}rn Vefferstad {Ness} and Berthet, Pierre and Mardal, Kent-Andre and Cauwenberghs, Gert and Tveito, Aslak}
}
@misc {26622,
	title = {Intracranial pressure elevation alters CSF clearance pathways},
	howpublished = {The 2019 CSF Symposium, Oslo, Norway},
	year = {2019},
	author = {Vinje, Vegard and St{\o}verud, Karen-Helene and Marie E. {Rognes} and Mardal, Kent-Andre and Eklund, Anders}
}
@book {27160,
	title = {Introduction to Numerical Methods for Variational Problems},
	volume = {21},
	year = {2019},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	isbn = {978-3-030-23787-5},
	issn = {1611-0994},
	doi = {10.1007/978-3-030-23788-2},
	url = {http://link.springer.com/10.1007/978-3-030-23788-2http://link.springer.com/content/pdf/10.1007/978-3-030-23788-2http://link.springer.com/content/pdf/10.1007/978-3-030-23788-2.pdf},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre}
}
@article {26758,
	title = {Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {57},
	year = {2019},
	month = {Feb-01-2019},
	pages = {1369 - 1394},
	publisher = {SIAM},
	address = {SIAM Journal of Numerical Analysis},
	issn = {0036-1429},
	doi = {10.1137/18M1212458},
	url = {https://epubs.siam.org/doi/10.1137/18M1212458https://epubs.siam.org/doi/pdf/10.1137/18M1212458},
	author = {Gergelits, Tom{\'a}{\v s} and Mardal, Kent-Andre and Bj{\o}rn Fredrik {Nielsen} and Strako{\v s}, Zden{\v e}k}
}
@article {lindstrom2019magnitude,
	title = {Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage},
	journal = {Acta neurochirurgica},
	volume = {161},
	number = {2},
	year = {2019},
	pages = {247{\textendash}256},
	publisher = {Springer},
	address = {Acta neurochirurgica},
	author = {Erika Kristina {Lindstr{\o}m} and Ringstad, Geir and Sorteberg, Angelika and Sorteberg, Wilhelm and Mardal, Kent-Andre and Per Kristian {Eide}}
}
@misc {26765,
	title = {Mathematical modeling of the g - lymphatic system {\textendash} preconditioning of Darcy - Stokes systems},
	howpublished = {Biomechanics of living systems, T{\o}yen hovedg{\r a}rd, Norway},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@misc {26762,
	title = {Mathematical modeling of the glymphatic system},
	howpublished = {ICIAM, Valencia, Spain},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@misc {26764,
	title = { Mathematical modeling of the g-lymphatic system {\textendash} preconditioning of Darcy - Stokes systems},
	howpublished = {IMG 2019, Kunming, China},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@article {paper25,
	title = {A mixed finite element method for nearly incompressible multiple-network poroelasticity},
	journal = {SIAM Journal on Scientific Computing},
	volume = {41},
	year = {2019},
	month = {03/2019},
	pages = {A722{\textendash}A747},
	publisher = {SIAM},
	doi = {https://doi.org/10.1137/18M1182395},
	url = {https://epubs.siam.org/doi/10.1137/18M1182395},
	author = {Lee, Jeonghun and Piersanti, Eleonora and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {baerland2019multigrid,
	title = {Multigrid Methods for Discrete Fractional Sobolev Spaces},
	journal = {SIAM Journal on Scientific Computing},
	volume = {41},
	number = {2},
	year = {2019},
	pages = {A948{\textendash}A972},
	publisher = {{SIAM},
	author = {B{\ae}rland, Trygve and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {26760,
	title = {Multi-resolution Bayesian CMB component separation through Wiener filtering with a pseudo-inverse preconditioner},
	journal = {Astronomy \& Astrophysics},
	volume = {627},
	year = {2019},
	month = {Jan-07-2019},
	pages = {A98},
	publisher = {EDP Sciences},
	issn = {0004-6361},
	doi = {10.1051/0004-6361/201732037},
	url = {https://www.aanda.org/10.1051/0004-6361/201732037https://www.aanda.org/10.1051/0004-6361/201732037/pdf},
	author = {D. S. {Seljebotn} and B{\ae}rland, T. and H. K. {Eriksen} and Mardal, Kent-Andre and I. K. {Wehus}}
}
@misc {26773,
	title = {An Observation On The Uniform Preconditioners For The Mixed Darcy Problem},
	year = {2019},
	publisher = {arXive},
	address = {https://arxiv.org/abs/1812.00653},
	author = {B{\ae}rland, Trygve and Kuchta, Miroslav and Mardal, Kent-Andre and Thompson, Travis}
}
@misc {26763,
	title = {Parameter Identification of Brain Cleaning},
	howpublished = {ICIAM, Valencia, Spain},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@misc {26761,
	title = {Preconditioning of multi-physics problems with applications to the biomechanics of the brain},
	howpublished = {MOX, Milan, Italy},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@article {26147,
	title = {Preconditioning trace coupled 3D-1D              systems using fractional Laplacian},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {35},
	year = {2019},
	month = {Apr-09-2019},
	pages = {375-393},
	publisher = { Wiley},
	address = {Numerical Methods for Partial Differential Equations},
	doi = {10.1002/num.22304},
	url = {http://doi.wiley.com/10.1002/num.22304http://onlinelibrary.wiley.com/wol1/doi/10.1002/num.22304/fullpdfhttps://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002\%2Fnum.22304},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Mortensen, Mikael}
}
@misc {26766,
	title = {Preconditioning with some application to brain modeling},
	howpublished = {Symposium on the occasion of Ragnar Winther{\textquoteright}s 70th birthday, Oslo, Norway},
	year = {2019},
	author = {Mardal, Kent-Andre}
}
@article {25857,
	title = {Respiratory influence on cerebrospinal fluid flow {\textendash} a computational study based on long-term intracranial pressure measurements},
	journal = {Scientific Reports},
	volume = {9},
	year = {2019},
	month = {07/2019},
	pages = {9732},
	publisher = {Springer Nature},
	doi = {https://doi.org/10.1038/s41598-019-46055-5},
	author = {Vinje, Vegard and Geir A. {Ringstad} and Erika Kristina {Lindstr{\o}m} and Lars Magnus {Valnes} and Marie E. {Rognes} and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@misc {26650,
	title = {Robust preconditioners for multiphysics problems involving porous flow in physiology modeling},
	howpublished = {ICIAM 2019, Valencia, Spain},
	year = {2019},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre}
}
@misc {26597,
	title = {Robust Preconditioners for Multiscale Systems in Biomechanics},
	howpublished = { 12th International Conference on  Large-Scale Scientific Computations, Sozopol, Bulgaria},
	year = {2019},
	type = {contributed},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {26148,
	title = {On the singular Neumann problem in linear elasticity},
	journal = {Numerical Linear Algebra with Applications},
	volume = {26},
	year = {2019},
	month = {Aug-08-2019},
	pages = {e2212},
	publisher = { Wiley},
	address = {Numerical Linear Algebra with Applications},
	doi = {10.1002/nla.2212},
	url = {http://doi.wiley.com/10.1002/nla.2212http://onlinelibrary.wiley.com/wol1/doi/10.1002/nla.2212/fullpdfhttps://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002\%2Fnla.2212},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Mortensen, Mikael}
}
@inproceedings {26348,
	title = {Sub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem},
	journal = {Numerical Mathematics and Advanced Applications ENUMATH 2017},
	year = {2019},
	pages = {35 - 47},
	publisher = {Springer International Publishing},
	address = {Cham},
	isbn = {978-3-319-96414-0},
	issn = {1439-7358},
	doi = {10.1007/978-3-319-96415-710.1007/978-3-319-96415-7_2},
	url = {http://link.springer.com/content/pdf/10.1007/978-3-319-96415-7.pdf},
	author = {Karl Erik {Holter} and Kuchta, Miroslav and Mardal, Kent-Andre},
	editor = {Florin Adrian {Radu} and Kumar, Kundan and Berre, Inga and Jan Martin {Nordbotten} and Iuliu Sorin {Pop}}
}
@article {ringstad2018brain,
	title = {Brain-wide glymphatic enhancement and clearance in humans assessed with MRI},
	journal = {JCI insight},
	volume = {3},
	number = {13},
	year = {2018},
	publisher = {American Society for Clinical Investigation},
	doi = {10.1172/jci.insight.121537},
	author = {Ringstad, Geir and Lars M {Valnes} and Anders M {Dale} and Are H {Pripp} and Svein-Are S {Vatnehol} and Kyrre E {Emblem} and Mardal, Kent-Andre and Per K {Eide}}
}
@article {26327,
	title = {{\textquotedblleft}Bucket{\textquotedblright} cerebrospinal fluid bulk flow: when the terrain disagrees with the map},
	journal = {Acta Neurochirurgica},
	volume = {161},
	year = {2018},
	month = {May-12-2019},
	pages = {259{\textendash}261},
	publisher = { Springer},
	issn = {0001-6268},
	doi = {10.1007/s00701-018-3775-6},
	url = {http://link.springer.com/10.1007/s00701-018-3775-6},
	author = {Per Kristian {Eide} and Sorteberg, Angelika and Sorteberg, Wilhelm and Erika Kristina {Lindstr{\o}m} and Mardal, Kent-Andre and Ringstad, Geir}
}
@article {lindstrom2018cerebrospinal,
	title = {Cerebrospinal fluid volumetric net flow rate and direction in idiopathic normal pressure hydrocephalus},
	journal = {NeuroImage: Clinical},
	volume = {20},
	year = {2018},
	pages = {731-741},
	publisher = {Elsevier},
	author = {Erika Kristina {Lindstr{\o}m} and Ringstad, Geir and Mardal, Kent-Andre and Per Kristian {Eide}}
}
@article {25781,
	title = {Comparison of phase-contrast MR and flow simulations for the study of CSF dynamics in the cervical spine},
	journal = {The Neuroradiology Journal},
	volume = {31},
	year = {2018},
	pages = {292-298},
	publisher = { SAGE Publications},
	doi = {10.1177/1971400918759812},
	author = {Erika Kristina {Lindstr{\o}m} and Schreiner, Jakob and Ringstad, Geir and Haughton, Victor and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@misc {26014,
	title = {Fluid dynamics in syringomyelia cavities},
	howpublished = {Vancouver, Canada},
	year = {2018},
	type = {Parallel paper session at the 56th annual meeting of the American Society of Neuroradiology},
	author = {Vinje, Vegard and Brucker, Justin and Marie E. {Rognes} and Mardal, Kent-Andre and Haughton, Victor}
}
@article {26045,
	title = {Fluid dynamics in syringomyelia cavities: Effects of heart rate, CSF velocity, CSF velocity waveform and craniovertebral decompression},
	journal = {The Neuroradiology Journal},
	volume = {31},
	year = {2018},
	month = {09/2018},
	pages = {482-489},
	publisher = { SAGE Publications},
	abstract = {Purpose: How fluid moves during the cardiac cycle within a syrinx may affect its development. We measured syrinx fluid velocities before and after craniovertebral decompression in a patient and simulated syrinx fluid velocities for different heart rates, syrinx sizes and CSF flow velocities in a model of syringomyelia.Materials and Methods: With Phase Contrast MR we measured CSF and syrinx fluid velocities in a Chiari patient before and after craniovertebral decompression. With an idealized 2D model of the subarachnoid space (SAS), cord and syrinx, we simulated fluid movement in the SAS and syrinx with the Navier-Stokes equations for different heart rates, inlet velocities and syrinx diameters.Results: In the patient, fluid oscillated in the syrinx at 200 to 210 cycles per minute before and after craniovertebral decompression. Velocities peaked at 3.6 and 2.0 cm/sec respectively in the SAS and the syrinx before surgery and at 2.7 and 1.5 cm/sec after surgery. In the model, syrinx velocity varied between 0.91 and 12.70 cm/sec. Increasing CSF inlet velocities from 1.56 to 4.69 cm/sec increased peak syrinx fluid velocities in the syrinx by 151 to 299\% for the three cycle rates. Increasing cycle rates from 60 to 120 cpm, increased peak syrinx velocities by 160 to 312\% for the three inlet velocities. Peak velocities changed inconsistently with syrinx size.Conclusions: CSF velocity, heart rate and syrinx diameter affect syrinx fluid velocities, but not the frequency of syrinx fluid oscillation. Craniovertebral decompression decreases both CSF and syrinx fluid velocities.},
	url = {http://journals.sagepub.com/doi/10.1177/1971400918795482},
	author = {Vinje, Vegard and Brucker, Justin and Marie E. {Rognes} and Mardal, Kent-Andre and Haughton, Victor}
}
@misc {26016,
	title = {The Influence of Breathing on Cerebrospinal Fluid Movement in the Brain},
	howpublished = {Glasgow, United Kingdom},
	year = {2018},
	type = {Minisymposium at the ECCOMAS: ECCM - ECFD conference},
	author = {Vinje, Vegard and Geir Andre {Ringstad} and Marie E. {Rognes} and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@article {26328,
	title = {Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage},
	journal = {Acta Neurochirurgica},
	volume = {161},
	year = {2018},
	month = {Mar-11-2019},
	pages = {247{\textendash}256},
	publisher = {Springer},
	address = {Vienna},
	issn = {0001-6268},
	doi = {10.1007/s00701-018-3730-6},
	url = {http://link.springer.com/10.1007/s00701-018-3730-6http://link.springer.com/content/pdf/10.1007/s00701-018-3730-6.pdfhttp://link.springer.com/content/pdf/10.1007/s00701-018-3730-6.pdfhttp://link.springer.com/article/10.1007/s00701-018-3730-6/fulltext.html},
	author = {Erika Kristina {Lindstr{\o}m} and Ringstad, Geir and Sorteberg, Angelika and Sorteberg, Wilhelm and Mardal, Kent-Andre and Per Kristian {Eide}}
}
@misc {26150,
	title = {Mathematical modeling of the glymphatic system {\textendash} the physics of Alzheimer{\textquoteright}s disease ?},
	howpublished = {Mathematical models in health sciences, Nantes, France},
	year = {2018},
	type = {Invited Plenary},
	author = {Mardal, Kent-Andre}
}
@misc {26149,
	title = {Mathematical modeling of the glymphatic system {\textendash} the physics of Alzheimer{\textquoteright}s disease?},
	howpublished = { INdAM, Rome, Italy},
	year = {2018},
	author = {Mardal, Kent-Andre}
}
@misc {26143,
	title = {Parameter-robust discretization and preconditioning of multiple-network poroelasticity equations},
	howpublished = {University of Oxford, UK},
	year = {2018},
	author = {Piersanti, Eleonora and Jeonghun J. {Lee} and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@misc {26144,
	title = {Parameter-robust discretization and preconditioning of multiple-network poroelasticity equations},
	howpublished = {Glasgow, UK},
	year = {2018},
	author = {Piersanti, Eleonora and Jeonghun J. {Lee} and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@misc {26151,
	title = {Preconditioners for PDE constrained optimization problems (coarse observations, boundary control)},
	howpublished = {SIAM ALA, Hong Kong, China},
	year = {2018},
	author = {Mardal, Kent-Andre}
}
@article {26192,
	title = {Real-World Variability in the Prediction of Intracranial Aneurysm Wall Shear Stress: The 2015 International Aneurysm CFD Challenge},
	journal = {Cardiovascular Engineering and Technology},
	volume = {9},
	year = {2018},
	month = {10/2018},
	pages = {544{\textendash}564},
	publisher = {Springer},
	address = {US},
	abstract = {PurposeImage-based computational fluid dynamics (CFD) is widely used to predict intracranial aneurysm wall shear stress (WSS), particularly with the goal of improving rupture risk assessment. Nevertheless, concern has been expressed over the variability of predicted WSS and inconsistent associations with rupture. Previous challenges, and studies from individual\&nbsp;groups,\&nbsp;have focused on individual aspects of the image-based CFD pipeline. The aim of this Challenge was to quantify the total variability of the whole pipeline.Methods3D rotational angiography image volumes of five middle cerebral artery aneurysms were provided to participants, who were free to choose their segmentation methods, boundary conditions, and CFD solver and settings. Participants were asked to fill out a questionnaire about their solution strategies and experience with aneurysm CFD, and provide surface distributions of WSS magnitude, from which we objectively derived a variety of hemodynamic parameters.ResultsA total of 28 datasets were submitted, from 26 teams with varying levels of self-assessed experience.\&nbsp;Wide\&nbsp;variability of segmentations, CFD model extents, and inflow rates resulted in interquartile ranges of sac average WSS up to 56\%, which reduced to \&lt; 30\% after normalizing by parent artery WSS. Sac-maximum WSS and low shear area were more variable, while rank-ordering of cases by low or high shear showed\&nbsp;only\&nbsp;modest consensus among teams.\&nbsp;Experience\&nbsp;was not a significant predictor of variability.ConclusionsWide variability exists in the prediction of intracranial aneurysm WSS. While segmentation and CFD solver techniques may be difficult to standardize across groups, our findings suggest that some of the variability in image-based CFD could be reduced by establishing guidelines for model extents, inflow rates, and blood properties, and by encouraging the reporting of normalized hemodynamic parameters.},
	keywords = {Intracranial aneurysm, Patient-specific modeling, Rupture risk, Uncertainty quantification, Wall shear stress},
	issn = {1869-408X},
	doi = {10.1007/s13239-018-00374-2},
	url = {https://goo.gl/mG9u9t},
	author = {Valen-Sendstad, Kristian and Bergersen, Aslak and Shimogonya, Yuji and Goubergrits, Leonid and Bruening, Jan and Pallares, Jordi and Cito, Salvatore and Piskin, Senol and Pekkan, Kerem and Arjan J. {Geers} and Larrabide, Ignacio and Rapaka, Saikiran and Mihalef, Viorel and Fu, Wenyu and Qiao, Aike and Jain, Kartik and Roller, Sabine and Mardal, Kent-Andre and Kamakoti, Ramji and Spirka, Thomas and Ashton, Neil and Revell, Alistair and Aristokleous, Nicolas and Houston, Graeme and Tsuji, Masanori and Ishida, Fujimaro and Prahlad G. {Menon} and Leonard D. {Browne} and Broderick, Stephen and Shojima, Masaaki and Koizumi, Satoshi and Barbour, Michael and Aliseda, Alberto and Hern{\'a}n G. {Morales} and Lef{\`e}vre, Thierry and Hodis, Simona and Yahia M. {Al-Smadi} and Justin S. {Tran} and Alison L. {Marsden} and Vaippummadhom, Sreeja and Einstein, Albert and Alistair G. {Brown} and Debus, Kristian and Niizuma, Kuniyasu and Rashad, Sherif and Sugiyama, Shin-ichiro and Owais Mohammad {Khan} and Adam R. {Updegrove} and Shawn C. {Shadden} and Bart M. W. {Cornelissen} and Charles B. L. M. {Majoie} and Ber, Philipp and Saalfield, Sylvia and Kono, Kenichi and David A. {Steinmam}}
}
@misc {26046,
	title = {Respiratory influence on intracranial pressure gradients and aqueductal flow in normal pressure hydrocephalus},
	year = {2018},
	month = {07/2018},
	type = {Poster Presentation at World Congress of Biomechanics},
	address = {Dublin, Ireland},
	abstract = {Phase contrast MRI does not take into account the role of respiration on cerebrospinal fluid (CSF) flow. We used in vivo pressure measurements from two locations in the intracranial space to calculate a pulsatile pressure gradient. This pressure data was used as input to an idealized model of the aqueduct to calculate CSF flow. We found the cardiac and respiratory cycle to contribute equally to CSF flow. The total flow volume was dominated by respiration, and all subjects showed variability in pressure gradients over time resulting also in variability in CSF flow.},
	url = {https://app.oxfordabstracts.com/stages/123/programme-builder/submission/20200?backHref=/events/123/programme-builder/view/sort/topic\&view=published},
	author = {Vinje, Vegard and Ringstad, Geir and Marie E. {Rognes} and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@misc {26139,
	title = {A Stokes-Biot Stable H(div)-based mixed method for generalized poroelasticity},
	howpublished = {SIAM Life Sciences 2018, Minneapolis, Minnesota, USA},
	year = {2018},
	author = {Thompson, Travis and Marie E. {Rognes}},
	editor = {Mardal, Kent-Andre}
}
@article {25229,
	title = {Variational data assimilation for transient blood flow simulations},
	journal = { International Journal for Numerical Methods in Biomedical Engineering},
	volume = {35},
	year = {2018},
	month = {10/2018},
	pages = {e3152},
	publisher = {John Wiley \& Sons},
