Aslak Tveito

• Tveito, Aslak; Jæger, Karoline Horgmo; Kuchta, Miroslav; Mardal, Kent-Andre & Rognes, Marie Elisabeth (2017). A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Frontiers in Physics.  ISSN 2296-424X.  5 . doi: 10.3389/fphy.2017.00048 Full text in Research Archive.
• Tveito, Aslak; Jæger, Karoline Horgmo; Lines, Glenn Terje; Paszkowski, Lukasz; Sundnes, Joakim; Edwards, Andrew; Mäki-Marttunen, Tuomo; Halnes, Geir & Einevoll, Gaute (2017). An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons. Frontiers in Computational Neuroscience.  ISSN 1662-5188.  11 . doi: 10.3389/fncom.2017.00027 Full text in Research Archive.
• Tveito, Aslak; Lines, Glenn Terje; Edwards, Andrew & McCulloch, Andrew (2016). Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states. Mathematical Biosciences.  ISSN 0025-5564.  277, s 126- 135 . doi: 10.1016/j.mbs.2016.04.011
• Li, Pan; Lines, Glenn Terje; Maleckar, Mary & Tveito, Aslak (2013). Mathematical Models of Cardiac Pacemaking Function. Frontiers in Physics.  ISSN 2296-424X.  1(20) . doi: 10.3389/fphy.2013.00020#sthash.vUsLBEYd.dpuf
• Tveito, Aslak; Lines, Glenn Terje; Edwards, Andrew G; Maleckar, Mary; Michailova, Anushka; Hake, Johan Elon & McCulloch, Andrew (2012). Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue. Progress in Biophysics and Molecular Biology.  ISSN 0079-6107.  110(2-3), s 295- 304 . doi: 10.1016/j.pbiomolbio.2012.07.005
• Tveito, Aslak; Lines, Glenn Terje; Hake, Johan Elon & Edwards, Andrew G (2012). Instabilities of the resting state in a mathematical model of calcium handling in cardiac myocytes. Mathematical Biosciences.  ISSN 0025-5564.  236(2), s 97- 107 . doi: 10.1016/j.mbs.2012.02.005
• Tveito, Aslak; Lines, Glenn Terje & Maleckar, Mary (2012). Note on a Possible Proarrhythmic Property of Antiarrhythmic Drugs Aimed at Improving Gap-Junction Coupling. Biophysical Journal.  ISSN 0006-3495.  102(2), s 231- 237 . doi: 10.1016/j.bpj.2011.11.4015
• Tveito, Aslak; Lines, Glenn Terje; Rognes, Marie Elisabeth & Maleckar, Mary (2012). AN ANALYSIS OF THE SHOCK STRENGTH NEEDED TO ACHIEVE DEFIBRILLATION IN A SIMPLIFIED MATHEMATICAL MODEL OF CARDIAC TISSUE. International Journal of Numerical Analysis & Modeling.  ISSN 1705-5105.  9(3), s 644- 657
• Hanslien, Monica; Artebrant, Robert; Tveito, Aslak; Lines, Glenn Terje & Cai, Xing (2011). STABILITY OF TWO TIME-INTEGRATORS FOR THE ALIEV-PANFILOV SYSTEM. International Journal of Numerical Analysis & Modeling.  ISSN 1705-5105.  8(3), s 427- 442
• Tveito, Aslak; Lines, Glenn Terje; Artebrant, Robert; Skavhaug, Ola & Maleckar, Mary (2011). Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts. Mathematical Biosciences.  ISSN 0025-5564.  230(2), s 79- 86 . doi: 10.1016/j.mbs.2011.01.004
• Tveito, Aslak; Lines, Glenn Terje; Li, Pan & McCulloch, Andrew (2011). DEFINING CANDIDATE DRUG CHARACTERISTICS FOR LONG-QT (LQT3) SYNDROME. Mathematical Biosciences and Engineering.  ISSN 1547-1063.  8(3), s 861- 873 . doi: 10.3934/mbe.2011.8.861
• Tveito, Aslak; Lines, Glenn Terje; Skavhaug, Ola & Maleckar, Mary (2011). Unstable eigenmodes are possible drivers for cardiac arrhythmias. Journal of the Royal Society Interface.  ISSN 1742-5662.  8(61), s 1212- 1216 . doi: 10.1098/rsif.2011.0152
• Tveito, Aslak; Skavhaug, Ola; Lines, Glenn Terje & Artebrant, Robert (2011). Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart. Computers in Biology and Medicine.  ISSN 0010-4825.  41(8), s 611- 618 . doi: 10.1016/j.compbiomed.2011.05.011
• Artebrant, Robert; Tveito, Aslak & Lines, Glenn Terje (2010). A METHOD FOR ANALYZING THE STABILITY OF THE RESTING STATE FOR A MODEL OF PACEMAKER CELLS SURROUNDED BY STABLE CELLS. Mathematical Biosciences and Engineering.  ISSN 1547-1063.  7(3), s 505- 526 . doi: 10.3934/mbe.2010.7.505
• Nielsen, Bjørn Fredrik; Lysaker, O.M.; Grøttum, Per; Mardal, Kent-Andre; Tveito, Aslak; Tarrou, Christian; Haugaa, K.; Abildgaard, A. & Fjeld, J.G. (2010). Can ECG recordings and mathematics tell the condition of your heart?, In Aslak Tveito; Are Magnus Bruaset & Olav Lysne (ed.),  Simula Research Laboratory - by thinking constantly about it.  Springer.  ISBN 978-3-642-01155-9.  22.  s 287 - 319
• Hanslien, M; Artebrant, R; Sundnes, Joakim; Sundnes, Joakim; Tveito, Aslak & Tveito, Aslak (2009). An unconditionally stable second order method for the Luo-Rudy 1 model used in simulations of defibrillation. International Journal of Numerical Analysis & Modeling.  ISSN 1705-5105.  6(4), s 627- 641
• Lines, Glenn Terje; MacLachlan, Mary Catherine; Linge, Svein & Tveito, Aslak (2009). Synchronizing Computer Simulations with Measurement Data for a Case of Atrial Flutter. Annals of Biomedical Engineering.  ISSN 0090-6964.  37(7), s 1287- 1293 . doi: 10.1007/s10439-009-9692-3
• Lines, GT; MacLachlan, Mary C; Linge, Svein & Tveito, Aslak (2009). Synchronizing Computer Simulations with Measurement Data for a Case of Atrial Flutter. Annals of Biomedical Engineering.  ISSN 0090-6964.  37(7), s 1287- 1293 . doi: 10.1007/s10439-009-9692-3 Show summary

