@article {Simula.SC.488,
	title = {Computing the Stability of Steady-State Solutions of Mathematical Models of the Electrical Activity in the Heart},
	journal = {Mathematical Biosciences and Engineering},
	volume = {41},
	number = {8},
	year = {2011},
	pages = {611-618},
	doi = {10.1016/j.compbiomed.2011.05.011},
	author = {Tveito, Aslak and Skavhaug, Ola and Glenn T. {Lines} and Artebrant, Robert}
}
@article {Simula.sc.838,
	title = {Existence of Excitation Waves for a Collection of Cardiomyocytes Electrically Coupled to Fibroblasts},
	journal = {Mathematical Biosciences},
	volume = {230},
	year = {2011},
	pages = {79-86},
	publisher = {Elsevier},
	abstract = {We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the myocardial tissue. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts.},
	doi = {10.1016/j.mbs.2011.01.004},
	author = {Tveito, Aslak and Glenn T. {Lines} and Artebrant, Robert and Skavhaug, Ola and Maleckar, Molly}
}
@article {Simula.SC.508,
	title = {Stability of Two Time-Integrators for the Aliev-Panfilov System},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {8},
	number = {3},
	year = {2011},
	pages = {427-442},
	author = {Hanslien, Monica and Artebrant, Robert and Tveito, Aslak and Glenn T. {Lines} and Cai, Xing}
}
@article {Simula.SC.464,
	title = {A Method for Analyzing the Stability of the Resting State for a Model of Pacemaker Cells Surrounded by Stable Cells},
	journal = {Mathematical Biosciences and Engineering},
	volume = {7},
	number = {3},
	year = {2010},
	pages = {505-526},
	abstract = {The purpose of this paper is to derive and analyze methods for examining the stability of solutions of partial differential equations modeling collections of excitable cells. In particular, we derive methods for estimating the principal eigenvalue of a linearized version of the Luo-Rudy I model close to an equilibrium solution. It has been suggested that the stability of a collection of unstable cells surrounded by a large collection of stable cells can be studied by considering only a collection of unstable cells equipped with a Dirichlet type boundary condition. This method has earlier been applied to analytically assess the stability of a reduced version the Luo-Rudy I model. In this paper we analyze the accuracy of this technique and apply it to the full Luo-Rudy I model. Furthermore, we extend the method to provide analytical results for the FitzHugh-Nagumo model in the case where a collection of unstable cells is surrounded by a collection of stable cells. All our analytical findings are complemented by numerical computations computing the principal eigenvalue of a discrete version of linearized models.},
	author = {Artebrant, Robert and Tveito, Aslak and Glenn T. {Lines}}
}
@article {Simula.SC.486,
	title = {Bifurcating Solutions to the Monodomain Model Equipped With FitzHugh-Nagumo Kinetics},
	journal = {Journal of Applied Mathematics},
	volume = {2009},
	year = {2009},
	publisher = {Hindawi Publishing Corporation},
	abstract = {We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.},
	doi = {10.1155/2009/292183},
	author = {Artebrant, Robert}
}
@article {Simula.SC.114,
	title = {A Second Order Algorithm for Solving Dynamic Cell Membrane Equations},
	journal = {IEEE Transactions on Biomedical Engineering},
	volume = {56},
	number = {10},
	year = {2009},
	pages = {2546-2548},
	abstract = {This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of non-linear terms in combination with the analytical solution of linear ordinary differential equations, to obtain a second order accurate numerical scheme. We compare the error and computational load of the second order scheme to the original Rush-Larsen method. For a given error tolerance, the second order method is from nine to 500 times faster than the original scheme, depending on the choice of model and tolerance.},
	author = {Sundnes, Joakim and Artebrant, Robert and Skavhaug, Ola and Tveito, Aslak}
}
@article {Simula.SC.76,