	abstract = {Several cardiovascular diseases are caused from localised abnormal blood flow\&nbsp;such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caused by abnormal wall-shear stress in focused\&nbsp;areas. \&nbsp;Computational fluid mechanics have arisen as a promising tool for\&nbsp;a more precise and quantitative analysis, in particular because the\&nbsp;anatomy is often readily available even by standard imaging techniques such as magnetic resolution and computed tomography angiography. \&nbsp;However,\&nbsp;computational fluid mechanics rely on accurate initial and boundary conditions which\&nbsp;is difficult to obtain. \&nbsp;In this paper we address the problem of recovering high resolution information from noisy, low-resolution\&nbsp;measurements of blood flow using variational data assimilation based on a transient Navier-Stokes model.\&nbsp;Numerical experiments are performed in both 2D and 3D and with pulsatile flow relevant for physiological flow in cerebral aneurysms.\&nbsp;The results demonstrate that, with suitable regularisation, the model accurately reconstructs flow, even in the presence of significant noise.\&nbsp;},
	keywords = {adjoint equations, blood flow, Finite element method, Navier-Stokes, optimal control, variational data assimilation},
	author = {Simon W {Funke} and Nordaas, Magne and Evju, {\O}yvind and Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@misc {25784,
	title = {Biographical note on biomedical   applications},
	howpublished = {International Conference on Computational Science and Engineering, Oslo, Norway},
	year = {2017},
	author = {Mardal, Kent-Andre}
}
@misc {25785,
	title = {Blood flow in cerebral aneurysms, water flow clearance in Alzheimer and operator preconditioning},
	howpublished = {Prague, Czech Republic},
	year = {2017},
	type = {Invited},
	author = {Mardal, Kent-Andre}
}
@misc {25706,
	title = {The Brain as a Poroelastic Medium - Simulating pulsatile motion and flow},
	howpublished = {Hamburg, Germany},
	year = {2017},
	abstract = {This talk presents a general overview of the numerical work at the Waterscape group at Simula. First, I present the governing equations, together with standard solving schemes and how to handle discretization in FEniCS. The total pressure formulation is introduced, and an optimal preconditioner for the total pressure formulation is presented.In the last five-ten years, fluid flow and solute transport in the human brain has gained rapid interest in the research community. The discoveries by Iliff and Nedergaard describing a glyphatic network washing solutes out of the brain through a bulk flow of fluid, followed by Xie et al.{\textquoteright}s study claiming that sleep enhances this mechanism was discoveries that also gained significant media attention.The brain has several more or less separated networks allowing for fluid flow; Blood vessels, paravascular spaces and interstitial fluid. The relation between fluid flow in these networks to each other and to the macroscoping displacement of brain tissue can be explained with the multiple network poroelastic theory (MPET). Because there are no consensus of the value of all material parameters the models we use need to be robust within a given parameter regime. In addition, as the number of networks grow, the system of equations becomes larger and the solvers we use must also be fast and efficient within the given range of the parameters.The total pressure formulation, presented in this talk, restores convergence related to the problem of "locking", and allows for a parameter robust preconditioner. Proof that the scheme is stable has been given earlier, and the current work aims to extend this proof to a general number of networks.},
	keywords = {Brain, Poroelasticity, Porous media, Total pressure, Waterscape},
	author = {Vinje, Vegard and Marie E. {Rognes} and Mardal, Kent-Andre and Piersanti, Eleonora}
}
@article {25486,
	title = {A cell-based framework for numerical modelling of electrical conduction in cardiac tissue},
	journal = {Frontiers in Physics, Computational Physics},
	volume = {5},
	year = {2017},
	month = {10/2017},
	publisher = {Frontiers},
	doi = {https://doi.org/10.3389/fphy.2017.00048},
	url = {https://www.frontiersin.org/articles/10.3389/fphy.2017.00048/full?\&utm_source=Email_to_authors_\&utm_medium=Email\&utm_content=T1_11.5e1_author\&utm_campaign=Email_publication\&field=\&journalName=Frontiers_in_Physics\&id=289187},
	author = {Tveito, Aslak and Karoline Horgmo {J{\ae}ger} and Kuchta, Miroslav and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@misc {25531,
	title = {Computational modeling of the glymphatic system: how is waste cleared from the brain?},
	howpublished = {Interpore 2017, Rotterdam, the Netherlands},
	year = {2017},
	type = {Invited, plenary},
	author = {Mardal, Kent-Andre}
}
@misc {25532,
	title = {Computational modeling of the glymphatic system: how is waste cleared from the brain?},
	howpublished = {HPCSE 2017, Ostrava, Czech Republic},
	year = {2017},
	type = {Invited, plenary},
	author = {Mardal, Kent-Andre}
}
@misc {25782,
	title = {Coupling CSF flow, perfusion and   glymphatics (?)},
	howpublished = {2nd Workshop on computational aspects of perfusion and flow in live tissue, Bergen, Norway},
	year = {2017},
	type = {invited},
	author = {Mardal, Kent-Andre}
}
@misc {25529,
	title = {Experimental investigation of transitional effects at low Reynolds number in blood vessels - X-ray, microphones and simulations},
	howpublished = {CMBE 2017, Pittsburgh, USA},
	year = {2017},
	author = {Mardal, Kent-Andre and Frostlid, Vetle and Jensen, Atle and Jain, Kartik}
}
@article {25515,
	title = {Interstitial Solute Transport in 3D Reconstructed Neuropil Occurs by Diffusion Rather than Bulk Flow},
	journal = {Proceedings of the National Academy of Sciences},
	volume = {114},
	year = {2017},
	pages = {9894-9899},
	publisher = {National Academy og Sciences},
	doi = {10.1073/pnas.1706942114},
	author = {Karl Erik {Holter} and Kehlet, Benjamin and Devor, Anna and Terrence J. {Sejnowski} and Anders M {Dale} and Stig W. {Omholt} and Ole P. {Ottesen} and Erlend A. {Nagelhus} and Mardal, Kent-Andre and Klas H. {Pettersen}}
}
@misc {25391,
	title = {Modelling pulsatility in the context of Normal-Pressure Hydrocephalus via multiple-network poroelasticity},
	howpublished = {5th International Conference on Computational and Mathematical Biomedical Engineering, Pittsburgh, US},
	year = {2017},
	author = {Piersanti, Eleonora and Jeunghun J. {Lee} and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {24810,
	title = {Non-invasive Assessment of Pulsatile Intracranial Pressure with Phase-Contrast Magnetic Resonance Imaging},
	journal = {PLoS ONE},
	volume = {12},
	year = {2017},
	pages = {e0188896},
	publisher = {PLOS ONE},
	doi = {10.1371/journal.pone.0188896},
	author = {Ringstad, Geir and Lindstr{\o}m, Erika and Svein Are {Vatnehol} and Mardal, Kent-Andre and Emblem, Kyrre and Per Kristian {Eide}}
}
@article {24809,
	title = {A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space},
	journal = {PLoS ONE},
	volume = {12},
	year = {2017},
	pages = {e0173680},
	publisher = {PLOS},
	doi = {    http://dx.doi.org/10.1371/journal.pone.0173680},
	author = {Per Thomas {Haga} and Pizzichelli, Giulia and Mortensen, Mikael and Kuchta, Miroslav and Soroush Heidari {Pahlavian} and Sinibaldi, Edovardo and Bryn A. {Martin} and Mardal, Kent-Andre}
}
@article {24720,
	title = {Numerical study of intrathecal drug delivery to a permeable spinal cord: effect of catheter position and angle},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {20},
	year = {2017},
	pages = {1599-1608},
	publisher = {Taylor \& Francis Online},
	doi = {10.1080/10255842.2017.1393805},
	author = {Pizzichelli, Giulia and Kehlet, Benjamin and Evju, {\O}yvind and Martin, Bryn and Marie E. {Rognes} and Mardal, Kent-Andre and Sinibaldi, Edoardo}
}
@misc {25783,
	title = {The operator preconditioning framework   with various applications to interstitial   fluid flow and the aging human brain},
	howpublished = {Enumath, Voss, Norway},
	year = {2017},
	author = {Mardal, Kent-Andre}
}
@article {24801,
	title = {Parameter-robust discretization and preconditioning of Biot{\textquoteright}s consolidation model},
	journal = {SIAM Journal of Scientific Computing},
	volume = {39},
	year = {2017},
	pages = {1-24},
	publisher = {SIAM},
	doi = {10.1137/15M1029473},
	author = {Lee, Jeonghun and Mardal, Kent-Andre and Winther, Ragnar}
}
@misc {25528,
	title = {Physics of oscillatory CSF Flow},
	howpublished = {ASSR, San Diego, USA},
	year = {2017},
	author = {Mardal, Kent-Andre and Erika Kristina {Lindstr{\o}m} and Haughton, Victor}
}
@misc {25579,
	title = {Is Respiration the main driver of CSF Flow?},
	howpublished = {International Convention Center, Kobe, Japan},
	year = {2017},
	type = {Seminar, Annual Meeting (IHIWG group)},
	abstract = {Recent studies using magnetic resonance imaging (MRI) have suggested cerebrospinal fluid (CSF) motion caused by respiration to play a more important role than previously thought. The cardiac cycle of CSF motion is used clinically, often to predict which hydrocephalus patients will respond to shunting and who will not.This talk asks the question whether CSF flow could also be regulated by the longer respiratory cycle. To assess this question we applied in vivo pressure measurements to a simplification of the spinal canal and the aqueduct. From this we can measure the amplitude of the flow components induced by the cardiac and respiratory cycle respectively.In our study the amplitude of CSF motion was higher for respiration in the spinal canal, and in the aqueduct cardiac the two amplitudes were approximately equal.This is a starting work, so no conclusions can be made yet. We emphasize the point that it is possible for small and long pressure waves in respiration to cause greater flow than a short cardiac pressure wave with a greater amplitude.\&nbsp;},
	keywords = {Brain, Cerebrospinal Fluid, Computational Fluid Dynamics, Pulsation, Respiration, Spinal Cord},
	author = {Vinje, Vegard},
	editor = {Per Kristian {Eide} and Marie E. {Rognes} and Mardal, Kent-Andre}
}
@article {25518,
	title = {Robustness of common hemodynamic indicators with respect to numerical resolution in 38 middle cerebral artery aneurysms.},
	journal = {PLoS ONE},
	volume = {12},
	year = {2017},
	pages = {e0177566},
	publisher = {Public Library of Science},
	abstract = {BACKGROUND:Using computational fluid dynamics (CFD) to compute the hemodynamics in cerebral aneurysms has received much attention in the last decade. The usability of these methods depends on the quality of the computations, highlighted in recent discussions. The purpose of this study is to investigate the convergence of common hemodynamic indicators with respect to numerical resolution.METHODS:38 middle cerebral artery bifurcation aneurysms were studied at two different resolutions (one comparable to most studies, and one finer). Relevant hemodynamic indicators were collected from two of the most cited studies, and were compared at the two refinements. In addition, correlation to rupture was investigated.RESULTS:Most of the hemodynamic indicators were very well resolved at the coarser resolutions, correlating with the finest resolution with a correlation coefficient \&gt;0.95. The oscillatory shear index (OSI) had the lowest correlation coefficient of 0.83. A logarithmic Bland-Altman plot revealed noticeable variations in the proportion of the aneurysm under low shear, as well as in spatial and temporal gradients not captured by the correlation alone.CONCLUSION:Statistically, hemodynamic indicators agree well across the different resolutions studied here. However, there are clear outliers visible in several of the hemodynamic indicators, which suggests that special care should be taken when considering individual assessment.},
	author = {Evju, {\O}yvind and Jose M. {Pozo} and Frangi, Alejandro and Mardal, Kent-Andre}
}
@misc {25530,
	title = {Simulating the fluid flow of the lymphatic system - extracellular fluid flow},
	howpublished = {The 4th CSF symposium, Atlanta, USA},
	year = {2017},
	author = {Mardal, Kent-Andre and Karl Erik {Holter} and Klas H {Pettersen}}
}
@misc {24827,
	title = {On accurate and efficient simulations of multiple-network poroelastic modelling with applications to interstitial fluid flow in the human brain},
	howpublished = {WCCM XII \& APCOM VI, Seoul },
	year = {2016},
	keywords = {Numerical Simulations, Poroelasticity, Preconditioner},
	author = {Jeonghun John {Lee} and Mardal, Kent-Andre and Piersanti, Eleonora and Marie E. {Rognes}}
}
@article {24822,
	title = {Association of pulse pressure gradient across cranio-cervical junction as derived from phase-contrast magnetic resonance imaging and invasively measured pulsatile intracranial pressure   in symptomatic patients with  Chiari malformation type 1},
	journal = {Acta Neurochirurgica},
	volume = {158},
	year = {2016},
	publisher = {Springer},
	author = {Fric, Radek and Erika Kristina {Lindstr{\o}m} and Ringstad, Geir and Mardal, Kent-Andre and Per Kristian {Eide}}
}
@misc {24814,
	title = {Brain \& Water:computational modeling of the aging brain},
	howpublished = {MedViz conference, Bergen},
	year = {2016},
	author = {Mardal, Kent-Andre}
}
@inbook {24803,
	title = {Cerebrospinal fluid flow in adults.},
	booktitle = {Handbook of clinical neurology},
	volume = {135},
	year = {2016},
	pages = {591-603},
	publisher = {Elsevier},
	organization = {Elsevier},
	isbn = {978-0-444-53485-9},
	author = {Bradley, WG and Haughton, Victor and Mardal, Kent-Andre},
	editor = {Joseph C. {Masdeu} and Gonzalez, Gilberto}
}
@article {24800,
	title = {Computational Investigation of Cerebrospinal Fluid Dynamics in the Posterior Cranial Fossa and Cervical Subarachnoid Space in Patients with Chiari I Malformation},
	journal = {PLOS ONE},
	volume = {11},
	number = {10},
	year = {2016},
	publisher = {PLOS ONE},
	author = {St{\o}verud, Karen-Helene and Hans Petter {Langtangen} and Geir A. {Ringstad} and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@article {24806,
	title = {Direct numerical simulations of transitional hydrodynamics of the cerebrospinal fluid in Chiari I malformation {\textendash} the role of cranio-vertebral junction},
	journal = {International Journal for Numerical Methods in Biomedical Engineering},
	year = {2016},
	publisher = {John Wiley \& Sons},
	author = {Jain, Kartik and Ringstad, Geir and Eide, Per-Kristian and Mardal, Kent-Andre}
}
@misc {24817,
	title = {Experimental investigation of transitional effects at low Reynolds number in blood vessels: X-ray, Microphones and Simulations},
	howpublished = { EarthFlows Workshop, UiO, Oslo},
	year = {2016},
	author = {Mardal, Kent-Andre and Frostlid, Vetle and Jensen, Atle}
}
@misc {24826,
	title = {Modelling and simulation of viscous and poroelastic fluid flow in the brain},
	howpublished = {FEniCS16, Simula Research Laboratory},
	year = {2016},
	keywords = {Finite elements, Numerical Simulations, Poroelasticity},
	author = {Jeonghun John {Lee} and Mardal, Kent-Andre and Piersanti, Eleonora and Marie E. {Rognes}}
}
@misc {24813,
	title = {Overview of the modeling of water flow in and surrounding the central nervous system},
	howpublished = { Istituto Italiano di Tecnologia, Piza, Italy},
	year = {2016},
	author = {Mardal, Kent-Andre}
}
@misc {24818,
	title = {Poroelastic modeling of the central nervous system: Chiari and dementia},
	howpublished = { Workshop on modeling of flow in live tissue: Methodological interaction between geo and life-sciences, CMR, Fantoft, Bergen},
	year = {2016},
	author = {Mardal, Kent-Andre}
}
@article {24799,
	title = {Preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains},
	journal = {SIAM Journal of Scientific Computing},
	volume = {38},
	year = {2016},
	publisher = {SIAM},
	author = {Kuchta, Miroslav and Nordaas, Magne and Joris C. G. {Verschaeve} and Mortensen, Mikael and Mardal, Kent-Andre}
}
@article {24805,
	title = {Robust preconditioners for PDE-constrained optimization with limited observations},
	journal = {BIT Numerical Mathematics},
	volume = {57},
	number = {2},
	year = {2016},
	pages = {405-431},
	publisher = {Springer},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Nordaas, Magne}
}
@misc {24816,
	title = {Robustness of common hemodynamics indicators with respect to numerical resolution in 38 middle cerebral artery aneurysms},
	howpublished = {MS at WCCM16, Seoul},
	year = {2016},
	author = {Mardal, Kent-Andre and Evju, {\O}yvind and Soler, Jose and Frangi, Alex}
}
@misc {24901,
	title = {Simulating Cerebrospinal Fluid Flow and Spinal Cord Movement Associated with Syringomyelia},
	howpublished = {Chalmers Institute of Technology},
	year = {2016},
	publisher = {Chalmers Publication Library},
	address = {Website},
	abstract = {In this study, we tested the hypothesis that fluid velocities within syringes in the spinal cord related to syringomyelia can be explained by fluid-structure interaction (FSI), and that spinal cord movements alter cerebrospinal fluid (CSF) dynamics in the subarachnoid space (SAS). We formulate the coupled fluid-structure interaction problem with an Arbitrary-Lagrangian-Eulerian formulation based on Eulerian coordinates in a moving domain. Our implementation is based on the FEniCS software. The model is then used to investigate FSI effects of syringomyelia in idealized geometries of the spinal cord and SAS.Our results indicate that FSI in a model of a healthy subject yields results quantitatively and qualitatively similar to computational fluid dynamics. In contrast, in the presence of a syrinx, FSI predicts greater displacements of the cord, and a nonlinear pressure distribution is introduced in the CSF along the cord. With a sinusoidally pulsating flow of CSF in the SAS, an opposing sinusoidal flow is seen within the syrinx. With CSF pulsation closer to the natural environment in the SAS, higher frequencies of oscillatory fluid flow are observed within the syrinx.},
	keywords = {Finite elements},
	url = {http://publications.lib.chalmers.se/publication/244480-proceedings-of-29th-nordic-seminar-on-computational-mechanics-nscm29},
	author = {Vinje, Vegard and Mardal, Kent-Andre and Haughton, Victor and Marie E. {Rognes}}
}
@misc {25470,
	title = {Solving singular problems. The right way.},
	howpublished = {FEniCS{\textquoteright}16 Workshop, Simula Research Laboratory, Oslo, Norway},
	year = {2016},
	type = {contributed},
	author = {Kuchta, Miroslav},
	editor = {Mortensen, Mikael}
}
@article {24808,
	title = {Transitional hemodynamics in intracranial aneurysms - Comparative velocity investigations with high resolution Lattice Boltzmann simulations, normal resolution ANSYS simulations and MR imaging},
	journal = {Medical Physics},
	volume = {43},
	year = {2016},
	publisher = {Medical Physics Online},
	author = {Jain, Kartik and Jiang, Jingfeng and Strother, Charles and Mardal, Kent-Andre}
}
@misc {24815,
	title = {Variational data assimilation for blood flow simulations},
	howpublished = { MS at SIAM UQ, Zurich},
	year = {2016},
	author = {Mardal, Kent-Andre and Simon W {Funke} and Nordaas, Magne and Evju, {\O}yvind and Martin Sandve {Aln{\ae}s}}
}
@inbook {Simula.simula.2832,
	title = {On the Assumption of Laminar Flow in Physiological Flows: Cerebral Aneurysms As an Illustrative Example},
	booktitle = {Modeling the Heart and the Circulatory System},
	series = {MS\&A},
	number = {14},
	year = {2015},
	pages = {177-195},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	chapter = {7},