  Atrial flutter is a common supraventricular tachycardia that can be treated using radiofrequency catheter ablation, a procedure that is guided by electroanatomical mapping systems. In this paper, we propose an algorithm for incorporating mapping data into computer simulations of atrial electrical activity with the purpose of creating a more accurate map of electrical activation. The algorithm takes as input the extracellular potential values recorded at a number of sites throughout the atria and estimates the activation time for the entire atrial domain. We test the algorithm using synthetic mapping data and an anatomically detailed atrial geometry with an activation pattern typical of atrial flutter. The results show that the algorithm performs well with synthetic mapping data with information from relatively few mapping sites and in the presence of modeling and measurement error.

• Linge, Geir; Sundnes, Joakim; Sundnes, Joakim; Hanslien, Monica; Lines, Glenn Terje; Tveito, Aslak & Tveito, Aslak (2009). Numerical solution of the bidomain equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.  ISSN 1364-503X.  367(1895), s 1931- 1951
• Linge, S; Sundnes, Joakim; Hanslien, M; Lines, Glenn Terje & Tveito, Aslak (2009). Numerical solution of the bidomain equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.  ISSN 1364-503X.  367(1895), s 1931- 1950 . doi: 10.1098/rsta.2008.0306
• Linge, Svein; Sundnes, J; Hanslien, M; Lines, GT & Tveito, Aslak (2009). Numerical solution of the bidomain equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.  ISSN 1364-503X.  367(1895), s 1931- 1950 . doi: 10.1098/rsta.2008.0306 Show summary

  Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.

