@article {23448,
	title = {Fast Computation of Eikonal and Transport Equations on GPU Computer Architectures},
	journal = {Geophysics},
	volume = {80},
	year = {2015},
	publisher = {Geophysics},
	author = {Noack, Marcus and Gillberg, Tor}
}
@inproceedings {19138,
	title = {Effective Multi-GPU Communication Using Multiple CUDA Streams and Threads},
	journal = {20th International Conference on Parallel and Distributed Systems (ICPADS 2014)},
	year = {2014},
	pages = {981-986},
	publisher = {IEEE},
	abstract = {In the context of multiple GPUs that share the same PCIe bus, we propose a new communication scheme that leads to a more effective overlap of communication and computation. Multiple CUDA streams and OpenMP threads are adopted so that data can simultaneously be sent and received. A representative 3D stencil example is used to demonstrate the effectiveness of our scheme. We compare the performance of our new scheme with an MPI-based state-of-the-art scheme. Results show that our approach outperforms the state-of-the-art scheme, being up to 1.85{\texttimes} faster. However, our performance results also indicate that the current underlying PCIe bus architecture needs improvements to handle the future scenario of many GPUs per node.},
	doi = {10.1109/PADSW.2014.7097919},
	author = {Sourouri, Mohammed and Gillberg, Tor and Baden, Scott and Cai, Xing}
}
@misc {23447,
	title = {Fast and accurate Solutions of the Eikonal and Transport Equations},
	howpublished = {Amsterdam},
	year = {2014},
	author = {Noack, Marcus and Gillberg, Tor and Clark, Stuart}
}
@misc {24879,
	title = { 	Parallel and simultaneous computation of eikonal and transport equations by taking full advantage of GPU computer architecture},
	howpublished = {Jena, Germany},
	year = {2014},
	author = {Noack, Marcus and Gillberg, Tor}
}
@article {Simula.simula.2858,
	title = {Parallel Solutions of Static Hamilton-Jacobi Equations for Simulations of Geological Folds},
	journal = {Journal of Mathematics in Industry},
	volume = {4},
	number = {10},
	year = {2014},
	publisher = {Springer},
	abstract = {Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. The performance of the new methods are investigate for tow types of static Hamilton-Jacobi formulations are investigated, the isotropic eikonal equation and an anisotropic formulation used to simulate different types of geological folding. Simulations of geological folding is a key component in an industrial software used in oil and gas exploration. In particular, our experiments indicate that the new algorithms would be capable of accelerating an existing industrial simulator substantially. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds. The new methods are now being migrated to the industrial software.},
	doi = {10.1186/2190-5983-4-10},
	author = {Gillberg, Tor and Are Magnus {Bruaset} and Hjelle, {\O}yvind and Sourouri, Mohammed}
}
@misc {Simula.simula.2004,
	title = {Developing and Implementing Parallel Algorithms for Fold Simulations in 3D},
	howpublished = {Presented during a workshop at Simula: Using the GPU for Scientific Computing: coding concepts and a look at applications in structural geology http://simula.no/intranet/news/using-the-gpu-for-scie\ ntific-computing-coding-concepts-and-a-look-at-appl},
	year = {2013},
	note = {Presented during a workshop at Simula: Using the GPU for Scientific Computing: coding concepts and a look at applications in structural geology http://simula.no/intranet/news/using-the-gpu-for-scientific-computing-coding-concepts-and-a-look-at-applications-in-structural-geology},
	month = {February},
	abstract = {The Compound Earth Simulator is an exploration software developed by Kalkulo for Statoil. In the Compound methodology, large folded geological structures are simulated repeatedly as geological models are investigated. Folded layers are modeled as positions of a front moving through a geological, and are computed using first-arrival-time equations. The numerical simulation times must be low for the software to function at interactive times, which is a challenge in 3D as the number of unknown nodes increases rapidly. This talk presents a new set of algorithms for such simulations, specifically developed for massively parallel compute architectures such as GPUs. A couple of optimization approaches and their effects are presented for the GPU implementation. Finally, some early result from a multicore CPU and a GPU implementation will be given.},
	keywords = {Workshop},
	author = {Gillberg, Tor}
}
@phdthesis {Simula.simula.2186,
	title = {Fast and Accurate Front Propagation for Simulation of Geological Folds},
	year = {2013},
	note = {http://urn.nb.no/URN:NBN:no-41672},
	month = {September},
	school = {Faculty of Mathematics and Natural Sciences, University of Oslo},
	type = {phd},
	address = {P.O box 1080 Blindern 0316 OSLO Norway},