	abstract = {In physiological fluid flows, except for in the heart and the aorta, the Reynolds numbers are moderate (below 1000). This is far below the typical point of transition in pipe flow, which occurs around Reynolds number 2300. Because of this, laminar flow is commonly assumed in the modelling of these flows, resulting in computational methods tailored for this flow regime.This chapter presents a critical review of this assumption, and both clinical and numerical evidence of transitional physiological flows are presented. The pulsatility and complex geometries in physiological flow are highlighted as the main reasons for a lower transition point in physiological flows.Furthermore, we discuss the threshold of transition in a particular case of an aneurysm with respect to resolution, Reynolds number and non-Newtonian viscosity modelling.},
	author = {Evju, {\O}yvind and Mardal, Kent-Andre},
	editor = {Quarteroni, A.}
}
@inproceedings {23909,
	title = {BEND|P|Y: Python framework for computing bending of complex plate-beam systems},
	journal = {MekIT{\textquoteright}15 8th National Conference on Computational Mechanics},
	year = {2015},
	month = {11/2015},
	pages = {307-320},
	publisher = {International Center for Numerical Methods in Engineering (CIMNE)},
	address = {Barcelona, Spain},
	isbn = {978-84-944244-9-6},
	author = {Mortensen, Mikael and Kuchta, Miroslav and Mardal, Kent-Andre and Verschaeve, Joris}
}
@inproceedings {23907,
	title = {Characterization of the space of rigid motions in arbitrary domains},
	journal = {MekIT{\textquoteright}15 8th National Conference on Computational Mechanics},
	year = {2015},
	pages = {259-274},
	publisher = {International Center for Numerical Methods in Engineering (CIMNE)},
	address = {Barcelona, Spain},
	isbn = {978-84-944244-9-6},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Mortensen, Mikael}
}
@misc {csf-symp,
	title = {On the complexity of the Cerebrospinal fluid flow in the upper spinal column {\textendash} is the assumption of laminar flow appropriate?},
	howpublished = {Cerebrospinal Fluid Dynamics Society Meeting, Amiens},
	year = {2015},
	type = {Invited talk},
	author = {Mardal, Kent-Andre and Jain, Kartik and St{\o}verud, Karen-Helene and Ringstad, Geir and Per Kristian {Eide}}
}
@article {23393,
	title = {Computational fluid dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm},
	journal = { Interventional Neuroradiology},
	volume = {21},
	year = {2015},
	pages = {586-591},
	publisher = { SAGE Publications},
	doi = {10.1177/1591019915597415},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre and S{\o}ren Jacob {Bakke} and Sorteberg, Angelika}
}
@misc {csf-rw1,
	title = {Computational modelling of the biomechanics in the central nervous system {\textendash} Chiari and syringomyelia},
	howpublished = {Simpla meeting, Oslo},
	year = {2015},
	type = {Invited talk},
	author = {Mardal, Kent-Andre}
}
@misc {24421,
	title = {Computational modelling of the biomechanics in the central nervous system {\textendash} Chiari and syringomyelia},
	howpublished = {Simula Research Laboratory, Oslo},
	year = {2015},
	month = {03/12/2015},
	author = {Mardal, Kent-Andre}
}
@misc {csf-rw,
	title = {Computational modelling of the biomechanics in the central nervous system {\textendash} Chiari and syringomyelia},
	howpublished = {Complex materials; Mathematical models and numerical methods, Oslo},
	year = {2015},
	author = {Mardal, Kent-Andre}
}
@misc {23345,
	title = {Effect of Spinal Cord Viscoelasticity on Its Response to CSF Pressure Waves: a Computational Study},
	howpublished = {ASNR 53rd Annual Meeting \& The Foundation of the ASNR Symposium 2015, April 25 {\textendash} 30, Chicago, Illinois},
	year = {2015},
	author = {Kylstad, Nina and Mardal, Kent-Andre and Haughton, Victor and Marie E. {Rognes}}
}
@inproceedings {jain2015exploring,
	title = {Exploring The Critical Reynolds Number For Transition In Intracranial Aneurysms{\textendash}highly Resolved Simulations Below Kolmogorov Scales},
	journal = {4th International Conference on Computational and Mathematical Biomedical Engineering - CMBE2015},
	year = {2015},
	author = {Jain, Kartik and Mardal, Kent-Andre}
}
@misc {earthflows,
	title = {Flows in complex geometries such as blood vessels and the central nervous system},
	howpublished = {EarthFlows kick-off meeting, Oslo},
	year = {2015},
	type = {Invited talk},
	author = {Mardal, Kent-Andre}
}
@article {23394,
	title = {Poro-elastic modeling of Syringomyelia {\textendash} a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord},
	journal = { Computer Methods in Biomechanics and Biomedical Engineering },
	volume = {19},
	year = {2015},
	pages = {686-698},
	publisher = {Taylor \& Francis Online},
	doi = {10.1080/10255842.2015.1058927},
	author = {St{\o}verud, Karen-Helene and Martin Sandve {Aln{\ae}s} and Hans Petter {Langtangen} and Haughton, Victor and Mardal, Kent-Andre}
}
@misc {asnr-plen,
	title = {Poroelastic modeling of Syringomyelia - the effects of pia mater, central canal, median fissure, white and grey matter on pressure wave propagation and fluid movement within the cervical spinal cord},
	howpublished = {International Hydrocephalus Imaging Working Group, Chicago},
	year = {2015},
	author = {Mardal, Kent-Andre}
}
@misc {24019,
	title = {Robust preconditioners for PDE-constrained optmization with limited data},
	howpublished = {2015 SIAM CSE, Salt Lake City},
	year = {2015},
	type = {Minisymposium },
	author = {Nordaas, Magne and Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik}
}
@misc {asnr-plen,
	title = {Role of CSF flow in the pathogenesis of Syringomyelia},
	howpublished = {ASNR 53rd Annual Meeting \& The Foundation of the ASNR Symposium 2015, April 25 {\textendash} 30, 2015; Chicago, Illinois},
	year = {2015},
	type = {Plenary talk},
	author = {Haughton, Victor and Mardal, Kent-Andre}
}
@article {jain2015transitional,
	title = {Transitional flow in intracranial aneurysms{\textendash}a space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method},
	journal = {Computers \& Fluids},
	year = {2015},
	publisher = {Elsevier},
	author = {Jain, Kartik and Roller, Sabine and Mardal, Kent-Andre}
}
@misc {Simula.simula.2914,
	title = {On the Assumption of Laminar Flow in the Modeling of Physiological Flow},
	howpublished = {Anvendt og beregningsorientert matematikk, Bergen},
	year = {2014},
	author = {Mardal, Kent-Andre}
}
@misc {Simula.simula.2916,
	title = {On the Assumption of Laminar Flow of CSF in Chiari Patients},
	howpublished = {international Chiari Research Group},
	year = {2014},
	author = {Mardal, Kent-Andre and Helgeland, Anders and Haughton, Victor and Bj{\o}rn Anders Petterson {Reif} and St{\o}verud, Karen-Helene}
}
@misc {Simula.simula.2922,
	title = {Cerebrospinal Fluid Flow in Association With the Central Nervous System - Chiari and Drug Delivery},
	howpublished = {MS on Computational Biomechanics, WCCM-ECCM-ECCOM},
	year = {2014},
	author = {Mardal, Kent-Andre and St{\o}verud, Karen-Helene and Mortensen, Mikael and Jain, Kartik and Martin, Bryn and Pahlavian, Souroush}
}
@misc {Simula.simula.2918,
	title = {CSF Flow at Foramen Magnum},
	howpublished = {International Hydrocephalus Imaging Working Group,Montreal, Canada},
	year = {2014},
	author = {Mardal, Kent-Andre and St{\o}verud, Karen-Helene and Ringstad, Geir and Per Kristian {Eide}}
}
@article {Simula.simula.2224,
	title = {Effect of Cranio-Vertebral Decompression on CSF Dynamics in Chiari I Malformation Studied With Computational Fluid Dynamics},
	journal = {Journal of Neurosurgery},
	volume = {21},
	year = {2014},
	month = {10/2014},
	pages = {559-564},
	publisher = {AANS},
	abstract = {Object. The effect of craniovertebral decompression surgery on CSF flow dynamics in Chiari I patients has been incompletely characterized. We used computational fluid dynamics to calculate the effect of decompression surgery on CSF flow dynamics in the posterior fossa and upper cervical spinal canal.Methods. Oscillatory flow was simulated in idealized 3D models of the normal adult and the Chiari I subarachnoid spaces (both previously described) and in three models of the Chiari malformation post cranio-vertebral decompressions. The three postoperative models were created from the Chiari model by virtually modifying the Chiari model subarachnoid space to simulate surgical decompressions of different magnitudes. Velocities and pressures were computed with the Navier-Stokes equations in Star-CD for multiple cycles of CSF flow oscillating at 80 cycles per minute. Pressure gradients and velocities were compared for 8 levels extending from the posterior fossa to the C3/4 level. Relative pressures and peak velocities were plotted by level from the posterior fossa to C3/4. The heterogeneity of flow velocity distribution around the spinal cord was compared between models.Results. Peak systolic velocities were generally lower in the post-operative models, than in the pre-operative Chiari model. The two larger surgical defects had peak systolic velocities that were closer to normal model velocities than the smallest surgical defect and equal to those in the normal model at the C3 and C4 levels. For the smallest defect, peak velocities were decreased, but not to levels in the normal model. In the postoperative models, heterogeneity in flow velocity distribution around the spinal cord increased from normal model levels as the degree of decompression increased. Pressures in the 5 models differed in magnitude and in pattern. Pressures gradients along the spinal canal in the normal and Chiari models were non-linear with steeper gradients below C3/4 than above. The Chiari model had a steeper pressure gradient than the normal model above C3/4 and the same gradient below. The postoperative models had lower pressure gradients than the Chiari model above C2/3. The most conservative decompression had smaller than normal model pressure gradients above C2/3 The two larger decompression defects had CSF pressure gradients below those in the normal model above C2/3. These two models had a less steep gradient above C3 and a steeper gradient below.Conclusions. In computer simulations, cranio-vertebral surgical defects generally diminished CSF velocities and CSF pressures.},
	author = {Linge, Svein and Mardal, Kent-Andre and Helgeland, Anders and Heiss, John and Haughton, Victor}
}
@misc {Simula.simula.2912,
	title = {Er Zombier En Trussel Mot Menneskeheten?},
	howpublished = {Upop aften - Det norske student samfund},
	year = {2014},
	author = {Mardal, Kent-Andre and Seland, Torbj{\o}rn and Hans Petter {Langtangen} and R{\o}tnes, P{\r a}l}
}
@misc {Simula.simula.2910,
	title = {On the Modeling of the Central Nervous System in Chiari Patients - Transitional Flow, Poroelasticity and Porous-Viscus Flow Couplings},
	howpublished = {Gordon Conference on Flow \& Transport in Permeable Media},
	year = {2014},
	author = {Mardal, Kent-Andre}
}
@article {Simula.simula.2298,
	title = {A Multilevel Solver for Gaussian Constrained CMB Realizations},
	journal = {The Astrophysical Journal Supplement Series},
	volume = {210},
	number = {2},
	year = {2014},
	publisher = { },
	author = {Dag Sverre {Seljebotn} and Mardal, Kent-Andre and Jewell, Jeff and Hans Kristian {Eriksen} and Bull, Philip}
}
@misc {Simula.simula.2920,
	title = {On Numerical Methods for Transitional Flow - Application to Blood Flow in Aneurysms},
	howpublished = {Quality and Validation of Computational Cardio-vascular Biomechanics, WCCM-ECCM-ECCOM},
	year = {2014},
	author = {Mardal, Kent-Andre and Owais Mohammad {Khan} and Valen-Sendstad, Kristian}
}
@article {Simula.simula.2296,
	title = {Numerical Simulations of the Pulsating Flow of Cerebrospinal Fluid Flow in the Cervical Spinal Canal of a Chiari Patient},
	journal = {Journal of Biomechanics},
	volume = {47},
	number = {47(5)},
	year = {2014},
	month = {03/2014},
	pages = {1082-90},
	publisher = { },
	author = {Helgeland, Anders and Mardal, Kent-Andre and Haughton, Victor and Bj{\o}rn Anders Petterson {Reif}}
}
@misc {23477,
	title = {Preliminary study of the impact of spinal cord nerve roots and denticulate ligaments on drug movement in the cervical spinal subarachnoid space},
	howpublished = {21 July, Barcelona, Spain},
	year = {2014},
	type = {Keynote},
	url = {http://www.wccm-eccm-ecfd2014.org/admin/files/fileabstract/a2880.pdf},
	author = {Mortensen, Mikael and Mardal, Kent-Andre and Martin, Bryn and Pahlavian, Soroush}
}
@article {Simula.simula.2830,
	title = {Spinal Fluid Biomechanics and Imaging: an Update for Neuroradiologists},
	journal = {American Journal of Neuroradiology},
	volume = {35},
	year = {2014},
	month = {10/2014},
	pages = {1864-1869},
	publisher = {American Society of Neuroradiology},
	abstract = {Flow imaging with cardiac-gated phase-contrast MR has applications in the management of neurologic disorders. Together with computational fluid dynamics, phase-contrast MR has advanced our understanding of spinal CSF flow. Phase-contrast MR is used to evaluate patients with Chiari I malformation who are candidates for surgical treatment. In theory, abnormal CSF flow resulting from the abnormal tonsil position causes syringomyelia and other neurologic signs and symptoms in patients with Chiari I. CSF flow imaging also has research applications in syringomyelia and spinal stenosis. To optimize MR acquisition and interpretation, neuroradiologists must have familiarity with healthy and pathologic patterns of CSF flow. The purpose of this review is to update concepts of CSF flow that are important for the practice of flow imaging in the spine.},
	doi = {10.3174/ajnr.A4023},
	url = {http://www.ncbi.nlm.nih.gov/pubmed/25012674},
	author = {Haughton, Victor and Mardal, Kent-Andre}
}
@article {Simula.simula.1238,
	title = {Analysis of the Minimal Residual Method Applied to Ill-Posed Optimality Systems},
	journal = {SIAM Journal on Scientific Computing},
	volume = {35},
	number = {2},
	year = {2013},
	pages = {A785-A814},
	author = {Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre}
}
@misc {Simula.simula.2162,
	title = {On the Assumption of Laminar Flow in the Modeling of Physiological Flow},
	howpublished = {Modelling of physiological flows (MPF 2013)},
	year = {2013},
	author = {Mardal, Kent-Andre}
}
@manual {Simula.simula.2084,
	title = {Combining FEniCS With Your Favorite Software in C, C++, Fortran, Or MATLAB},
	year = {2013},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@article {Stoeverud2012(submitted)c,
	title = {CSF Pressure and Velocity in Obstructions of the Subarachnoid Spaces},
	journal = {The Neuroradiology Journal},
	volume = {26},
	number = {2},
	year = {2013},
	author = {St{\o}verud, Karen-Helene and Hans Petter {Langtangen} and Haughton, Victor and Mardal, Kent-Andre}
}
@inproceedings {Simula.simula.2460,
	title = {Effect of Oscillatory Cerebrospinal Fluid Pressure on Fluid Movement in the Spinal Cord},
	journal = {Seventh National Conference on Computational Mechanics (MekIT{\textquoteright}13)},
	year = {2013},
	publisher = {Tapir Akademisk Forlag},
	type = {Conference},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Hans Petter {Langtangen}},
	editor = {Bj{\o}rn H. {Skallerud} and Helge I. {Andersson}}
}
@article {Simula.simula.2294,
	title = {Effect of the Central Canal in the Spinal Cord on Fluid Movement Within the Cord},
	journal = {The Neuroradiology Journal},
	volume = {26},
	number = {5},
	year = {2013},
	pages = {585-590},
	author = {Ida Nordehaug {Dr{\o}sdal} and Mardal, Kent-Andre and St{\o}verud, Karen-Helene and Haughton, Victor}
}
@misc {Simula.simula.2166,
	title = {Efficient Preconditioning of Optimality Systems With Non-Self-Adjoint State Operators},
	howpublished = {IFIP 2013, minisymposia Preconditioning for PDE-Constrained Optimization, Linz, Austria},
	year = {2013},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik}
}
@inbook {Simula.simula.1130,
	title = {Escaping the Zombie Threat by Mathematics},
	booktitle = {Zombies in the Academy: Living Death in Higher Education},
	year = {2013},
	publisher = {University of Chicago Press},
	organization = {University of Chicago Press},
	chapter = {18},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre and R{\o}tnes, P{\r a}l}
}
@article {CSF-resistance,
	title = {Estimation of CSF Flow Resistance in the Upper Cervical Spine},
	journal = {The Neuroradiology Journal},
	volume = {3},
	number = {2},
	year = {2013},
	pages = {49-53},
	author = {Mardal, Kent-Andre and Rutkowska, Gabriela and Linge, Svein and Haughton, Victor}
}
@article {Simula.simula.1698,
	title = {High-Resolution Computational Fluid Dynamics Detects High-Frequency Velocity Fluctuations in Bifurcation, But Not Sidewall, Aneurysms of the Middle Cerebral Artery},
	journal = {Journal of Biomechanics},
	volume = {46},
	year = {2013},
	pages = {402-407},
	publisher = {Elsevier},
	abstract = {High-frequency flow fluctuations in intracranial aneurysms have previously been reported in vitro and in vivo. On the other hand, the vast majority of image-based computational fluid dynamics (CFD) studies of cerebral aneurysms report periodic, laminar flow. We have previously demonstrated that transitional flow, consistent with in vivo reports, can occur in a middle cerebral artery (MCA) bifurcation aneurysm when ultra-high-resolution direct numerical simulation methods are applied. The object of the present study was to investigate if such high-frequency flow fluctuations might be more widespread in adequately-resolved CFD models. A sample of N=12 anatomically realistic MCA aneurysms (five unruptured, seven ruptured), was digitally segmented from CT angiograms. Four were classified as sidewall aneurysms, the other eight as bifurcation aneurysms. Transient CFD simulations were carried out assuming a steady inflow velocity of 0.5 m/s, corresponding to typical peak systolic conditions at the MCA. To allow for detection of clinically-reported high-frequency flow fluctuations and resulting flow structures, temporal and spatial resolutions of the CFD simulations were in the order of 0.1 ms and 0.1 mm, respectively. A transient flow response to the stationary inflow conditions was found in five of the 12 aneurysms, with energetic fluctuations up to 100 Hz, and in one case up to 900 Hz. Incidentally, all five were ruptured bifurcation aneurysms, whereas all four sidewall aneurysms, including one ruptured case, quickly reached a stable, steady state solution. Energetic, rapid fluctuations may be overlooked in CFD models of bifurcation aneurysms unless adequate temporal and spatial resolutions are used. Such fluctuations may be relevant to the mechanobiology of aneurysm rupture, and to a recently reported dichotomy between predictors of rupture likelihood for bifurcation vs. sidewall aneurysms.},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and David A. {Steinman}}
}
@techreport {Simula.simula.2090,
	title = {A Multilevel Solver for Gaussian Constrained CMB Realizations},
	year = {2013},
	author = {Dag Sverre {Seljebotn} and Mardal, Kent-Andre and Jewell, Jeff and Hans Kristian {Eriksen} and Bull, Philip}
}
@misc {Simula.simula.2164,
	title = {Operator Preconditioning for Well-Posed and Ill-Posed Problems},
	howpublished = {Preconditioning 2013},
	year = {2013},
	author = {Mardal, Kent-Andre}
}
@misc {Simula.simula.2154,
	title = {Patient-Specific Simulations of Vasospasm in 3 Different Cases},
	howpublished = {Modelling Physiological Flows},
	year = {2013},
	month = {June},