• Nielsen, Bjørn Fredrik; Cai, Xing; Sundnes, Joakim & Tveito, Aslak (2009). Towards a computational method for imaging the extracellular potassium concentration during regional ischemia. Mathematical Biosciences.  ISSN 0025-5564.  220(2), s 118- 130 . doi: 10.1016/j.mbs.2009.05.004
• Nielsen, Bjørn Fredrik; Tveito, Aslak & Hackbusch, W (2009). Preconditioning by inverting the Laplacian: an analysis of the eigenvalues. IMA Journal of Numerical Analysis.  ISSN 0272-4979.  29(1), s 24- 42 . doi: 10.1093/imanum/drm018
• Sundnes, Joakim; Artebrant, R; Skavhaug, Ola & Tveito, Aslak (2009). A Second-Order Algorithm for Solving Dynamic Cell Membrane Equations. IEEE Transactions on Biomedical Engineering.  ISSN 0018-9294.  56(10), s 2546- 2548 . doi: 10.1109/TBME.2009.2014739
• Linge, Svein; Lines, Glenn Terje; Sundnes, Joakim & Tveito, Aslak (2008). On the frequency of automaticity during ischemia in simulations based on stochastic perturbations of the Luo-Rudy 1 model. Computers in Biology and Medicine.  ISSN 0010-4825.  38(11-12), s 1218- 1227 . doi: 10.1016/j.compbiomed.2008.10.002
• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2008). Penalty methods for the numerical solution of American multi-asset option problems. Journal of Computational and Applied Mathematics.  ISSN 0377-0427.  222(1), s 3- 16 . doi: 10.1016/j.cam.2007.10.041
• Cai, Xing; Nielsen, Bjørn Fredrik & Tveito, Aslak (2007). A note on the efficiency of the conjugate gradient method for a class of time-dependent problems. Numerical Linear Algebra with Applications.  ISSN 1070-5325.  14(5), s 459- 467 . doi: 10.1002/nla.527
• Hanslien, Monica; Sundnes, Joakim & Tveito, Aslak (2007). An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation. Mathematical Biosciences.  ISSN 0025-5564.  s 375- 392
• Nielsen, Bjørn Fredrik; Ruud, Tomas Syrstad; Lines, Glenn Terje & Tveito, Aslak (2007). Optimal monodomain approximations of the bidomain equations. Applied Mathematics and Computation.  ISSN 0096-3003.  184(2), s 276- 290
• MacLachlan, MC; Nielsen, Bjørn Fredrik; Lysaker, M & Tveito, Aslak (2006). Computing the size and location of myocardial ischemia using measurements of ST-segment shift. IEEE Transactions on Biomedical Engineering.  ISSN 0018-9294.  53, s 1024- 1031
• Sundnes, Joakim; Nielsen, Bjørn Fredrik; Mardal, Kent-Andre; Cai, Xing; Lines, Glenn Terje & Tveito, Aslak (2006). On the computational complexity of the bidomain and the monodomain models of electrophysiology. Annals of Biomedical Engineering.  ISSN 0090-6964.  34(7), s 1088- 1097
• Nielsen, Bjørn Fredrik; Lysaker, Ola Marius; Tarrou, C; Abildgaard, A; MacLachlan, Mary Catherine & Tveito, Aslak (2005). On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease, In Alan Murray (ed.),  Computers in Cardiology.  IEEE.  ISBN 0-7803-9337-6.  Kapittel.  s 1005 - 1008
• Hanslien, Monica; Karlsen, Kenneth Hvistendahl & Tveito, Aslak (2005). A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model. BIT Numerical Mathematics.  ISSN 0006-3835.  45(4), s 725- 741
• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2005). An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso. Mathematical Biosciences.  ISSN 0025-5564.  194(2), s 233- 248
• Cai, Xing; Lines, Glenn Terje & Tveito, Aslak (2004). Parallel Solution of the Bidomain Equations with High Resolutions, In G. R. Joubert; W. E. Nagel & F. J Peters (ed.),  Parallel Computing: Software Technology, Algorithms, Architectures \& Applications},.  Elsevier.  Kapittel.
• Cai, Xing; Acklam, E; Langtangen, Hans Petter & Tveito, Aslak (2003). Parallel Computing, In  Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming.  Springer.  ISBN 3-540-01438-1.  Kapittel.  s 1 - 55
• Cai, Xing; Bruaset, Are Magnus; Langtangen, Hans Petter; Lines, Glenn Terje; Samuelsson, K; Chen, W; Tveito, Aslak & Zumbusch, G (2003). Performance Modeling of PDE Solvers, In  Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming.  Springer.  ISBN 3-540-01438-1.  Kapittel.  s 361 - 399
• Ingebrigtsen, Linda; Nilssen, Trygve Kastberg; Langtangen, Hans Petter & Tveito, Aslak (2003). On the accuracy of operator splitting for a fluid-structure interaction problem. International journal of nonlinear sciences and numerical simulation.  ISSN 1565-1339.  4, s 209- 218
• Skavhaug, Ola; Nielsen, Bjørn Fredrik & Tveito, Aslak (2003). Mathematical Models of Financial Derivatives, In  Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming.  Springer.  ISBN 3-540-01438-1.  Kapittel.  s 451 - 482
• Skavhaug, Ola; Nielsen, Bjørn Fredrik & Tveito, Aslak (2003). Numerical Methods for Financial Derivatives, In  Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming.  Springer.  ISBN 3-540-01438-1.  Kapittel.  s 483 - 506
• Sundnes, Joakim; Lines, Glenn Terje; Grøttum, Per & Tveito, Aslak (2003). Electrical activity in the human heart, In  Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming.  Springer.  ISBN 3-540-01438-1.  Kap. 10.  s 401 - 449
• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2002). Penalty and front-fixing methods for the numerical solution of American option problems. Journal of Computational Finance.  ISSN 1460-1559.  5(4), s 69- 97
• Sundnes, Joakim; Lines, Glenn Terje; Mardal, Kent-Andre & Tveito, Aslak (2002). Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart. Computer Methods in Biomechanics and Biomedical Engineering.  ISSN 1025-5842.  5(6)
• Lines, Glenn Terje; Buist, Martin L.; Grøttum, Per; Pullan, Andrew J.; Sundnes, Joakim & Tveito, Aslak (2002). Mathematical Models and Numerical Methods for the Forward Problem in Cardiac Electrophsysiology. Computing and Visualization in Science.  ISSN 1432-9360.
• Sundnes, Joakim; Lines, Glenn Terje; Mardal, Kent-Andre & Tveito, Aslak (2002). Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in cardiac cells. Computer Methods in Biomechanics and Biomedical Engineering.  ISSN 1025-5842.
• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2001). Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells. Mathematical Biosciences.  ISSN 0025-5564.  172, s 55- 72 Show summary