	title = {An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {6},
	number = {4},
	year = {2009},
	pages = {627-641},
	abstract = {Simulations of cardiac defibrillation are associated with considerable numerical challenges. The cell models have traditionally been discretized by first order explicit schemes, which are associated with severe stability issues. The sharp transition layers in the solution call for stable and efficient solvers. We propose a second order accurate numerical method for the Luo-Rudy phase 1 model of electrical activity in a cardiac cell, which provides sequential update of each governing ODE. An \textit{a priori} estimate for the scheme is given, showing that the bounds of the variables typically observed during electric shocks constitute an invariant region for the system, regardless of the time step chosen. Thus the choice of time step is left as a matter of accuracy. Conclusively, we demonstrate the theoretical result by some numerical examples, illustrating second order convergence for the Luo-Rudy 1 model.},
	author = {Hanslien, Monica and Artebrant, Robert and Sundnes, Joakim and Tveito, Aslak}
}
@article {Simula.SC.394,
	title = {Increasing the Accuracy in Locally Divergence-Preserving Finite Volume Schemes for MHD},
	journal = {Journal of Computational Physics},
	volume = {227},
	year = {2008},
	pages = {3405-3427},
	publisher = {Elsevier},
	author = {Artebrant, Robert and Torrilhon, Manuel}
}
@inproceedings {Simula.SC.406,
	title = {Locally Divergence-Preserving Schemes of Higher Order},
	journal = {PAMM, Proceedings in Applied Mathematics and Mechanics},
	volume = {7},
	number = {1},
	year = {2007},
	pages = {2020077-2020078},
	publisher = {Wiley InterScience},
	type = {Conference},
	isbn = {1617-7061},
	author = {Artebrant, Robert}
}
@article {Simula.SC.396,
	title = {Third Order Accurate Non-Polynomial Reconstruction on Rectangular and Triangular Meshes},
	journal = {Journal of Scientific Computing},
	volume = {30},
	number = {2},
	year = {2007},
	pages = {193-221},
	author = {Artebrant, Robert}
}
@article {Simula.SC.398,
	title = {Limiter-Free Third Order Logarithmic Reconstruction},
	journal = {SIAM Journal on Scientific Computing},
	number = {28},
	year = {2006},
	pages = {359-381},
	author = {Artebrant, Robert and Hans Joachim {Schroll}}
}
@inproceedings {Simula.SC.408,
	title = {Logarithmic Reconstructions},
	journal = {Hyperbolic Problems: Theory, Numerics, Applications},
	number = {I},
	year = {2006},
	pages = {271-278},
	publisher = {Yokohama Publishers, Inc},
	type = {Conference},
	isbn = {4-946552-21-9},
	author = {Artebrant, Robert and Hans Joachim {Schroll}},
	editor = {Asakura, F. and Kawashima, S. and Matsumura, A. and Nishibata, S. and K., Nishihara}
}
@article {Simula.SC.400,
	title = {Numerical Simulation of Camassa-Holm Peakons by Adaptive Upwinding},
	journal = {Applied Numerical Mathematics},
	volume = {56},
	number = {5},
	year = {2006},
	pages = {695-711},
	author = {Artebrant, Robert and Hans Joachim {Schroll}}
}
@article {Simula.SC.404,
	title = {Comment on {\textquoteright}Finite-Volume Component-Wise TVD Schemes for 2D Shallow Water Equations{\textquoteright}},
	journal = {Advances in Water Resources},
	number = {28},
	year = {2005},
	pages = {423-425},
	author = {Artebrant, Robert}
}
@article {Simula.SC.402,
	title = {Conservative Logarithmic Reconstructions and Finite Volume Methods},
	journal = {SIAM Journal on Scientific Computing},
	volume = {27},
	number = {1},
	year = {2005},
	pages = {294-314},
	author = {Artebrant, Robert and Hans Joachim {Schroll}}
}
@inproceedings {Simula.SC.410,
	title = {High-Resolution Riemann-Solver-Free Methods for Conservation Laws},
	journal = {Hyperbolic Problems: Theory, Numerics, Applications},
	year = {2003},
	pages = {305-314},
	publisher = {Springer},
	type = {1},
	isbn = {3540443339},
	author = {Artebrant, Robert and Hans Joachim {Schroll}},
	editor = {T.Y., Hou and E., Tadmor}
}