	abstract = {Background: Subarachnoid hemorrhage from a ruptured intracranial aneurysm may give rise to cerebral vasospasm. Cerebral vasospasm is an inflammatory response that may develop from day 4 after the ictus and persists for a variable time period. The inflammation causes vessel wall thickening and accordingly a decrease in inner vessel diameter, potentially causing cerebral malperfusion. Cerebral vasospasm represents a feared complication and is a common cause of poor outcome after aneurysmal hemorrhage. Due to the risk for cerebral ischemia, the aneurysm cannot be secured surgically until the vasospasm resolves. In addition, the risk for re-rupture of the aneurysm is considered very high during the phase where the vasospasms resolve. It is unknown how the geometry and flow into an aneurysm changes through a phase of vasospasm of the parent artery, and which risk factors for rupture those changes may effect. By use of computational fluid dynamics (CFD), hemodynamics have previously been shown to correlate with aneurysm growth and rupture, and may be a factor in the development of this disease. The vasospasm may severely affect the geometry of the blood vessels, and thus also the hemodynamics. In this study, we will simulate 3 different cases of vasospasm and discuss the subsequent hemodynamic consequences and development of associated aneurysms. Methods: In three different cases, CT angiography scans were performed to determine the severity of the vasospasms. In addition, Doppler velocity measurements were made in relevant arteries. Based on these data, we performed CFD simulations to investigate the hemodynamic changes in patients only a few days apart. In addition to qualitative studies of the flow patterns, we will calculate the wall shear stress and known hemodynamic indicators of aneurysm development, and analyse for any variations Results: Case A: Rupture in an ICA sidewall aneurysm caused vasospasms. The vasospasms appeared to cause large variations in flow velocity. At day 1 the flow rate was large, and CFD revealed severely disturbed flow patterns around the aneurysm. At day 5, at approximately one third of the flow rate, CFD showed a largely undisturbed flow pattern. However, the CT data showed a clear growth of the aneurysm. Case B: Rupture of a large right ICA sidewall aneurysm caused vasospasms in the left parts of the circle of Willis, where aneurysms were located in the ICA (sidewall) and MCA (bifurcation). In the ICA, the vasospasms caused the most severe constriction immediately downstream of the aneurysm. This appeared to have little effect on the flow patterns around the aneurysm. Just prior to the MCA bifurcation aneurysm, a constriction in the artery caused the concentration of a flow jet into the aneurysm. The CT images showed aneurysm growth. Case C: Rupture of an ACA (A2) aneurysm. Doppler measurements indicated changing flow ratio between left and right ACA. CFD showed that this caused direction change in the anterior communicating artery, and CT images showed aneurysm growth. Conclusions: Cerebral vasospasm may cause severe temporary changes in the vasculature, and thus effect the hemodynamics in and around cerebral aneurysms. Indications are found that the hemodynamic consequences of vasospams may cause growth or re-growth of aneurysms, potentially increasing the risk of rupture.},
	author = {Evju, {\O}yvind and Mardal, Kent-Andre and S{\o}ren Jacob {Bakke} and Angelica Gabriele {Sorteberg}}
}
@inproceedings {Simula.simula.2446,
	title = {Preliminary Study of the Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Drug Movement in the Cervical Spinal Subarachnoid Space},
	journal = {The Nordic Seminar on Computational Mechanics},
	year = {2013},
	type = {Conference},
	author = {Mortensen, Mikael and Mardal, Kent-Andre and Martin, Bryn and Pahlavian, Souroush},
	editor = {Mardal, Kent-Andre and Massing, Andre and Logg, Anders}
}
@book {Simula.simula.2478,
	title = {Proceedings of the 26th Nordic Seminar on Computational Machanics},
	year = {2013},
	month = {October},
	publisher = {Simula Research Laboratory},
	isbn = {978-82-92593-12-7},
	author = {Logg, Anders and Mardal, Kent-Andre and Massing, Andre}
}
@inproceedings {Simula.simula.2444,
	title = {A Second Order Fast Sweeping Method for the Eikonal Equation Based on Minimization},
	journal = {The Nordic Seminar on Computational Mechanics},
	year = {2013},
	type = {Conference},
	author = {Kuchta, Miroslav and Mortensen, Mikael},
	editor = {Mardal, Kent-Andre and Massing, Andre and Logg, Anders}
}
@article {Simula.simula.1386,
	title = {Simulating CSF Flow Dynamics in the Normal and the Chiari I Subarachnoid Space During Rest and Exertion},
	journal = {American Journal of Neuroradiology},
	volume = {34},
	number = {1},
	year = {2013},
	pages = {41-15},
	abstract = {Purpose: CSF fluid dynamics in normal subjects and Chiari I patients have been characterized during rest with Phase contrast MR and Computational Fluid Dynamics (CFD). CSF flow velocities and pressures in the non-resting state have not been adequately characterized. We used computer simulations to study CSF dynamics during increased heart rate in the normal and the Chiari I subarachnoid space. Materials and Methods: Cyclic CSF flow was simulated for multiple cycles in idealized 3D models of the subarachnoid space for normal and Chiari I malformation subarachnoid spaces, with flow cycles corresponding to 80 or 120 heart beats per minute. Flow velocities and pressures were computed by the Navier-Stokes equations. Synchronous bidirectional flow and flow patterns were displayed in Star-CD and inspected visually. Peak velocities and pressure differences in the two models were compared for the two cycle frequencies. Results: Elevating the cycle rate from 80 to 120 cpm increased peak superior-inferior pressure gradients (top-bottom) by just 0.01\% in the normal model and 2\% in the Chiari model. Corresponding average pressure gradients increased by 92\% and 100\%, respectively. Also, in both models, the range of synchronous bidirectional flow velocities increased. Systolic velocities had smaller increases with faster cycling. For each cycle rate, peak and average pressure gradients in the Chiari model were greater than in the normal by 11\% - 16\%. Conclusions: Rising the cycle rate from 80 to 120 cpm increased superior-inferior average pressure gradients and the range of synchronous bidirectional flow velocities in the normal and Chiari I models.},
	author = {Linge, Svein and Mardal, Kent-Andre and Haughton, Victor and Helgeland, Anders}
}
@inproceedings {Simula.simula.2406,
	title = {A Stabilized Nitsche Fictitious Domain Formulation for the Three-Field Stokes Problem},
	journal = {The 26th Nordic Seminar on Computational Mechanics},
	year = {2013},
	type = {Conference},
	isbn = {978-82-92593-12-7},
	author = {Claus, Susanne and Massing, Andre and Burman, Erik},
	editor = {Logg, Anders and Mardal, Kent-Andre and Massing, Andre}
}
@article {Simula.simula.1796,
	title = {A Study of Wall Shear Stress in 12 Aneurysms With Respect to Different Viscosity Models and Flow Conditions},
	journal = {Journal of Biomechanics},
	volume = {46},
	number = {16},
	year = {2013},
	month = {November},
	pages = {2802-2808},
	abstract = {Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behavior of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed. This study investigates the effects of 4 different viscosity models, 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms. The differences are quantified in terms of 3 different wall shear stress (WSS) metrics, involving maximal WSS, average WSS, and proportion of aneurysm sac area with low WSS. The results were compared with common geometrical metrics such as volume, aspect ratio, size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type. The results demonstrate strong correlations between the different viscosity models and boundary conditions. The correlation between the different WSS metrics range from weak to medium. No strong correlations were found between the different WSS metrics and the geometrical metrics or classifications.},
	author = {Evju, {\O}yvind and Valen-Sendstad, Kristian and Mardal, Kent-Andre}
}
@article {Simula.simula.836,
	title = {A Uniformly Stable Fortin Operator for the Taylor-Hood Element},
	journal = {Numerische Mathematik},
	volume = {123},
	number = {3},
	year = {2013},
	pages = {537-551},
	doi = {dx.doi.org/10.1007/s00211-012-0492-6},
	author = {Mardal, Kent-Andre and Schoberl, Joachim and Winther, Ragnar}
}
@inbook {Simula.simula.1110,
	title = {An Adaptive Finite Element Solver for Fluid-structure Interaction Problems},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {554-572},
	publisher = {Springer},
	organization = {Springer},
	chapter = {29},
	isbn = {978-3-642-23098-1},
	author = {Selim, Kristoffer},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {zombie-rf,
	title = {Are Zombies a Threat to Mankind?},
	howpublished = {Invited talk for the opening of RF kjelleren at the University of Oslo},
	year = {2012},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen} and R{\o}tnes, P{\r a}l}
}
@book {Simula.simula.1062,
	title = {Automated Solution of Differential Equations by the Finite Element Method},
	year = {2012},
	publisher = {Springer},
	isbn = {3642230989},
	author = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1114,
	title = {Automated Testing of Saddle Point Stability Conditions},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {655-670},
	publisher = {Springer},
	organization = {Springer},
	chapter = {36},
	isbn = {978-3-642-23098-1},
	author = {Marie E. {Rognes}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1112,
	title = {Block Preconditioning of Systems of PDEs},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {643-654},
	publisher = {Springer},
	organization = {Springer},
	chapter = {35},
	isbn = {978-3-642-23098-1},
	author = {Mardal, Kent-Andre and Joachim Berdal {Haga}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {sdu-mardal,
	title = {Blood Flow in Cerebral Aneurysms - Can Turbulence Be a Risk Indicator?},
	howpublished = {SDU workshop},
	year = {2012},
	author = {Mardal, Kent-Andre}
}
@inbook {Simula.simula.1104,
	title = {Cerebrospinal Fluid Flow},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {455-470},
	publisher = {Springer},
	organization = {Springer},
	chapter = {24},
	isbn = {978-3-642-23098-1},
	author = {St{\o}le-Hentschel, Susanne and Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1070,
	title = {Common and Unusual Finite Elements},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {91-116},
	publisher = {Springer},
	organization = {Springer},
	chapter = {3},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Logg, Anders and Marie E. {Rognes} and Andy R. {Terrel}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.acdc.38,
	title = {A Comparison of Some Common Finite Element Schemes for the Incompressible Navier-Stokes Equations},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {395-418},
	publisher = {Springer},
	organization = {Springer},
	chapter = {21},
	isbn = {978-3-642-23098-1},
	author = {Valen-Sendstad, Kristian and Logg, Anders and Mardal, Kent-Andre and Narayanan, Harish and Mortensen, Mikael},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1108,
	title = {A Computational Framework for Nonlinear Elasticity},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {527-544},
	publisher = {Springer},
	organization = {Springer},
	chapter = {27},
	isbn = {978-3-642-23098-1},
	author = {Narayanan, Harish},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.acdc.40,
	title = {Computational Hemodynamics},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {439-454},
	publisher = {Springer},
	organization = {Springer},
	chapter = {23},
	isbn = {978-3-642-23098-1},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Logg, Anders},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1080,
	title = {Constructing General Reference Finite Elements},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {117-128},
	publisher = {Springer},
	organization = {Springer},
	chapter = {4},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Mardal, Kent-Andre},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.958,
	title = {A Coupled Stochastic and Deterministic Model of Ca2+ Dynamics in the Dyadic Cleft},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {611-627},
	publisher = {Springer},
	organization = {Springer},
	chapter = {33},
	isbn = {978-3-642-23098-1},
	author = {Johan Elon {Hake}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {Simula.simula.1852,
	title = {CSF Flow Dynamics: Effects of Viscosity and Inertia},
	howpublished = {ANSR 2012, New York},
	year = {2012},
	author = {St{\o}verud, Karen-Helene and Haughton, Victor and Hans Petter {Langtangen} and Mardal, Kent-Andre}
}
@inbook {Simula.simula.1082,
	title = {Discrete Optimization of Finite Element Matrix Evaluation},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {161-168},
	publisher = {Springer},
	organization = {Springer},
	chapter = {9},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Matthew G. {Knepley} and Logg, Anders and Scott, Ridgway and Andy R. {Terrel}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.962,
	title = {DOLFIN: a C++/Python Finite Element Library},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {173-225},
	publisher = {Springer},
	organization = {Springer},
	chapter = {10},
	isbn = {978-3-642-23098-1},
	author = {Logg, Anders and Garth N. {Wells} and Johan Elon {Hake}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.396,
	title = {Dynamic Simulations of Convection in the Earth{\textquoteright}s Mantle},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {587-602},
	publisher = {Springer},
	organization = {Springer},
	chapter = {31},
	address = {Berlin Heidelberg},
	abstract = {In this chapter, we model dynamic convection processes in the Earth{\textquoteright}s mantle: linking the geodynamical equations, numerical implementation and Python code tightly together. The convection is generated by heating from below with a compositionally distinct and denser layer at the bottom. The time-dependent nonlinear partial differential equations to be solved are the quasi-static Stokes equations with depth- and temperature-dependent viscosity and advection-diffusion equations for the composition and temperature. We present a numerical algorithm for the simulation of these equations as well as an implementation of this algorithm using the DOLFIN Python interface. The results show the compositional heterogeneities persist, but interact strongly with the convecting system, generating upwellings and moving as material from the surface displaces them. This chapter will be of interest to those seeking to model fluid discontinuities using field methods as well as those interested in mantle convection simulations.},
	isbn = {978-3-642-23098-1},
	author = {Vynnytska, Lyudmyla and Clark, Stuart and Marie E. {Rognes}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {emg-12-talk,
	title = {Efficient Preconditioning of Optimality Systems},
	howpublished = {EMG 2012},
	year = {2012},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Martin Sandve {Aln{\ae}s}}
}
@inbook {Simula.simula.1064,
	title = {A FEniCS Tutorial},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	year = {2012},
	pages = {1-70},
	publisher = {Springer},
	organization = {Springer},
	chapter = {1},
	isbn = {978-3-642-23098-1},
	author = {Hans Petter {Langtangen}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1088,
	title = {FErari: an Optimizing Compiler for Variational Forms},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {235-243},
	publisher = {Springer},
	organization = {Springer},
	chapter = {12},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Logg, Anders},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1084,
	title = {FFC: the FEniCS Form Compiler},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {223-234},
	publisher = {Springer},
	organization = {Springer},
	chapter = {11},
	isbn = {978-3-642-23098-1},
	author = {Logg, Anders and Kristian B. {{\O}lgaard} and Marie E. {Rognes} and Garth N. {Wells}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1074,
	title = {Finite Element Assembly},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {137-142},
	publisher = {Springer},
	organization = {Springer},
	chapter = {6},
	isbn = {978-3-642-23098-1},
	author = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {talk-steinman-lab,
	title = {The Finite Element Library FEniCS},
	howpublished = {Steinman{\textquoteright}s lab, University of Toronto},
	year = {2012},
	author = {Mardal, Kent-Andre}
}
@misc {talk-marsden-lab,
	title = {The Finite Element Library FEniCS + Blood Flow Simulations in Cerebral Aneurysms},
	howpublished = {Marsden{\textquoteright}s lab at UCSD},
	year = {2012},
	author = {Mardal, Kent-Andre}
}
@inbook {Simula.simula.1068,
	title = {The Finite Element Method},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {73-90},
	publisher = {Springer},
	organization = {Springer},
	chapter = {2},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Logg, Anders},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1078,
	title = {Finite Element Variational Forms},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lec},
	volume = {84},
	year = {2012},
	pages = {129-136},
	publisher = {Springer},
	organization = {Springer},
	chapter = {5},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Logg, Anders},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1090,
	title = {Instant: Just-in-Time Compilation of C/C++ in Python},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {253-268},
	publisher = {Springer},
	organization = {Springer},
	chapter = {14},
	isbn = {978-3-642-23098-1},
	author = {Wilbers, Ilmar and Mardal, Kent-Andre and Martin Sandve {Aln{\ae}s}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.960,
	title = {Lessons Learned in Mixed Language Programming},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	volume = {84},
	year = {2012},
	pages = {363-381},
	publisher = {Springer},
	organization = {Springer},
	chapter = {19},
	isbn = {978-3-642-23098-1},
	author = {Johan Elon {Hake} and Mardal, Kent-Andre},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {Simula.simula.1240,
	title = {The Minimal Residual Method Applied to Ill-Posed Optimality Systems; Eigenvalues and Convergence Properties},
	howpublished = {Numerical Methods for Optimal Control and Inverse Problems workshop, Munich, Germany},
	year = {2012},
	author = {Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre}
}
@misc {Simula.simula.1816,
	title = {On Non-Newtonian Effects in Cerebral Aneurysms: a Computational Study on 12 Patient Specific Aneurysms},
	year = {2012},
	author = {Evju, {\O}yvind and Mardal, Kent-Andre and Valen-Sendstad, Kristian}
}
@misc {Simula.simula.1890,
	title = {Non-Newtonian Effects in Cerebral Aneurysms. a Computational Study on 12 Patient Specific Aneurysms},
	howpublished = {ICS {\textquoteright}12},
	year = {2012},
	author = {Evju, {\O}yvind and Valen-Sendstad, Kristian and Mardal, Kent-Andre}
}
@article {Simula.simula.854,
	title = {Patient-Specific 3D Simulation of Cyclic CSF Flow at the Cranio-Cervical Region},
	journal = {American Journal of Neuroradiology},
	volume = {33},
	number = {9},
	year = {2012},
	pages = {1756-1762},
	publisher = {American Society of Neuroradiology},
	author = {Rutkowska, Gabriela and Haughton, Victor and Linge, Svein and Mardal, Kent-Andre}
}
@misc {Simula.simula.1288,
	title = {Revisiting {\textquoteright}Turbulence{\textquoteright} in Cerebral Aneurysms},
	year = {2012},
	abstract = {One of the commonly made assumptions in Computational Fluid Dynamics (CFD) is that cerebral blood flow is laminar, i.e., viscous forces are dominating and the flow is smooth. The numerical methods that are used, are chosen or tailored accordingly, i.e., to converge to such a laminar flow solution with the minimal amount of work1-2. The flow is modeled with a temporal resolution far below the clinically reported frequencies3 and thus any potential flow disturbances, if physically present, are being numerically suppressed. Since no potential disturbances are resolved, no disturbances are observed and the assumption of laminar flow is therefore a self-fulfilling prophecy. Even though recent laminar CFD studies can discriminate between ruptured and unruptured aneurysms better than, e.g. aneurysm size, the link between the proposed hemodynamic agonists and the mechanisms of rupture is unclear. However, the literature contains much evidence which supports that certain aneurysms exhibit energetic high frequency flow fluctuations. For example, high frequency flow fluctuations are known to produce sound, and clinicians have reported such sound or {\textquoteright}bruits{\textquoteright} from aneurysms during craniotomy.3 The predominant frequencies were at 460 Hz, which is consistent with the energy peaks at higher frequencies recorded acoustically on the eyes in patients with aneurysms.4 Unstable flow has also been reported in glass model studies of aneurysms.5 This evidence seems to have been ignored, or at least has not received much attention in computational modeling studies. The goal of the present study was to investigate if such high-frequency flow fluctuations in intracranial aneurysms might be a common occurrence, by using thousands of time steps in contrast to, e.g., one hundred2.},