  The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ordinary differential equations, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

• Langtangen, Hans Petter & Tveito, Aslak (2000). How should we prepare the Students of Science and Technology for Life in the Computer Age?, In  Mathematics Unlimited.   s 809 - 827
• Nielsen, Bjørn Fredrik; Cai, Xing & Tveito, Aslak (1999). An analysis of a preconditioner for the discretized pressure equation arising in reservoir simulation. IMA Journal of Numerical Analysis.  ISSN 0272-4979.  19(2), s 291- 316
• Shen, Wen; Tveito, Aslak & Winther, Ragnar (1999). On the zero relaxation limit for a system modeling the motions of a viscoelastic solid. SIAM Journal on Mathematical Analysis.  ISSN 0036-1410.  30(5), s 1115- 1135
• Shen, Wen; Tveito, Aslak & Winther, Ragnar (1999). On the zero relaxation limit for a system modeling the motions of a viscoelastic solid. SIAM Journal on Mathematical Analysis.  ISSN 0036-1410.  30, s 1115- 1135
• Nielsen, Bjørn Fredrik & Tveito, Aslak (1998). An upscaling method for one-phase flow in heterogeneous reservoirs; a weighted output least squares (WOLS) approach. Computational Geosciences.  ISSN 1420-0597.  2, s 93- 123