	abstract = {Front propagations described by static Hamilton-Jacobi equations can be used to simulate folded geological structures. Simulations of geological folds are a key ingredient in the Compound Earth Simulator (CES), an industrial software tool used in the exploration of oil and gas. In this thesis, local approximation techniques are investigated with respect to accuracy and efficiency. Several novel algorithms are also introduced, of which some are accelerated by parallel implementations on both multicore CPUs and Graphic Processing Units. These algorithms are able to simulate folds at a fraction of the time needed by the CES industry code, while retaining the same level of accuracy. Complicated tasks that previously needed several minutes to be computed can now be performed in just a matter of a few seconds, thus significantly improving the CES user experience.},
	author = {Gillberg, Tor}
}
@techreport {parallel-solvers-for-static-hamilton-jacobi-equations,
	title = {Parallel Solvers for Static Hamilton-Jacobi Equations in Three Dimensions},
	year = {2013},
	month = {September},
	publisher = {Simula Research Laboratory},
	abstract = {Three algorithms for numerical solution of static Hamilton-Jacobi equations on parallel computers are presented in this paper. The proposed algorithms are applicable to both isotropic and anisotropic problems, and are here used to simulate folded geological structures of high complexity. Our algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well on parallel architectures. In particular, these experiments indicate that the new algorithms would be capable of accelerate an existing industrial simulator to a level where detailed three-dimensional studies of complicated geological scenarios can be performed interactively. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds.},
	author = {Gillberg, Tor and Are Magnus {Bruaset} and Sourouri, Mohammed and Hjelle, {\O}yvind}
}
@article {Simula.simula.622,
	title = {Accuracy and Efficiency of Stencils for the Eikonal Equation in Earth Modelling},
	journal = {Computational Geosciences},
	volume = {16},
	number = {4},
	year = {2012},
	month = {September},
	pages = {933-952},
	abstract = {Motivated by the needs for creating fast and accurate models of complex geological scenarios, accuracy and efficiency of three stencils for the isotropic eikonal equation on rectangular grids are evaluated using a Fast Marching implementation. The stencils are derived by direct modelling of the wave front, resulting in new and valuable insight in terms of improved upwind and causality conditions. After intro- ducing a method for generalising first order upwind stencils to higher order, a new second order Diagonal stencil is presented. Similarly to the Multistencils Fast Marching ap- proach, the Diagonal stencil makes use of nodes in the diagonal directions, whereas the traditional Godunov stencil uses solely edge-connected neighbours. The Diagonal stencil uses nodes close to each other, reaching upwind, to get a more accurate estimate of the angle of incidence of the arriving wave front. Although the stencils are evaluated in a Fast Marching setting, they can be adapted to other efficient eikonal solvers. All first and second order stencils are evaluated in a range of tests. The first test case models a folded structure from the Zagros fold belt in Iran. The other test cases are constructed to investigate specific properties of the examined stencils. The numerical investigation considers convergence rates and CPU times for non-constant and constant speed first-arrival computations. In conclusion, the Diagonal stencil is the most efficient and accurate of the three alternatives.},
	keywords = {Workshop},
	doi = {10.1007/s10596-012-9296-0},
	author = {Gillberg, Tor and Hjelle, {\O}yvind and Are Magnus {Bruaset}}
}
@misc {Simula.simula.1126,
	title = {Massively Parallel Front Tracking},
	howpublished = {Computational Geoscience Workshop, 18-20 January 2012 in Geilo},
	year = {2012},
	month = {January 2012},
	abstract = {We present a novel method for three dimensional anisotropic front propagation, and apply it to the simulation of geological folding. The iterative algorithm has a simple structure, and a high level of fine grained parallelism. The source-code translator Mint is used to generate Cuda code executable on Graphic Processor Units (GPUs) from our C implementation. Our numerical section present results of such an approach, and that of a multicore implementation. The implementations have been tested and compared on several examples of three dimensional geological folding.},
	keywords = {Workshop},
	author = {Gillberg, Tor}
}
@inproceedings {Simula.simula.1518,
	title = {A New Parallel 3D Front Propagation Algorithm for Fast Simulation of Geological Folds},
	journal = {The International Conference on Computational Science, ICCS 2012},
	volume = {9},
	year = {2012},
	pages = {947-955},
	publisher = {ICCS},
	type = {Conference},
	address = {Amsterdam},
	abstract = {We present a novel method for 3D anisotropic front propagation and apply it to the simulation of geological folding. The new iterative algorithm has a simple structure and abundant parallelism, and is easily adapted to multithreaded architectures using OpenMP. Moreover, we have used the automated C-to-CUDA source code translator, Mint, to achieve greatly enhanced computing speed on GPUs. Both OpenMP and CUDA implementations have been tested and benchmarked on several examples of 3D geological folding.},
	keywords = {Conference},
	doi = {10.1016/j.procs.2012.04.101},