	keywords = {Conference},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and David A. {Steinman}}
}
@inbook {Simula.simula.1102,
	title = {Simulation of Transitional Flows},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {419-438},
	publisher = {Springer},
	organization = {Springer},
	chapter = {22},
	isbn = {978-3-642-23098-1},
	author = {Mortensen, Mikael and Mardal, Kent-Andre and Hans Petter {Langtangen}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1092,
	title = {SyFi and SFC: Symbolic Finite Elements and Form Compilation},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {269-278},
	publisher = {Springer},
	organization = {Springer},
	chapter = {15},
	isbn = {978-3-642-23098-1},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1076,
	title = {Tensor Representation of Finite Element Variational Forms},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {157-167},
	publisher = {Springer},
	organization = {Springer},
	chapter = {8},
	isbn = {978-3-642-23098-1},
	author = {Robert C. {Kirby} and Logg, Anders},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1094,
	title = {UFC: a Finite Element Code Generation Interface},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {279-298},
	publisher = {Springer},
	organization = {Springer},
	chapter = {16},
	isbn = {978-3-642-23098-1},
	author = {Martin Sandve {Aln{\ae}s} and Logg, Anders and Mardal, Kent-Andre},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1096,
	title = {UFL: a Finite Element Form Language},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {299-334},
	publisher = {Springer},
	organization = {Springer},
	chapter = {17},
	isbn = {978-3-642-23098-1},
	author = {Martin Sandve {Aln{\ae}s}},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@techreport {Simula.simula.2086,
	title = {A Uniform Inf-Sup Condition With Applications to Preconditioning},
	year = {2012},
	publisher = {Simula},
	author = {Mardal, Kent-Andre and Schoberl, Joachim and Winther, Ragnar}
}
@misc {Simula.simula.1900,
	title = {On Well-Posedness and Stability},
	howpublished = {CBC Seminar series},
	year = {2012},
	author = {Mardal, Kent-Andre}
}
@misc {fenics-mardal-talk,
	title = {Will FEniCS Fly?},
	howpublished = {FEniCS 12 workshop},
	year = {2012},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@inproceedings {Simula.simula.786,
	title = {Cerebrospinal Fluid Flow Characteristics at Double Heart Rate},
	journal = {Neuroradiology, 53 (Suppl. 1), S33, 35th European Soc of Neuroradiology ann. meeting, Antwerpen, Belgium},
	year = {2011},
	publisher = {Proc. of the 35th European Society of Neuroradiology Ann. Meeting, Antwerpen, Belgium, 21-25 Sept, Springer Verlag},
	type = {Conference},
	abstract = {Purpose. Cerebrospinal fluid (CSF) flow has been much studied for human beings at rest, i.e. with a correspondingly low heart rate. Current measurement procedures, e.g. with MRI, can not easily collect data at higher heart rates. However, such restrictions may be circumvented by computer simulations. The goal of the present study was to characterize CSF flow at double heart rate for the cranio-vertebral region of a healthy subject though computer simulations. Methods. Several cycles of CSF flow were simulated with a 3D idealized model of the relevant region at a heart rate of 120 bpm. Velocity and pressure were calculated by solving the Navier-Stokes equations numerically. Velocity and pressure characteristics from different times and locations were then compared to corresponding data achieved from the same model with normal heart rate (defined as 60 bpm here). For simplicity, prescribed flow velocities at model boundaries were defined as sinusoidal. Results. It was found that flow velocities and pressure gradients increased substantially. Maximum velocities at the cranio-vertebral junction doubled (to more than 4 cm/s), while pressure gradients along the flow channel increased by a factor 4. Synchronous bidirectional flow also became much more prominent. Conclusions. Our findings suggest that CSF flow velocities and pressure gradients are substantially higher during typical day to day activities than during rest, which is the state commonly reported on in the literature. Our finding may have implications for our understanding of how, e.g., Chiari malformation and Syringomyelia develop.},
	isbn = {0028-3940},
	author = {Linge, Svein and Mardal, Kent-Andre and Haughton, Victor and Helgeland, Anders},
	editor = {PM, Parizel and JV, Goethem}
}
@misc {Simula.simula.768,
	title = {Cerebrospinal Fluid Flow in the Upper Cervical Canal in Patients With the Chiari I Malformation},
	howpublished = {1ST CSF Hydrodynamics Symposium},
	year = {2011},
	author = {Mardal, Kent-Andre and St{\o}verud, Karen-Helene and Haughton, Victor and Linge, Svein and Hans Petter {Langtangen} and Rutkowska, Gabriela and Ida Nordehaug {Dr{\o}sdal}}
}
@inproceedings {Simula.simula.638,
	title = {On the Complexity of Stationary Flow in Patient-Specific Aneurysms},
	journal = {MekIT{\textquoteright}11 Sixth national conference on Computational Mechanics},
	year = {2011},
	pages = {379-392},
	publisher = {tapir academic press},
	type = {Conference},
	abstract = {Summary Sound or bruits in the vasculatory system at the range of 1Hz-1kHz is known to occur, and frequency peaks at high frequencies are associated with sick blood vessels. The exact reason for these sounds are not known, but the sound may be generated by turbulence. Turbulence generated sound is typically associated with high frequencies but also with low energy levels. Unfortunately, most blood flow simulations are performed with space and time resolutions where rapid fluctuations typ- ically associated with non-laminar flow cannot be captured. Complex non-laminar flow and the subsequent oscillatory wall stresses can po- tentially be of importance in understanding aneurysm rupture through the local arterial wall response. To investigate the possible presence of complex non-laminar blood flow in intracranial aneurysms, we per- formed high resolution computational fluid dynamics (CFD) simulations for patient specific middle cerebral artery (MCA) aneurysms with sta- tionary inflow conditions. The current study confirms, through high resolution simulations, that complex oscillatory flow may occur in in- tracranial aneurysms. CFD practitioners should therefore be aware of the potentially strong demands to space-time computational resolution in blood flow simulations.},
	isbn = {978-82-519-2798-7},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}},
	editor = {Bj{\o}rn H. {Skallerud} and Helge I. {Andersson}}
}
@misc {Simula.simula.408,
	title = {Computational Cerebral Hemodynamics},
	howpublished = {The Norwegian Defence Research Establishment},
	year = {2011},
	month = {March},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@inbook {Simula.sc.862,
	title = {Construction of Preconditioners by Mapping Properties for Systems of Partial Differential Equations},
	booktitle = {Efficient preconditioning methods for elliptic partial differential equations},
	year = {2011},
	pages = {65-84},
	publisher = {Bentham Science Publishers},
	organization = {Bentham Science Publishers},
	chapter = {4},
	isbn = {978-1-60805-291-2},
	author = {Mardal, Kent-Andre and Winther, Ragnar},
	editor = {Axelsson, Owe and Karatson, Janos}
}
@misc {Simula.simula.776,
	title = {On the Construction of Preconditioners for Systems of PDEs},
	howpublished = {SIAM Conference on Computational Science and Engineering, MS2},
	year = {2011},
	author = {Mardal, Kent-Andre}
}
@article {Simula.simula.620,
	title = {CSF Flow in Chiari I and Syringomyelia From the Perspective of Computational Fluid Dynamics},
	journal = {The Neuroradiology Journal},
	volume = {24},
	number = {1},
	year = {2011},
	month = {February},
	pages = {20-23},
	abstract = {Phase contrast MR in patients with the Chiari I malformation demonstrates abnormal CSF flow in the foramen magnum and upper cervical spinal canal, related to abnormal pressure gradients. The purpose of this study was to analyze the role of CSF pressure in the pathogenesisof syringomyelia, with computational models. The spinal cord was modeled as a cylindrical poro-elastic structure with homogenous and isotropic permeability. The permeability was then made heterogeneous and anisotropic to represent the different properties of the central canal, gray and white matter. Fluid with a defined pressure, varying both in time and space, was prescribed in the SAS. Simulations were performed to quantify deformations and fluid movement within the cord. In the simulations with uniform permeability fluid moved into the cord in regions of higher pressure and out of the cord in regions of lower pressure. With permeability differences simulating gray and white matter the pattern was more complex, but similar. Adding the central spinal canal, fluid moved into the cord as in the previous case. However, preferential flow along the central canal hindered fluid from flowing back into the SAS. Pressure gradients in the SAS produce movement of fluid in the spinal cord. Assuming different relative permeability in gray matter, white matter and the central spinal canal, abnormal CSF gradients lead to accumulation of fluid within and adjacent to the spinal cord central canal.},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@inproceedings {Simula.simula.682,
	title = {Cyclic Cerebrospinal Fluid Flow (I): Towards the Understanding of Cerebrospinal Fluid Flow Dynamics in Chiari I Malformation},
	journal = {ASNR 49th Annual Meeting \& the Foundation of the ASNR Symposium, June 4 - 9, 2011.},
	year = {2011},
	type = {Conference},
	abstract = {Purpose Chiari I malformation leads to abnormal cerebrospinal fluid (CSF) flow dynamics and often is accompanied by syrinx formation. Phase constrast MR investigations reveal that peak flow velocities increase, whereas the altered pressure gradients are much more difficult to assess noninvasively. In this study, we use computer simulations to investigate how tonsil herniation changes pressure dynamics and flow in the cervical subarachnoid space. Materials and Methods. A 3D mathematical model of the cervical subarachnoid space, with and without herniated tonsils, was used to simulate CSF flow dynamics over several cycles of sinusoidal flow. Simulation results for the case with herniated tonsils were compared with corresponing results for normally positioned tonsils, while keeping all other parameters the same. Results Tonsil herniation caused pressure gradients to increse both in the superior-inferior direction and in axial planes of the model. The change in pressure dynamics caused a more complex flow velocity pattern with higher peak velocities, pronounced synchronous bi-directional flow, and larger velocity components within axial planes. Conclusion Chiari I malformation increases pressure gradients and flow complexity in the cervical subarachnoid space. This implies, e.g., that the spinal cord-CSF interaction dynamics changes following tonsil herniation, something which might have a role to play in syrinx formation.},
	isbn = {XXXX},
	author = {Linge, Svein and Haughton, Victor and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Helgeland, Anders and Hans Petter {Langtangen} and St{\o}verud, Karen-Helene}
}
@article {Simula.simula.636,
	title = {Direct Numerical Simulation of Transitional Flow in a Patient-Specific Intracranial Aneurysm},
	journal = {Journal of Biomechanics},
	volume = {44},
	number = {16},
	year = {2011},
	pages = {2826-2832},
	abstract = {In experiments turbulence has previously been shown to occur in intracranial aneurysms, but the turbulent effects on the arterial wall have not been investigated. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture due to the local arterial wall response to such hemodynamical forces. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulations in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, and the turbulent fluctuations increased in intensity until mid deceleration, before relaminarization occurred during diastole. The flow impinged with an angle nearly normal onto the aneurysm dome, and the turbulence structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5 Pa. The recorded frequencies were predominantly in the range of 1-500 Hz. The current study confirms, through properly resolved CFD simulations, that turbulence can occur in intracranial aneurysms. Because of the local arterial wall response to hemodynamical forces, the effects of oscillatory WSS caused by turbulence, could be correlated with aneurysm rupture, and should be investigated experimentally. Keywords: Computational fluid dynamics, Blood flow, Direct Numerical Simulation, Turbulence, Middle cerebral artery aneurysm},
	doi = {doi:10.1016/j.jbiomech.2011.08.015},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@misc {Simula.simula.826,
	title = {Direct Numerical Simulation of Transitional Flow in Patient-Specific Intracranial Aneurysms},
	howpublished = {ASME 2011 Summer Bioengineering Conference},
	year = {2011},
	month = {June},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@article {Simula.simula.24,
	title = {Effect of Tonsilar Herniation on Cyclic CSF Flow Studied With Computational Flow Analysis},
	journal = {American Journal of Neuroradiology},
	volume = {32},
	number = {5},
	year = {2011},
	pages = {1474-1481},
	abstract = {Purpose: The Chiari I malformation, characterized by tonsils extending below the foramen magnum, has increased cerebrospinal fluid (CSF) velocities compared to normal subjects. Measuring the effect of tonsilar herniation on CSF flow in humans is confounded by inter-individual variation. The goal of this study was to determine the effect of herniated tonsils on flow velocity and pressure dynamics. Materials and Methods: A previously described 3D mathematical model of the normal subarachnoid space was modified by extending the tonsils inferiorly. The chamber created was compared with the anatomy of the subarachnoid space. Pressures and velocities were calculated by Computational Fluid Analysis (CFA) methods for sinusoidal flow of a Newtonian fluid. Results were displayed as 2D color-coded plots and 3D animations. Pressure gradients and flow velocities were compared with those in the normal model. Velocity distributions were also compared with those in clinical images of CSF flow. Results: The model represented grossly the subarachnoid space of a Chiari patient. Fluid flow patterns in the Chiari model were complex with jets in some locations and stagnant flow in others. Flow jets, synchronous bi-directional flow, and pressure gradients were greater in the Chiari model than in the normal model. The distribution of flow velocities in the model corresponded well with those observed in clinical images of CSF flow in Chiari I patients. Conclusions: Tonsilar herniation per se increases the pressure gradients and the complexity of flow patterns associated with oscillatory CSF flow.},
	author = {Linge, Svein and Haughton, Victor and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Helgeland, Anders and Hans Petter {Langtangen}}
}
@inproceedings {Simula.simula.630,
	title = {The Effect of Varying Cross-Sectional Areas on Cerebrospinal Fluid Flow and Pressure in the Cervical Spine},
	journal = {MekIT{\textquoteright}11. Sixth national conference on Computational Mechanics},
	year = {2011},
	publisher = {Tapir Academic Press},
	type = {Conference},
	abstract = {The aim of this study was to determine CSF pressure and velocities in idealized geometries representing the stenosed spinal canal found in Chiari patients.We applied the Navier-Stokes equation to simulate the cyclic CSF flow during one cardiac cycle. Hereby, we have illuminated a well-established medical hypothesis for the relation between the Chiari I malformation and syringomyelia: namely that spinal cord cysts are caused by the so-called Venturi effect (predicted by Bernoulli\&$\#$39;s law) appearing in fluids that flow through obstructed areas. The results showed that the pressure gradient in geometries with obstructions comparable to Chiari patients may be 10 times as high as under normal flow conditions. The results also showed that the pressure gradients at the level of an obstruction may be twice as large as that predicted from steady flow or Bernoulli\&$\#$39;s law.},
	isbn = {978-82-519-2798-7},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Hans Petter {Langtangen} and Haughton, Victor},
	editor = {Bj{\o}rn H. {Skallerud} and Andersson, H.I.}
}
@misc {Simula.simula.780,
	title = {Efficient Preconditioning of Optimality Systems},
	howpublished = {Precond 11},
	year = {2011},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik}
}
@misc {Simula.simula.778,
	title = {FEniCS: an Attempt to Combine Simplicity, Generality, Efficiency and Reliability},
	howpublished = {Python-based Software for Solving Partial Differential Equations Minisymposium at SIAM Conference on Computational Science and Engineering},
	year = {2011},
	author = {Mardal, Kent-Andre}
}
@misc {Simula.simula.782,
	title = {The Finite Element Library FEniCS and Simulation of Blood Flow in Cerebral Aneurysms},
	howpublished = {Talk at CSB Seminar, University of Stuttgart},
	year = {2011},
	author = {Mardal, Kent-Andre and Valen-Sendstad, Kristian and Martin Sandve {Aln{\ae}s} and Mortensen, Mikael and Hans Petter {Langtangen} and Bj{\o}rn Anders Petterson {Reif}}
}
@article {Simula.bioflows.2,
	title = {Flow Characteristics in a Canine Aneurysm Model: A Comparison of 4-D Accelerated Phase-Contrast MR Measurements and Computational Fluid Dynamics Simulations},
	journal = {Medical Physics},
	volume = {38},
	number = {11},
	year = {2011},
	pages = {6300-6313},
	publisher = {Med Phys},
	author = {Jiang, Jingfeng and Johnson, Kevin and Valen-Sendstad, Kristian and Mardal, Kent-Andre and Wieben, Oliver and Strother, Charles}
}
@inproceedings {Simula.simula.646,
	title = {Investigations of Transistional Flows Using Image Based Hemodynamics},
	journal = {8th International Conference on CFD in Oil \& Gas, Metallurgical and Process Industries},
	year = {2011},
	month = {June},
	type = {Conference},
	abstract = {We investigated the complexity of blood flow in intracranial aneurysms in terms of the frequency spectrum of pointwise velocity and pressure fluctuations. The investigations were performed using high-resolution computational fluid dynamics (CFD) simulations for patient-specific middle cerebral artery (MCA) aneurysms, using realistic inflow profile. Through these simulations, the study confirmed that complex transitional flow can occur in intracranial aneurysms. In particular, we found fluctuations of the order of 500- 1000 Hz.},
	author = {Valen-Sendstad, Kristian and Mortensen, Mikael and Mardal, Kent-Andre and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@article {Simula.SC.35,
	title = {Order Optimal Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {27},
	year = {2011},
	note = {Listed in annual report 2010. Published online june 2010.},
	pages = {1290-1312},
	publisher = {Wiley Subscription Services, Inc., A Wiley Company},
	abstract = {The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge-Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge-Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly positive-definite matrices is introduced and analyzed.},
	doi = {10.1002/num.20582},
	author = {Nilssen, Trygve Kastberg and Gunnar Andreas {Staff} and Mardal, Kent-Andre}
}
@inproceedings {Simula.simula.628,
	title = {Porous and Viscous Flow Modeling on the Study of Cyst Development in the Human Spinal Cord},
	journal = {8th International Conference on CFD in Oil \& Gas, Metallurgical and Process Industries},
	year = {2011},
	type = {Conference},
	abstract = {In this study, we apply an incremental pressure correction scheme to a coupled Navier-Stokes-Darcy problem in order to model porous and viscous flow in and around the human spinal cord. Simulations show that the central canal, a narrow channel in the spinal cord which is usually only partly present in most adults, has a profound effect on pressure distributions within the spinal cord - an effect that can be of importance in the study of cyst formation in the cord. The numerical method was verified using the method of manufactured solutions, showing that the simple operator splitting scheme produces reliable results in this complex case.},
	author = {Ida Nordehaug {Dr{\o}sdal} and Haughton, Victor and Mardal, Kent-Andre and St{\o}verud, Karen-Helene},
	editor = {Jan Erik {\O}vre {Olsen} and Stein Tore {Johansen}}
}
@article {Simula.SC.570,
	title = {Preconditioning Discretizations of Systems of Partial Differential Equations},
	journal = {Numerical Linear Algebra with Applications},
	volume = {18},
	number = {1},
	year = {2011},
	note = {Listed in annual report 2010. Appeared online April 2010.},
	pages = {1-40},
	abstract = {This survey paper is based on three talks given by the second author at the London Mathematical Society Durham Symposium on Computational Linear Algebra for Partial Differential Equations in the summer of 2008. The main focus will be on an abstract approach to the construction of preconditioners for symmetric linear systems in a Hilbert space setting. Typical examples that are covered by this theory are systems of partial differential equations which correspond to saddle point problems. We will argue that the mapping properties of the coefficient operators suggest that block diagonal preconditioners are natural choices for these systems. To illustrate our approach a number of examples will be considered. In particular, parameter-dependent systems arising in areas like incompressible flow, linear elasticity, and optimal control theory will be studied. The paper contains analysis of several models which have previously been discussed in the literature. However, here each example is discussed with reference to a more unified abstract approach.},
	doi = {10.1002/nla.716},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@article {Simula.simula.634,
	title = {A Quantitative Characterization of Differences in Flow Patterns in Ruptured Versus Unruptured MCA Aneurysms},
	journal = {journal},
	year = {2011},
	abstract = {The rupture of an intracranial aneurysm is often associated with death or severe neurological deficits. When detected, the physician has to evaluate the risk of rupture and determine the optimal treatment. Risk estimation based on computational fluid dynamics (CFD) and wall shear stress (WSS) has recently been the focus of many studies. Here, we introduce new indicators for assessing risk of aneurysm rupture based on fluid mechanical properties such as the kinetic energy, vorticity and pressure drop over the aneurysm.},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Isaksen, J{\o}rgen and Mortensen, Mikael}
}
@misc {Simula.simula.770,
	title = {Simulating Blood Flow in Cerebral Aneurysm},
	howpublished = {Minisymposium Numerical Methods for Biomedical Problems on Enumath},
	year = {2011},
	author = {Mardal, Kent-Andre and Valen-Sendstad, Kristian and Evju, {\O}yvind}
}
@misc {Simula.simula.406,
	title = {Simulation Methodology for Cerebral Blood Flow},
	howpublished = {Biomedical Simulation Lab, Institute of Biomaterials and Biomedical Engineering at the University of Toronto},
	year = {2011},
	month = {March},
	abstract = {In experiments turbulence has previously been shown to occur in intracranial aneurysms, but the turbulent effects on the arterial wall have not been investigated. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture due to the local arterial wall response to such hemodynamical forces. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulations in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, and the turbulent fluctuations increased in intensity until mid deceleration, before relaminarization occurred during diastole. The flow impinged with an angle nearly normal onto the aneurysm dome, and the turbulence structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5 Pa. The recorded frequencies were predominantly in the range of 1-500 Hz. The current study confirms, through properly resolved CFD simulations, that turbulence can occur in intracranial aneurysms. Because of the local arterial wall response to hemodynamical forces, the effects of oscillatory WSS caused by turbulence, could be correlated with aneurysm rupture, and should be investigated experimentally.},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@misc {Simula.simula.846,
	title = {{\textquoteright}Turbulence{\textquoteright} in Cerebral Aneurysms},
	howpublished = {CBC Workshop on Biomechanics, 17-18 November},
	year = {2011},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Hans Petter {Langtangen} and Bj{\o}rn Anders Petterson {Reif} and David A. {Steinman}}
}
@misc {Simula.simula.828,
	title = {Why Blood Flow in the Vicinity of Aneurysms Is Difficult to Compute},
	howpublished = {Talk at CBC Workshop on CBC Key Topics},
	year = {2011},
	month = {August},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Mortensen, Mikael and Bj{\o}rn Anders Petterson {Reif} and Hans Petter {Langtangen}}
}
@inbook {Simula.SC.178,
	title = {Automatic Calibration of Depositional Models},
	booktitle = {Automated Scientific Computing},
	year = {2010},
	publisher = {Springer},
	organization = {Springer},
	abstract = {A novel concept for calibrating depositional models is presented. In this approach transport coefficients are determined from well output measurements. Finite element implementation of the multi-lithology models and their duals is automated by the FEniCS project DOLFIN using a python interface.},
	author = {Schroll, Achim},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@misc {Simula.simula.269,
	title = {The Baby Justicia Project: Biomechanical Investigations of the Shaken Baby Syndrome (SBS)},
	howpublished = {WCB2010, Seminar session, Head/Brain Injury - Models},
	year = {2010},
	month = {August},
	author = {Blechingberg, Anna and Mardal, Kent-Andre and Strisland, Frode and Sundnes, Joakim and Torleiv Ole {Rognum} and Vege, {\r A}shild and Weensvangen, Morten and Stray-Pedersen, Arne}
}
@misc {Simula.simula.342,
	title = {Cerebrospinal Fluid (CSF) - Oscillating Flow and Pressure},
	howpublished = {CBC Workshop on Aerosols: Dispersion, Transport and Effects, Simula, November 10},
	year = {2010},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.simula.338,
	title = {Cerebrospinal Fluid (CSF) - Oscillating Flow and Pressure},
	howpublished = {Selected Topics Seminar IWS Stuttgart},
	year = {2010},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@article {Simula.SC.648,
	title = {Characterization of Cyclical CSF Flow in the Foramen Magnum and Upper Cervical Spinal Canal With MR Flow Imaging and Computational Fluid Dynamics},
	journal = {American Journal of Neuroradiology},
	volume = {31},
	number = {6},
	year = {2010},
	month = {June-July},
	pages = {997-1002},
	abstract = {SUMMARYCSF flow has been shown to exhibit complex patterns in MR images in both healthy subjects and in patients with Chiari I. Abnormal CSF flow oscillations, according to prevailing opinion, cause syringomyelia and other clinical manifestations that affect some patients with the Chiari I malformation. For this article, we reviewed the literature on PC MR of CSF flow, collected the published CFD studies relevant to CSF flow, and performed flow simulations. PC MR creates cine and still images of CSF flow and measurements of flow velocities. CFD, a technique used to compute flow and pressure in liquid systems, simulates the CSF flow patterns that occur in a specific geometry or anatomy of the SAS and a specific volume of flow. Published PC MR studies show greater peak CSF velocities and more complex flow patterns in patients with Chiari I than in healthy subjects, with synchronous bidirectional flow one of the characteristic markers of pathologic flow. In mathematic models of the SAS created from high-resolution MR images, CFD displays complex CSF flow patterns similar to those shown in PC MR in patients. CFD shows that the pressure and flow patterns vary from level to level in the upper spinal canal and differ between patients with Chiari and healthy volunteers. In models in which elasticity and motion are incorporated, CFD displays CSF pressure waves in the SAS. PC MR and CFD studies to date demonstrate significant alterations of CSF flow and pressure patterns in patients with Chiari I. CSF flow has nonlaminar complex spatial and temporal variations and associated pressure waves and pressure gradients. Additional simulations of CSF flow supplemented by PC MR will lead to better measures for distinguishing pathologic flow abnormalities that cause syringomyelia, headaches, and other clinical manifestations in Chiari I malformations.},
	doi = {10.3174/ajnr.A1995},
	author = {Hentschel, Susanne and Mardal, Kent-Andre and Alf Emil {L{\o}vgren} and Linge, Svein and Haughton, Victor}
}
@inproceedings {Simula.simula.830,
	title = {Comparison of Aneurismal Hemodynamics Between 4D Accelerated Phase-Contrast MR Angiography and Computational Fluid Dynamics Simulations: Initial Experience in a Canine Aneurysm Model},
	journal = {Proceedings of the ASME 2010 Summer Bioengineering Conference},
	year = {2010},
	month = {June},
	pages = {SBC2010-19455 223},
	publisher = {American Society of Mechanical Engineers},
	type = {Conference},
	author = {Jiang, Jingfeng and Johnson, Kevin and Valen-Sendstad, Kristian and Mardal, Kent-Andre and Consigny, Dan and Wieben, Oliver and Strother, Charles}
}
@inproceedings {Simula.simula.344,
	title = {CSF Flow in Chiari I and Syringomyelia - From the Perspective of Fluid Dynamics},
	journal = {Proceedings of the XIX Symposium Neuroradiologicum, Bologna, Italy},
	year = {2010},
	type = {Conference},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.simula.340,
	title = {CSF Hydrodynamic in Patients With Syringomyelia and Chiari I Malformations},
	howpublished = {Annual NUPUS meeting in Freudenstadt},
	year = {2010},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.simula.284,
	title = {CSF Str{\o}mning I Forbindelse Med Chiari Malformasjon Og Syringomyelia},
	howpublished = {CBC Workshop on Clinical Issues Related to the Cerebrospinal Fluid},
	year = {2010},
	author = {Mardal, Kent-Andre}
}
@article {Simula.SC.110,
	title = {On the Efficiency of Symbolic Computations Combined With Code Generation for Finite Element Methods},
	journal = {ACM Transactions on Mathematical Software},
	volume = {37},
	number = {1},
	year = {2010},
	abstract = {Efficient and easy implementation of variational forms for finite element discretization can be accomplished with meta-programming. Using a high-level language like Python and symbolic mathematics makes an abstract problem definition possible, but the use of a low-level compiled language is vital for run-time efficiency. By generating low-level C++ code based on symbolic expressions for the discrete weak form, it is possible to accomplish a high degree of abstraction in the problem definition while surpassing the run-time efficiency of traditional hand written C++ codes. We provide several examples where we demonstrate orders of magnitude in speed-up.},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@article {Simula.SC.105,
	title = {Efficient Preconditioners for Optimality Systems Arising in Connection With Inverse Problems},
	journal = {SIAM Journal on Control and Optimization},
	volume = {48},
	number = {8},
	year = {2010},
	doi = {10.1137/080719960},
	author = {Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre}
}
@misc {Simula.simula.336,
	title = {From a Physical Problem to Computer Simulations},
	howpublished = {CBC Workshop on Cerebrospinal Fluid Flow in the Brain and Spinal Canal - Clinical, Experimental and Mathematical Models and Problems, Simula, May 28},
	year = {2010},
	author = {St{\o}verud, Karen-Helene and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {Simula.simula.257,
	title = {An Operator Theoretical Approach to Preconditioning Optimality Systems},
	howpublished = {Talk at European Multi-Grid Conference, EMG, 2010},
	year = {2010},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik}
}
@article {Simula.sc.772,
	title = {Sex Differences in Intracranial Arterial Bifurcations},
	journal = {Gender Medicine},
	volume = {7},
	number = {2},
	year = {2010},
	publisher = {Gend Med},
	abstract = {Background: Subarachnoid hemorrhage (SAH) is a serious condition, occurring 50-70\% more frequently in females than males. SAH is mainly caused by rupture of an intracranial aneurysm. An intracranial aneurysm is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. The female preponderance is usually explained by systemical factors (hormonal influences and intrinsic wall weakness). Objective: To explore any sex variation in the bifurcation anatomy of the MCA and ICA, and the subsequent hemodynamic impact. Methods: We measured vessel radii and bifurcation angles in 47 middle cerebral artery (MCA) and 52 internal carotid artery (ICA) bifurcations in 49 patients (32 females and 17 males). The measurements were used to create idealized, averaged bifurcations of the MCA and ICA for females and males. Computational fluid dynamics simulations were performed to calculate hemodynamic forces in the models. Results: The measurements showed statistically significant sex differences in vessel diameter (men larger than females), but not in bifurcation angles. Computational fluid dynamics simulations showed higher wall shear stress in the female MCA bifurcation (19 \%) and ICA bifurcation (50 \%) compared with the male bifurcations. Conclusions: The present study suggests that sex differences in vessel size and blood flow velocity result in higher hemodynamic forces acting upon the female vessel wall. This is a new hypothesis that may partially explain why intracranial aneurysms and SAH are more likely to occur in females than males.},
	author = {Haakon {Lindekle, iv} and Valen-Sendstad, Kristian and Michael K. {Morgan} and Mardal, Kent-Andre and Faulder, Kenneth and Magnus, Jeanette and Waterloo, Knut and Romner, Bertil and Ingebrigtsen, Tor}
}
@article {Simula.sc.854,
	title = {Stability Analysis of the Inverse Transmembrane Potential Problem in Electrocardiography},
	journal = {Inverse Problems},
	volume = {26},
	number = {10},
	year = {2010},
	doi = {10.1088/0266-5611/26/10/105012},
	author = {Burger, Martin and Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik}
}
@misc {Simula.simula.259,
	title = {Is Zombies a Threat to Mankind?},
	howpublished = {Talk presented at FEniCS 2010},
	year = {2010},
	address = {FEniCS 2010},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen} and R{\o}tnes, P{\r a}l}
}
@inbook {Simula.SC.482,
	title = {Can ECG Recordings and Mathematics Tell the Condition of Your Heart?},
	booktitle = {Simula Research Laboratory - by thinking constantly about it},
	year = {2009},
	pages = {287-319},
	publisher = {Springer},
	organization = {Springer},
	chapter = {22},
	address = {Heidelberg},
	isbn = {978-3-642-01156-6},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Gr{\o}ttum, Per and Mardal, Kent-Andre and Tveito, Aslak and Tarrou, Christian and Haugaa, Kristina and Abildgaard, Andreas and Jan Gunnar {Fjeld}},
	editor = {Tveito, Aslak and Are Magnus {Bruaset} and Lysne, Olav}
}
@misc {Simula.sc.784,
	title = {Cerebral Blood Flow},
	howpublished = {Invited talk at Telemark College, Engineering Faculty, Porsgrunn, Norway, 2009},
	year = {2009},
	author = {Mardal, Kent-Andre and Hentschel, Susanne and Logg, Anders and Valen-Sendstad, Kristian}
}
@misc {Simula.SC.434,
	title = {Cerebrospinal Fluid Flow Investigations With Modelling and Simulation},
	howpublished = {invited talk at The Chiari Institute, 14th of January, New York, U.S.A.},
	year = {2009},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@article {Simula.SC.522,
	title = {CSF Flow Dynamics at the Cranio-Vertebral Junction Studied With an Idealized Model of the Subarachnoid Space and Computational Flow Analysis},
	journal = {American Journal of Neuroradiology},
	volume = {31},
	number = {1},
	year = {2009},
	pages = {185-192},
	author = {Linge, Svein and Haughton, Victor and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {Simula.sc.782,
	title = {CSF Flow Modelling},
	howpublished = {Invited talk at CSR Flow Research Conference at University of Wisconsin, Nov 9},
	year = {2009},
	author = {Mardal, Kent-Andre and Haughton, Victor and Hentschel, Susanne and Hans Petter {Langtangen} and Linge, Svein and Alf Emil {L{\o}vgren} and Valen-Sendstad, Kristian}
}
@inproceedings {Simula.SC.606,
	title = {Effect of Tonsilar Position on Cerebrospinal Fluid Flow in the Spinal Subarachnoid Space Studied With Computational Fluid Dynamics},
	journal = {ASNR - 47th Annual Meeting of the American Society of Neuroradiology},
	year = {2009},
	type = {Conference},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.sc.1154,
	title = {Implementing a K-E Turbulence Model in the FEniCS Finite Element Programming Environment},
	howpublished = {Talk at MekIT{\textquoteright}09: Fifth National Conference on Computational Mechanics, Trondheim, May 26-27},
	year = {2009},
	author = {Valen-Sendstad, Kristian and Mortensen, Mikael and Hans Petter {Langtangen} and Bj{\o}rn Anders Petterson {Reif} and Mardal, Kent-Andre}
}
@inproceedings {Simula.SC.584,
	title = {Implementing a K-E Turbulence Model in the FEniCS Finite Element Programming Environment},
	journal = {MekIT{\textquoteright}09.~~Fifth~~national~~conference~~on~~Computational~~Mechanics},
	year = {2009},
	publisher = {Tapir},
	type = {Conference},
	isbn = {9788251924214},
	author = {Valen-Sendstad, Kristian and Mortensen, Mikael and Hans Petter {Langtangen} and Bj{\o}rn Anders Petterson {Reif} and Mardal, Kent-Andre},
	editor = {Bj{\o}rn H. {Skallerud} and Andersson, Helge}
}
@misc {Simula.SC.640,
	title = {An Operator Theoretical Approach to Preconditioning Optimality Systems},
	howpublished = {Presented at the Applied Inverse Problems conference, Vienna, Austria},
	year = {2009},
	author = {Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre}
}
@misc {Simula.sc.778,
	title = {Patient-Specific Hemodynamics in FEniCS},
	howpublished = {Presentation at the FEniCS 09 Workshop},
	year = {2009},
	author = {Mardal, Kent-Andre and Logg, Anders and Hentschel, Susanne and Oddrun Christin {Myklebust} and Valen-Sendstad, Kristian}
}
@misc {Simula.sc.786,
	title = {Patient-Specific Hemodynamics in FEniCS},
	howpublished = {Invited talk at the minisymposium on Computational Vascular and Cardiovascular Mechanics at USNCCM 2009},
	year = {2009},
	author = {Mardal, Kent-Andre and Hentschel, Susanne and Logg, Anders and Valen-Sendstad, Kristian}
}