	author = {Gillberg, Tor and Sourouri, Mohammed and Cai, Xing},
	editor = {Ali, Hesham and Shi, Yong and Khazanchi, Deepak and Lees, Michael and van Albada, Dick and Dongarra, Jack and Peter M.A. {Sloot} and Dongarra, Jack}
}
@inproceedings {Simula.simula.1118,
	title = {A Parallel 3D Front Propagation Algorithm for Simulation of Geological Folding on GPUs},
	journal = {EAGE 74th Conference \& Exhibition, Copenhagen},
	year = {2012},
	month = {June},
	publisher = {EAGE},
	type = {Conference},
	abstract = {A 3D front propagation algorithm for the simulation of geological folding is presented. The algorithm is implemented on multicore and GPU architectures. Numerical experiments based on OpenMP show an almost perfect scaling. Using the automatic code translator Mint, Cuda code is created from seqential C code. On a GPU the Cuda code runs 67-95 times faster than sequential code, and allows 3D grids to be computed at interactive times.},
	keywords = {Conference},
	author = {Gillberg, Tor and Hjelle, {\O}yvind and Are Magnus {Bruaset}},
	editor = {Eage, }
}
@misc {Simula.simula.1454,
	title = {A Parallel 3D Front Propagation Algorithm for Simulation of Geological Folding on GPUs},
	howpublished = {EAGE 74th Conference \& Exhibition},
	year = {2012},
	month = {June},
	abstract = {A 3D front propagation algorithm for the simulation of geological folding is presented. The algorithm is implemented on multicore and GPU architectures. Numerical experiments based on OpenMP show an almost perfect scaling. Using the automatic code translator Mint, Cuda code is created from seqential C code. On a GPU the Cuda code runs 67-95 times faster than sequential code, and allows large 3D grids to be computed at interactive times.},
	keywords = {Conference},
	author = {Gillberg, Tor}
}
@misc {Simula.simula.878,
	title = {A Semi-Ordered Fast Iterative Method (SOFI) for Monotone Front Propagation in Simulations of Geological Folding},
	howpublished = {The 19th International Congress on Modelling and Simulation (MODSIM2011)},
	year = {2011},
	month = {December},
	keywords = {Conference},
	author = {Gillberg, Tor}
}
@inproceedings {Simula.simula.734,
	title = {A Semi-Ordered Fast Iterative Method (SOFI) for Monotone Front Propagation in Simulations of Geological Folding},
	journal = {MODSIM2011, 19th International Congress on Modelling and Simulation},
	year = {2011},
	month = {December},
	pages = {631-647},
	publisher = {Modelling and Simulation Society of Australia and New Zealand},
	type = {Conference},
	abstract = {This paper present a novel algorithm for monotone front propagation of anisotropic nature. In several examples the new algorithm is shown to be fast and able to solve a general class of front propagation problems. The algorithm is inspired by Huygens{\textquoteright} principle in that the front is described using a list of nodes that are used as source points to evolve the front. Nodes affected by the source points are either directly used as source points or temporarily paused, depending on their solution value and the average solution value of all source points. This feature makes the algorithm semi-ordered. Still, nodes may be used as source points several times, making the algorithm iterative of nature. Together, these features create the Semi-Ordered Fast Iterative (SOFI) method.},
	keywords = {Conference},
	isbn = {978-0-9872143-1-7},
	author = {Gillberg, Tor},
	editor = {Chan, F. and Marinova, D. and Anderssen, Bengt}
}
@mastersthesis {Simula.simula.624,
	title = {Worst Case Hedges for Derivative Contracts},
	year = {2009},
	month = {January},
	publisher = {Lund Institute of Technology},
	type = {masters},
	abstract = {There is a wide range of stocks, commodities and banks to invest in on the market. In addition there are numerous bets on future rates and prices. Those bets are called derivatives. A reasonable price of a derivative is the expected profit from the bet. Financial mathematics aim at specifying the prices of derivatives. Almost all financial models assume the underlying (price or rate) to behave as a certain stochastic process. In this way all future values of the underlying is assigned a probability, and one may calculate the expected profit. This thesis investigates a model assuming nothing of that kind. No assumptions on the underlyings probability distribution are made. Instead one speci- fies what is not allowed to happen by having bounds on the evolution of the underlying. Such a model was introduced by Paul Wilmott and David Epstein in 1999. We search for a value spread of a portfolio on one underlying. The portfolio may consist of any simple derivatives as well as the underlying. Assuming the underlying takes the \&$\#$39;worst\&$\#$39; possible path allowed by the bounds, one gets a lower value of a contract. This value is called the worst value. Similarly the worst value for a negative share of a contract, a sold contract, is called the best value. The model is derived in a very general setting so that the underlying may refer to either a stock, rate or commodity price process. The works from Epstein and Wilmott are solely dedicated to interest rate markets, why the result section focuses on a stock market.},
	author = {Gillberg, Tor}
}