@misc {Simula.sc.780,
	title = {Patient-Specific Simulations of Stroke and Syringomyelia},
	howpublished = {Talk : Advisory commitee meeting FFI project P1112 Aerosols: Dispersion, Transport and Consequences, Nov 03},
	year = {2009},
	author = {Mardal, Kent-Andre and Hentschel, Susanne and Helgeland, Anders and Hans Petter {Langtangen} and Linge, Svein and Alf Emil {L{\o}vgren} and Logg, Anders and Valen-Sendstad, Kristian}
}
@misc {Simula.SC.436,
	title = {Simulating Normal and Abnormal CSF Flow With Idealized Geometries},
	howpublished = {talk, seminar on cerebrospinal fluid flow, 16th of January, University of Wisconsin, U.S.A.},
	year = {2009},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.sc.774,
	title = {Simulation Methodology for Bioflows},
	howpublished = {Talk : Advisory commitee meeting FFI project P1112 Aerosols: Dispersion, Transport and Consequences, May 05},
	year = {2009},
	author = {Valen-Sendstad, Kristian and Mardal, Kent-Andre and Logg, Anders}
}
@misc {Simula.SC.636,
	title = {Some Biomedical Applications at Simula},
	howpublished = {Talk at the CBC Workshop on Computational Biology with UMB},
	year = {2009},
	author = {Mardal, Kent-Andre and Helgeland, Anders and Hentschel, Susanne and Hans Petter {Langtangen} and Logg, Anders and Linge, Svein and Alf Emil {L{\o}vgren} and Valen-Sendstad, Kristian}
}
@misc {Simula.SC.590,
	title = {Tonsilar Herniation - How Is the CSF Flow Influenced?},
	howpublished = {Invited talk at Rikshospitalet University Hospital, Oslo, Norway, 5th of June},
	year = {2009},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@article {Simula.SC.21,
	title = {Unified Finite Element Discretizations of Coupled Darcy-Stokes Flow},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {25},
	year = {2009},
	pages = {311-326},
	publisher = {Wiley Periodicals},
	author = {Trygve K. {Karper} and Mardal, Kent-Andre and Winther, Ragnar}
}
@article {Simula.SC.96,
	title = {Unified Framework for Finite Element Assembly},
	journal = {International Journal of Computational Science and Engineering},
	volume = {4},
	number = {4},
	year = {2009},
	pages = {231-244},
	author = {Martin Sandve {Aln{\ae}s} and Logg, Anders and Mardal, Kent-Andre and Skavhaug, Ola and Hans Petter {Langtangen}}
}
@misc {Simula.SC.252,
	title = {Blood Flow Computations at Simula},
	howpublished = {Invited talk at Medical Physics, University of Wisconsin, March 11.},
	year = {2008},
	author = {Mardal, Kent-Andre and Valen-Sendstad, Kristian and Oddrun Christin {Myklebust} and Hentschel, Susanne}
}
@misc {Simula.SC.256,
	title = {Cerebrospinal Fluid Flow in Normal and Chiari Subjects},
	howpublished = {talk, Seminar at CBC (Simula Research Laboratory), 16th of December, Oslo, Norway},
	year = {2008},
	month = {December},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.SC.258,
	title = {Cerebrospinal Fluid Flow Simulations - Normal Subjects and Patients With Chiari I Malformation},
	howpublished = {talk, Seminar at CBC (Simula Research Laboratory), 31st of October, Oslo, Norway)},
	year = {2008},
	month = {October},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.SC.140,
	title = {CFD Analysis of Cerebrospinal Fluid Flow in the Cranio-Cervical Region},
	howpublished = {Invited talk at the 21st Nordic Seminar on Computational Mechanics, Trondheim, October 16-17},
	year = {2008},
	author = {Alf Emil {L{\o}vgren} and Linge, Svein and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@inproceedings {Simula.SC.144,
	title = {CFD Analysis of Cerebrospinal Fluid Flow in the Cranio-Cervical Region},
	journal = {21st Nordic Seminar on Computational Mechanics},
	year = {2008},
	pages = {94-97},
	publisher = {CIMNE},
	type = {Conference},
	isbn = {978-84-96736-56-6},
	author = {Alf Emil {L{\o}vgren} and Linge, Svein and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}},
	editor = {Kvamsdal, T. and Mathisen, K.M. and Pettersen, B.}
}
@misc {Simula.SC.246,
	title = {Chiari Malformation - the Problem and a Mathematical Approach},
	howpublished = {Invited talk, Vindern Medical Center, 8th of December, Oslo, Norway},
	year = {2008},
	month = {December},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Haughton, Victor and Hans Petter {Langtangen}}
}
@misc {Simula.SC.348,
	title = {Developing Flow Solver Methodology for Patientspecific Simulation of Hemodynamics},
	howpublished = {Talk at Workshop on Finite Element Methods for Fluids and Fluid-Structure Interaction, June 5},
	year = {2008},
	author = {Valen-Sendstad, Kristian and Logg, Anders and Mardal, Kent-Andre}
}
@misc {Simula.SC.254,
	title = {Hemodynamics in the Circle of Willis},
	howpublished = {Invited talk at Institute for Computational and Applied Mathematics, Muenster, Germany, November 18},
	year = {2008},
	author = {Mardal, Kent-Andre}
}
@inproceedings {Simula.SC.188,
	title = {Patient-Specific Computational Fluid Dynamic Simulations in the Circle of Willis},
	journal = {21st Nordic Seminar on Computational Mechanics},
	year = {2008},
	pages = {98-100},
	publisher = {CIMNE},
	type = {Conference},
	isbn = {978-84-96736-56-6},
	author = {Oddrun Christin {Myklebust} and Hentschel, Susanne and Mardal, Kent-Andre},
	editor = {Kvamsdal, T. and Mathisen, K.M. and Pettersen, B.}
}
@misc {Simula.SC.128,
	title = {Patient-Specific Computational Fluid Dynamic Simulations in the Circle of Willis},
	howpublished = {Invited talk at the 21st Nordic Seminar on Computational Mechanics, Trondheim, October 16-17},
	year = {2008},
	author = {Oddrun Christin {Myklebust} and Hentschel, Susanne and Mardal, Kent-Andre}
}
@misc {Simula.SC.248,
	title = {Scientific Computing at Simula},
	howpublished = {Invited Talk at Workshop on Cerebral Aneurysms and Subarachnoidal Hemorrhage, Troms{\o} Jan 24-26},
	year = {2008},
	author = {Mardal, Kent-Andre and Valen-Sendstad, Kristian and Oddrun Christin {Myklebust} and Hentschel, Susanne}
}
@misc {Simula.SC.416,
	title = {SFC - the SyFi Form Compiler},
	howpublished = {Talk at the FEniCS 08 Workshop, March 5-7,Baton Rouge, Louisiana},
	year = {2008},
	month = {March},
	abstract = {The SyFi Form Compiler was presented along with some preliminary timing results.},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@misc {Simula.SC.260,
	title = {Simulating the Cerebral Fluid Flow Associated With Chiari I Malformation in Idealized Geometries},
	howpublished = {talk, Seminar at CBC (Simula Research Laboratory), 25th of June, Oslo, Norway.},
	year = {2008},
	month = {June},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {Simula.SC.262,
	title = {Simulating the Cerebral Fluid Flow Associated With Chiari I Malformation in Idealized Geometries},
	howpublished = {talk, Seminar at CBC (Simula Research Laboratory), 20th of May, Oslo, Norway.},
	year = {2008},
	month = {May},
	author = {Linge, Svein and Alf Emil {L{\o}vgren} and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@article {Simula.SC.344,
	title = {Simulation of Hemodynamics in the Aneurysm Neck After Coiling},
	journal = {Neuroradiology},
	year = {2008},
	author = {Isaksen, J{\o}rgen and Valen-Sendstad, Kristian and Mardal, Kent-Andre and Ingebrigtsen, Tor}
}
@misc {Simula.SC.250,
	title = {Two Steps Towards Automating Efficient Solution of Inverse Problems},
	howpublished = {Invited Talk at the FEniCS 08 Workshop, March 5-7,Baton Rouge, Louisiana},
	year = {2008},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Martin Sandve {Aln{\ae}s}}
}
@inproceedings {Simula.SC.22,
	title = {Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity},
	journal = {Fourth national conference on Computational Mechanics (MekIT{\textquoteright}07)},
	year = {2007},
	month = {May},
	pages = {87-101},
	publisher = {Tapir Academic Press},
	type = {Conference},
	address = {NO-7005 Trondheim},
	abstract = {The present paper addresses the use of high level languages, symbolic mathematical tools and code generation in an implementation of the finite element method, using a nonlinear hyperelasticity equation as example. Advantages of the software development method that will be demonstrated include closeness to the mathematics, enabling high human efficiency with easy to use high level languages, while still keeping a high computational efficiency by generating tailored inner loop code for the problem at hand. The application we have in mind for the equations presented here is the simulation of the passive elastic properties of heart and blood vessel tissue.},
	isbn = {978-82-519-2235-7},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre and Sundnes, Joakim},
	editor = {Bj{\o}rn H. {Skallerud} and Andersson, H.I.}
}
@misc {Simula.SC.23,
	title = {Application of Symbolic Finite Element Tools to Nonlinear Hyperelasticity},
	howpublished = {Talk at MekIT{\textquoteright}07: Fourth National Conference on Computational Mechanics},
	year = {2007},
	month = {May},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre and Sundnes, Joakim}
}
@misc {Simula.SC.95,
	title = {Computation of Hemodynamics in the Circle of Willis},
	howpublished = {Talk at Workshop: Modelling and Computation of Biomedical Processes - June 7-14, 2007},
	year = {2007},
	address = {CBC Workshop},
	author = {Mardal, Kent-Andre}
}
@article {Simula.SC.16,
	title = {Computation of Hemodynamics in the Circle of Willis},
	journal = {Stroke},
	volume = {38},
	number = {9},
	year = {2007},
	month = {September},
	pages = {2500-2505},
	author = {Martin Sandve {Aln{\ae}s} and J{\o}rgen Gjernes {Isaksen} and Mardal, Kent-Andre and Romner, Bertil and Michael K. {Morgan} and Ingebrigtsen, Tor}
}
@misc {Simula.SC.61,
	title = {A Finite Element Model of Cardiac Electrophysiology and Mechanics},
	howpublished = {VII International conference on computational plasticity},
	year = {2007},
	month = {September},
	abstract = {Background Computer models of heart function has the potential to become a valuable tool both for medical research and clinical practice. Simulations based on accurate biophysical models increase our understanding of heart physiology and pathology, and may also predict the outcome of therapeutic interventions and drugs. This has been an active research area for decades, but the models, and in particular their application in clinical practice, are still in an early development stage. Unresolved challenges in the field include the extreme complexity of the biological processes involved, and the multiscale nature of the problem, covering processes from molecular level to the complete organ system. Models and methods Passive heart tissue is commonly modeled as a hyperelastic material, which undergoes large deformations during normal heart function. We apply an exponential stress-strain relation, resulting in a strongly non-linear elasticity equation describing the deformations of the muscle. In order to model the actively contracting muscle, the elasticity equation is coupled to systems of ordinary differential equations (ODEs) which describes the electrical activation and active force development in the muscle cells. These systems are in turn coupled to a system of partial differential equations (PDEs) known as the bidomain model, which describes propagation of the electrical signal through the heart muscle. We apply operator splitting to divide the complete model into two separate PDE systems, describing electrophysiology and mechanics on tissue level, and one system of ODEs that describes electro-mechanical coupling on cell level. These individual systems are then discretized in time with implicit schemes of first or second order, and in space with the finite element method. Simple no-flux boundary conditions are applied for the electrophysiology problem, but the mechanics problem is subject to fairly complex dynamic boundary conditions resulting from the interaction with the blood flow. To avoid solving a fluid-structure interaction problem involving the full Navier-Stokes equation for blood flow, we employ a lumped parameter model to describe the circulation. This model is a system of ODEs that describes pressures, volumes and flows through a simplified, closed loop vessel system. When this model is coupled to the finite element model for the heart muscle the result is an index one differential-algebraic (DAE) system, where the algebraic part contains the finite element based electro-mechanics model. We propose to solve the DAE system with a Runge-Kutta method of Radau type, where the time step is automatically adjusted to the different phases of the heart cycle. Results Combining the Radau solver with operator splitting and finite element discretization results in a fairly robust method, which is flexible with respect to changing or replacing individual parts of the model. Initial test results confirm the robustness and convergence of the algorithm, and verifies that the mechanics part of the problem can be solved with good accuracy. The elecrophysiology part, which contains very steep gradients, has still not been solved with the desired accuracy.},
	author = {Sundnes, Joakim and Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@misc {Simula.SC.94,
	title = {Finite Elements With Symbolic Computations and Code Generation},
	howpublished = {Talk at Software Issues in Computational Science and Engineering (SCSE 2007), Uppsala, 2007-08-11},
	year = {2007},
	address = {Software Issues in Computational Science and Engineering, Uppsala},
	author = {Mardal, Kent-Andre}
}
@inbook {Simula.SC.33,
	title = {A Hybrid Approach to Efficient Finite Element Code Development},
	booktitle = {Petascale Computing - Algorithms and Applications},
	series = {Computational Science},
	year = {2007},
	publisher = {Chapman and Hall},
	organization = {Chapman and Hall},
	chapter = {19},
	isbn = {978-1584889090},
	author = {Logg, Anders and Mardal, Kent-Andre and Martin Sandve {Aln{\ae}s} and Hans Petter {Langtangen} and Skavhaug, Ola},
	editor = {David A. {Bader}}
}
@article {Mardal.2006.5,
	title = {Order Optimal Preconditioners for Implicit Runge-Kutta Schemes Applied to Parabolic PDE{\textquoteright}s},
	journal = {SIAM Journal on Scientific Computing},
	volume = {29},
	number = {1},
	year = {2007},
	note = {Accepted for publication at SIAM Journal of Scientific Computing},
	pages = {361-375},
	abstract = {In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank-Nicolson schemes can be reused for higher-order fully implicit Runge-Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order-optimal for A-stable and irreducible Runge-Kutta schemes with invertible coefficient matrices. The theoretical investigations are confirmed by numerical experiments.},
	author = {Mardal, Kent-Andre and Nilssen, Trygve Kastberg and Gunnar Andreas {Staff}}
}
@article {Mardal.2006.4,
	title = {An Order Optimal Solver for the Discretized Bidomain Equations},
	journal = {Numerical Linear Algebra with Applications},
	volume = {14},
	number = {2},
	year = {2007},
	pages = {83-98},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Cai, Xing and Tveito, Aslak}
}
@manual {Simula.SC.32,
	title = {UFC Specification and User Manual 1.0},
	year = {2007},
	note = {http://www.fenics.org/ufc/},
	month = {July},
	edition = {1.0},
	author = {Martin Sandve {Aln{\ae}s} and Logg, Anders and Mardal, Kent-Andre and Skavhaug, Ola and Hans Petter {Langtangen}}
}
@article {Mardal.2006.7,
	title = {Using Python to Solve Partial Differential Equations},
	journal = {Computing in Science \& Engineering},
	volume = {9},
	number = {3},
	year = {2007},
	month = {May/June},
	pages = {48-51},
	author = {Mardal, Kent-Andre and Skavhaug, Ola and Glenn T. {Lines} and Gunnar Andreas {Staff} and {\O}deg{\r a}rd, {\r A}smund}
}
@inproceedings {Staff.2006.2,
	title = {Block Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations},
	journal = {ECCOMAS CFD 06},
	year = {2006},
	note = {The proceeding is published electronically},
	pages = {1-15},
	publisher = {European Community on Computational Methods in Applied Sciences},
	type = {Conference},
	abstract = {Recently, the authors presented different block preconditioners for implicit Runge-Kutta discretization of the heat equation. The preconditioners were block Jacobi and block Gauss-Seidel preconditoners where the blocks reused existing preconditioners for the implicit Euler discretization of the same equation. In this paper we will introduce similar block preconditioners for the implicit Runge-Kutta discretization of the Bidomain equation. We will, by numerical experiments, show the properties of the preconditoners, and that higher-order Runge-Kutta discretization of the Bidomain equation may be superior to lower-order in some cases.},
	isbn = {90-9020970-0},
	author = {Gunnar Andreas {Staff} and Mardal, Kent-Andre and Nilssen, Trygve Kastberg},
	editor = {Wesseling, P. and O{\~n}ate, E. and P{\'e}riaux, J.}
}
@article {Sundnes.2006.1,
	title = {On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology},
	journal = {Annals of Biomedical Engineering},
	volume = {34},
	number = {7},
	year = {2006},
	month = {July},
	pages = {1088-1097},
	author = {Sundnes, Joakim and Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre and Cai, Xing and Glenn T. {Lines} and Tveito, Aslak}
}
@misc {Nielsen.2006.3,
	title = {Computational Issues in Heart Modeling},
	howpublished = {Presented at the Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria},
	year = {2006},
	month = {April},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Cai, Xing and Mardal, Kent-Andre and Tarrou, Christian and Mary C. {MacLachlan} and Sundnes, Joakim and Glenn T. {Lines} and Tveito, Aslak}
}
@book {Sundnes.2006.2,
	title = {Computing the Electrical Activity in the Heart},
	year = {2006},
	publisher = {Springer},
	organization = {Springer},
	address = {Berlin Heidelberg},
	abstract = {This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology, who face the challenge of solving these complex mathematical models efficiently. The book will also serve as a valuable introduction to a new and exciting field for computational scientists and applied mathematicians.},
	isbn = {3-540-33432-7},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Cai, Xing and Nielsen, Bj{\o}rn Fredrik and Mardal, Kent-Andre and Tveito, Aslak}
}
@inproceedings {Nielsen.2006.6,
	title = {Identifying Ischemic Heart Disease in Terms of ECG Recordings and an Inverse Problem for the Bidomain Equations; Modeling and Experiments},
	journal = {The Third International Conference "Inverse Problems: Modeling and Simulation"},
	year = {2006},
	pages = {138-140},
	publisher = {Literat{\"u}r Yayincilik Ltd.},
	type = {Conference},
	isbn = {975-04-0381-9},
	author = {Tarrou, Christian and Ola Marius {Lysaker} and Cai, Xing and Mardal, Kent-Andre and Tarrou, Christian and Tomas Syrstad {Ruud} and Mary C. {MacLachlan} and Tveito, Aslak},
	editor = {Kunisch, K. and S. I. {Kabanikhin} and Hasanov, A. and H. T. {Banks}}
}
@misc {Langtangen.2006.4,
	title = {Mathematical Modeling of Blood Flow},
	howpublished = {Lecture at Svalbard summer school},
	year = {2006},
	note = {European Mathematical Society Summer School Mathematical Modeling of the Heart. Longyearbyen, Svalbard, Norway,},
	month = {may},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre}
}
@article {Mardal.2006.1,
	title = {An Observation on Korn{\textquoteright}s Inequality for Nonconforming Finite Element Methods},
	journal = {Math. Comp.},
	volume = {75},
	number = {253},
	year = {2006},
	pages = {1-6},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@article {Staff.2006.1,
	title = {Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs},
	journal = {Model. Identif. Control},
	volume = {27},
	number = {2},
	year = {2006},
	note = {An earlier version of this paper var publisehd in SIMS05. 46th Conference on Simulation and Modeling, Trondheim, October 13-14, edited by J{\o}rn Amundsen, Helge I. Andersson, Elena Celledoni, Tommy Gravdahl, Finn A. Michelsen, Henrik R. Nagel, Thorvald Natvig. Tapir Academic Press, pages 315-324, 2005.},
	pages = {109-123},
	abstract = {Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs \cite{mns}. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or Crank-Nicolson. It was proven that the preconditioner is optimal with respect to the timestep and the discretization parameter in space. In this paper we will improve the convergence by considering other preconditioners like the upper and the lower block Gauss-Seidel preconditioners, both in a left and right preconditioning setting. Finally, we improve the condition number by using a generalized Gauss-Seidel preconditioner.},
	author = {Gunnar Andreas {Staff} and Mardal, Kent-Andre and Nilssen, Trygve Kastberg}
}
@misc {Alnes.2006.1,
	title = {Python in High Performance Computing},
	howpublished = {Tutorial presented at the Para06 Workshop},
	year = {2006},
	author = {Martin Sandve {Aln{\ae}s} and Are Magnus {Bruaset} and Cai, Xing and Hans Petter {Langtangen} and Mardal, Kent-Andre and Moe, Halvard and Skavhaug, Ola and {\O}deg{\r a}rd, {\r A}smund}
}
@article {Mardal.2006.2,
	title = {Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs},
	journal = {Journal of Numerical Mathematics},
	volume = {14},
	number = {2},
	year = {2006},
	pages = {103-122},
	author = {Mardal, Kent-Andre and Nilssen, Trygve Kastberg}
}
@misc {Simula.SC.5,
	title = {SyFi - a Package for Symbolic Finite Element Computations},
	howpublished = {Presented at the Fenics06 workshop in Delft, Netherlands, 2006.},
	year = {2006},
	author = {Mardal, Kent-Andre}
}
@misc {Mardal.2006.3,
	title = {SyFi - an Element Matrix Factory, With Emphasis on the Incompressible Navier-Stokes Equations},
	howpublished = {Presentation held at the Para06 workshop},
	year = {2006},
	note = {Presentation held at the Para06 workshop},
	author = {Mardal, Kent-Andre}
}
@inproceedings {Mardal.2006.6,
	title = {SyFi - an Element Matrix Factory, With Emphasis on the Incompressible Navier-Stokes Equations},
	journal = {Para{\textquoteright}06},
	year = {2006},
	type = {Workshop},
	author = {Mardal, Kent-Andre}
}
@manual {Simula.SC.1,
	title = {SyFi User Manual},
	year = {2006},
	author = {Martin Sandve {Aln{\ae}s} and Mardal, Kent-Andre}
}
@inproceedings {Nielsen.2006.9,
	title = {On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem},
	journal = {Computers in Cardiology 2006},
	year = {2006},
	note = {ISSN 0276-6547},
	pages = {797-800},
	publisher = {Computers in Cardiology},
	type = {Conference},
	isbn = {0276-6547},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Tarrou, Christian and Sundnes, Joakim and Cai, Xing and Mardal, Kent-Andre},
	editor = {Murray, A.}
}
@misc {Nielsen.2006.10,
	title = {On the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout the Heart Wall: an Inverse Problem},
	howpublished = {Presented at the Computers in Cardiology conference in Valencia, Spain},
	year = {2006},
	month = {September},
	author = {Nielsen, Bj{\o}rn Fredrik and Ola Marius {Lysaker} and Tarrou, Christian and Sundnes, Joakim and Cai, Xing and Mardal, Kent-Andre}
}
@inproceedings {Staff.2005.1,
	title = {The Accuracy of the Velocity Approximation With Respect to the Pressure Approximation for Incompressible Fluid Flow},
	journal = {Third National Conference on Computational Mechanics (MekIT 05)},
	year = {2005},
	month = {May},
	pages = {297-311},
	publisher = {Tapir Academic Press},
	type = {1},
	edition = {first},
	address = {Trondheim, May 11-12},
	abstract = {We consider the accuracy of the velocity approximation with respect to the pressure approximation using various standard finite element methods for incompressible fluid flow. Of particular interest is the case where the hydrostatic part of the pressure is dominating, which implies that the pressure may be large relative to the velocity. Some standard mixed elements like the Mini element and the Taylor-Hood element handle this case well, while others like the P\_2-P\_0 element and the Crouzeix-Raviart element do not. This seems to be related to the fact that the Taylor-Hood and the Mini elements yield a stable approximation of the mixed Poisson problem.},
	author = {Gunnar Andreas {Staff} and Mardal, Kent-Andre},
	editor = {Bj{\o}rn H. {Skallerud} and Helge I. {Andersson}}
}
@techreport {25346,
	title = {An Order Optimal Solver for the Discretized Bidomain Equations},
	year = {2005},
	note = {This technical report is an earlier version of a journal article. The journal article\&nbsp;can be found here:https://www.simula.no/publications/order-optimal-solver-discretized-bidomain-equations},
	publisher = {Simula Research Laboratory},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Cai, Xing and Tveito, Aslak}
}
@misc {Mardal.2005.5,
	title = {Preconditioners for Elliptic Problems With Variable Coefficients},
	howpublished = {Presented at the SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, France},
	year = {2005},
	author = {Mardal, Kent-Andre and Nielsen, Bj{\o}rn Fredrik and Tveito, Aslak}
}
@inproceedings {Staff.2005.2,
	title = {Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs},
	journal = {SIMS05. 46th Conference on Simulation and Modeling, Trondheim, October 13-14},
	year = {2005},
	pages = {315-324},
	publisher = {Tapir Academic Press},
	type = {1},
	abstract = {Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs \cite{mns}. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or Crank-Nicolson. It was proven that the preconditioner is optimal with respect to the timestep and the discretization parameter in space. In this paper we will improve the convergence by considering other preconditio ners like the upper and the lower block Gauss-Seidel preconditioners, both in a left and right preconditioning setting . Finally, we improve the condition number by using a generalized Gauss-Seidel p reconditioner.},
	author = {Gunnar Andreas {Staff} and Mardal, Kent-Andre and Nilssen, Trygve Kastberg},
	editor = {Amundsen, J{\o}rn and Helge I. {Andersson} and Celledoni, Elena and Gravdahl, Tommy and Finn A. {Michelsen} and Henrik R. {Nagel} and Natvig, Thorvald}
}
@techreport {Skavhaug.2005.4,
	title = {A Python Framework for Verifying Codes for Numerical Solutions of Partial Differential Equations},
	number = {2005-18},
	year = {2005},
	publisher = {Simula Research Laboratory},
	author = {Skavhaug, Ola and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {Bruaset.2005.2,
	title = {Scientific Computing in Python},
	howpublished = {Tutorial ASIM 2005},
	year = {2005},
	author = {Are Magnus {Bruaset} and Martin Sandve {Aln{\ae}s} and Hans Petter {Langtangen} and Mardal, Kent-Andre and Moe, Halvard and Skavhaug, Ola and {\O}deg{\r a}rd, {\r A}smund}
}
@misc {SC.8.Mardal.2004,
	title = {Block Preconditioners for PDEs Arising From the Bi-Domain Model of the Electrical Activity in the Heart},
	howpublished = {Talk at the Copper Mountain Conference, Colorado, USA},
	year = {2004},
	note = {Presented by K.-A. Mardal},
	month = {April},
	author = {Mardal, Kent-Andre and Tveito, Aslak}
}
@techreport {SC.7.Boehm.2004,
	title = {Diffpack Implementation of Edge-Based Non-Standard Finite Element Methods},
	number = {2004-11},
	year = {2004},
	publisher = {Simula Research Laboratory},
	author = {B{\"o}hm, Peter and Are Magnus {Bruaset} and Hans Petter {Langtangen} and Mardal, Kent-Andre and Wachutka, Gerhard}
}
@misc {SC.8.Oedegaard.2004.b,
	title = {High Performance Computing in Python},
	howpublished = {Tutorial, SC2004},
	year = {2004},
	month = {November},
	author = {{\O}deg{\r a}rd, {\r A}smund and Mardal, Kent-Andre and Miller, P. and Moe, Halvard and Skavhaug, Ola and Are Magnus {Bruaset} and Hans Petter {Langtangen}}
}
@misc {SC.8.Westile.2004,
	title = {Making a Python Interface to the C++ Library Diffpack},
	howpublished = {Talk at the EuroPython 2004 Conference, Gothenburg, Sweden},
	year = {2004},
	note = {Presented by M. Westlie},
	month = {June},
	author = {Westlie, M. and Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {SC.8.Nilssen.2004,
	title = {Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs},
	howpublished = {Talk at the Eigth Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, USA},
	year = {2004},
	author = {Nilssen, Trygve Kastberg and Mardal, Kent-Andre}
}
@article {SC.4.Mardal.2004,
	title = {Uniform Preconditioners for the Time Dependent Stokes Problem},
	journal = {Numerische Mathematik},
	volume = {98},
	number = {2},
	year = {2004},
	pages = {305-327},
	author = {Mardal, Kent-Andre and Winther, Ragnar}
}
@inbook {SC.5.Mardal.2003.b,
	title = {Block Preconditioning and Systems of PDEs},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {199-236},
	publisher = {Springer},
	organization = {Springer},
	author = {Mardal, Kent-Andre and Sundnes, Joakim and Hans Petter {Langtangen} and Tveito, Aslak},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@misc {SC.8.Tveito.2003,
	title = {Computing the Electrical Activity in the Human Heart},
	howpublished = {Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic},
	year = {2003},
	month = {August},
	author = {Tveito, Aslak and Glenn T. {Lines} and Sundnes, Joakim and Nielsen, Bj{\o}rn Fredrik and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@misc {SC.8.Lines.2003,
	title = {Computing the Electrical Activity in the Human Heart},
	howpublished = {Presented at the Centre of Mathematics for Applications, Oslo},
	year = {2003},
	author = {Glenn T. {Lines} and Nielsen, Bj{\o}rn Fredrik and Tveito, Aslak and Sundnes, Joakim and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@misc {SC.8.Tveito.2003.b,
	title = {Computing the Heart},
	howpublished = {Presented at the 21st CAD-FEM users{\textquoteright} meeting 2003 - International congress on FEM technology, Potsdam, Germany},
	year = {2003},
	month = {November},
	author = {Tveito, Aslak and Glenn T. {Lines} and Nielsen, Bj{\o}rn Fredrik and Sundnes, Joakim and Gr{\o}ttum, P. and Cai, Xing and Mardal, Kent-Andre}
}
@inproceedings {SC.6.Mardal.2003,
	title = {Error Estimates for the Linear Navier-Stokes Equations},
	journal = {Proceedings of the Second National Conference on Computational Mechanics (MekIT{\textquoteright}03)},
	year = {2003},
	pages = {225-237},
	publisher = {Tapir Academic Press},
	type = {1},
	isbn = {9788251918688},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen} and Winter, R.},
	editor = {Bj{\o}rn H. {Skallerud} and Andersson, H.I.}
}
@inbook {SC.5.Mardal.2003.c,
	title = {Mixed Elements in Diffpack},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {153-198},
	publisher = {Springer},
	organization = {Springer},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen}},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@inbook {SC.5.Mardal.2003.a,
	title = {Multigrid Methods in Diffpack},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {97-152},
	publisher = {Springer},
	organization = {Springer},
	author = {Mardal, Kent-Andre and Zumbusch, G. and Hans Petter {Langtangen}},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@misc {Mardal.2003.1,
	title = {Numerical Modeling of Crust and Mantle Movement},
	howpublished = {Talk presented at SIAM Conference on Mathematical and Computational Issues in the Geosciences (GS0 3), March 17-20, 2003, Austin, Texas.},
	year = {2003},
	author = {Mardal, Kent-Andre and Huerta, Audrey and Hans Petter {Langtangen} and Harry, Dennis}
}
@phdthesis {SC.3.Mardal.2003,
	title = {Software and Numerical Methods for the Incompressible Navier-Stokes Equations},
	year = {2003},
	school = {Faculty of Mathematics and Natural Sciences, University of Oslo},
	type = {phd},
	author = {Mardal, Kent-Andre}
}
@inproceedings {SC.6.Kristoffersen.2003,
	title = {Solving Heat Distribution in Room Using Mixed Finite Element for Coupling the Navier-Stokes Equations and the Heat Equation},
	journal = {Proceedings of the Second National Conference on Computational Mechanics (MekIT{\textquoteright}03)},
	year = {2003},
	pages = {211-225},
	publisher = {Tapir Academic Press},
	type = {1},
	author = {Kristoffersen, A. and Mardal, Kent-Andre}
}
@inbook {SC.5.Langtangen.2003.a,
	title = {Using Diffpack From Python Scripts},
	booktitle = {Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming},
	series = {Lecture Notes in Computational Science and Engineering},
	year = {2003},
	pages = {321-360},
	publisher = {Springer},
	organization = {Springer},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre},
	editor = {Hans Petter {Langtangen} and Tveito, Aslak}
}
@misc {SC.8.Lines.2002,
	title = {Diffpack Simulation of the Electrical Activity in the Heart},
	howpublished = {Invited minisymposium talk at the 20th CAD-FEM User{\textquoteright}s Meeting, Friedrichshafen, Germany},
	year = {2002},
	note = {Presented by A. M. Bruaset},
	month = {October},
	author = {Glenn T. {Lines} and Sundnes, Joakim and Tveito, Aslak and Cai, Xing and Mardal, Kent-Andre and Are Magnus {Bruaset}}
}
@techreport {SC.7.Mardal.2002,
	title = {How to Use MATLAB in C++ Programs},
	year = {2002},
	note = {Simula 2002-08},
	publisher = {Simula Research Laboratory},
	author = {Mardal, Kent-Andre and Acklam, E. and Calhoun, D.}
}
@article {SC.4.Sundnes.2002,
	title = {Multigrid Block Preconditioning for a Coupled System of Partial Differential Equations Modeling the Electrical Activity in the Heart},
	journal = {Computer Methods in Biomechanics and Biomedical Engineering},
	volume = {5},
	number = {6},
	year = {2002},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Mardal, Kent-Andre and Tveito, Aslak}
}
@article {SC.4.Langtangen.2002.b,
	title = {Numerical Methods for Incompressible Viscous Flow},
	journal = {Advances in Water Resources},
	volume = {25},
	number = {8},
	year = {2002},
	pages = {1125-1146},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre and Winther, Ragnar}
}
@article {SC.4.Mardal.2002,
	title = {A Robust Finite Element Method for Darcy-Stokes Flow},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {40},
	year = {2002},
	pages = {1605-1631},
	author = {Mardal, Kent-Andre and Tai, Xue-Cheng and Winther, Ragnar}
}
@inproceedings {SC.5.Langtangen.2002,
	title = {A Software Framework for Mixed Finite Element Programming},
	journal = {Proceedings of the 2nd International Conference on Computational Science},
	year = {2002},
	publisher = {Springer-Verlag},
	type = {1},
	author = {Hans Petter {Langtangen} and Mardal, Kent-Andre}
}
@inproceedings {SC.5.Mardal.2001,
	title = {An Efficient Parallel Iterative Approach to a Fully Implicit Mixed Finite Element Formulation for the Navier-Stokes Equations},
	journal = {ECCOMAS CFD 2001, Computational Fluid Dynamics Conference Proceedings},
	year = {2001},
	publisher = {Swansea, 2001, CD-ROM, European Community on Computational Methods in Applied Sciences, ISBN 0 905 091 12 4},
	type = {1},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen}}
}
@misc {Sundnes.2001.1,
	title = {On Numerical Techniques for the Bidomain Model},
	howpublished = {Presented at the SIAM Annual meeting, San Diego, California},
	year = {2001},
	month = {July},
	author = {Sundnes, Joakim and Glenn T. {Lines} and Mardal, Kent-Andre and Tveito, Aslak}
}
@inproceedings {SC.6.Mardal.2001,
	title = {An Optimal Iterative Method for the Time-Dependent Stokes Problem},
	journal = {Tenth Conference Virtual Proceedings, Copper Mountain Conference on Multigrid Methods},
	year = {2001},
	publisher = {MGNet},
	type = {1},
	address = {Copper Mountain, CO, USA},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen} and Winter, R.}
}
@inproceedings {Mardal.2000.2,
	title = {An Effective Iterative Approach to a Fully Implicit Mixed Finite Element Formulation for the Navier-Stokes Equations},
	journal = {13th Nordic Seminar on Computational Mechanics (NSCM-13)},
	year = {2000},
	pages = {86-89},
	publisher = {Mechanics and Applied Mathematics Series, No. 7, October 2000},
	type = {1},
	author = {Mardal, Kent-Andre and Hans Petter {Langtangen}},
	editor = {Osnes J. {Hellesland} and Skeie, G.}
}
@article {budisa2022haznics,
	title = {HAZniCS{\textendash}Software Components for Multiphysics Problems},
	journal = {arXiv preprint arXiv:2210.13274},
	publisher = {Arxiv},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@article {boon2021parameter,
	title = {Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers},
	journal = {arXiv preprint arXiv:2111.05653},
	publisher = {arxiv},
	author = {Wietse M {Boon} and Hornkj{\o}l, Martin and Kuchta, Miroslav and Mardal, Kent-Andre and Ruiz-Baier, Ricardo}
}
@article {doi:10.1002/num.22304,
	title = {Preconditioning trace coupled 3d-1d systems using fractional Laplacian},
	journal = {Numerical Methods for Partial Differential Equations},
	volume = {35},
	number = {1},
	pages = {375-393},
	publisher = { Wiley},
	abstract = {Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d-1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three-dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well-defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.},
	keywords = {Lagrange multipliers, preconditioning, saddle-point problem, trace},
	doi = {10.1002/num.22304},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22304},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Mortensen, Mikael}
}
@article {budisa2022rational,
	title = {Rational approximation preconditioners for multiphysics problems},
	journal = {arXiv preprint arXiv:2209.11659},
	publisher = {Arxiv},
	author = {Budisa, Ana and Hu, Xiaozhe and Kuchta, Miroslav and Mardal, Kent-Andre and Ludmil Tomov {Zikatanov}}
}
@article {hong2021robust,
	title = {Robust approximation of generalized Biot-Brinkman problems},
	journal = {arXiv preprint arXiv:2112.13618},
	publisher = {arxiv},
	author = {Hong, QINGGUO and Kraus, JOHANNES and Kuchta, Miroslav and Lymbery, MARIA and Mardal, Kent-Andre and Marie E. {Rognes}}
}
@article {boon2021robust,
	title = {Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form},
	journal = {arXiv preprint arXiv:2110.07486},
	publisher = {arxiv},
	author = {Wietse M {Boon} and Koch, Timo and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {holter2020robust,
	title = {Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form},
	journal = {arXiv preprint arXiv:2001.05529},
	publisher = {Elsavier},
	author = {Karl Erik {Holter} and Kuchta, Miroslav and Mardal, Kent-Andre}
}
@article {doi:10.1002/nla.2212,
	title = {On the singular Neumann problem in linear elasticity},
	journal = {Numerical Linear Algebra with Applications},
	volume = {26},
	number = {1},
	note = {e2212 nla.2212},
	pages = {e2212},
	publisher = { Wiley},
	abstract = {Summary The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a nonsingular linear system. However, they often cause reduced accuracy or lead to poor convergence of the iterative solvers. In this paper, different well-posed formulations of the problem are studied through discretization by the finite element method, and preconditioning strategies based on operator preconditioning are discussed. For each formulation, we derive preconditioners that are independent of the discretization parameter. Preconditioners that are robust with respect to the first Lam{\'e} constant are constructed for the pure displacement formulations, whereas a preconditioner that is robust in both Lam{\'e} constants is constructed for the mixed formulation. It is shown that, for convergence in the first Sobolev norm, it is crucial to respect the orthogonality constraint derived from the continuous problem. On the basis of this observation, a modification to the conjugate gradient method is proposed, which achieves optimal error convergence of the computed solution.},
	keywords = {conjugate gradient, Linear elasticity, preconditioning, rigid motions, singular problems},
	doi = {10.1002/nla.2212},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2212},
	author = {Kuchta, Miroslav and Mardal, Kent-Andre and Mortensen, Mikael}
}