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• Bruaset, Are Magnus & Tveito, Aslak (2013). Conversations About Challenges in Computing. Springer.  ISBN 978-3-319-00209-5.  101 s.
• Tveito, Aslak; Bruaset, Are Magnus & Lysne, Olav (ed.) (2010). Simula Research Laboratory - by thinking constantly about it. Springer.  ISBN 978-3-642-01155-9.  656 s.
• Tveito, Aslak; Langtangen, Hans Petter; Nielsen, Bjørn Fredrik & Cai, Xing (2010). Elements of scientific computing. Springer.  ISBN 9783642112980.  459 s.
• Sundnes, Joakim; Lines, Glenn Terje; Cai, Xing; Nielsen, Bjørn Fredrik; Mardal, Kent-Andre & Tveito, Aslak (2006). Computing the electrical activity in the heart. Springer.  ISBN 978-3-540-33432-3.  311 s.
• Bruaset, Are Magnus & Tveito, Aslak (ed.) (2005). Numerical Solution of Partial Differential Equations on Parallel Computers. Springer.  ISBN 3-540-29076-1.
• Langtangen, Hans Petter & Tveito, Aslak (2003). Advanced topics in computational partial differential equations. Numerical methods and Diffpack programming. Springer.  ISBN 3-540-01438-1.  658 s.
• Tveito, Aslak & Winther, Ragnar (2002). Einfuhrung in partielle differentalgleichungen, Ein numerischer zugang. Springer.  ISBN 3-540-42404-0.  392 s.
• Winther, Ragnar & Tveito, Aslak (2002). Einfuhrung in die Theorie der partiellen Differentialgleichungen;Ein numericher Zugang. Springer.

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• Lysaker, Ola Marius; Nielsen, Bjørn Fredrik; Tveito, Aslak; Lines, Glenn Terje; Sundnes, Joakim & Tarrou, C (2005). Kan man simulere et hjerteslag?.
• Mardal, Kent-Andre; Nielsen, Bjørn Fredrik; Cai, Xing & Tveito, Aslak (2005). An order optimal solver for the discretized Bidomain equations.
• Mardal, Kent-Andre; Nielsen, Bjørn Fredrik; Cai, Xing & Tveito, Aslak (2005). Optimal Preconditioners for Discrete Versions of the Bidomain Model.
• Mardal, Kent-Andre; Nielsen, Bjørn Fredrik & Tveito, Aslak (2005). Preconditioners for Elliptic Problems with Variable Coefficients.
• Nielsen, Bjørn Fredrik; Lysaker, Ola Marius; MacLachlan, Mary Catherine & Tveito, Aslak (2005). On the use of level set techniques for identifying heart infarctions.
• Nielsen, Bjørn Fredrik; Lysaker, Ola Marius; Tarrou, C; MacLachlan, Mary Catherine; Abildgaard, A & Tveito, Aslak (2005). On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease.
• Lie, K. A. & Tveito, Aslak (2004). Development of a staggered central difference scheme that does not use a spatial reconstruction.
• MacLachlan, Mary Catherine; Nielsen, Bjørn Fredrik & Tveito, Aslak (2004). On the use of ST shifts to identify ischemic heart disease: Towards a computational approach.
• Mardal, Kent-Andre & Tveito, Aslak (2004). Block Preconditioners for PDEs Arising from the Bi-domain Model of the Electrical Activity in the Heart.
• Nilssen, Trygve Kastberg; Ingebrigtsen, Linda; Hanslien, Monica; Lines, Glenn Terje & Tveito, Aslak (2004). Resolution requirements for a 1D monodomain model for simulating.
• Tveito, Aslak; Almås, Aslaug Grov; Goebel, Vera; Heggernes, Pinar; Ingebrigtsen, Kjell Arne; Johansen, Dag; Kløve, Torleiv; Opdahl, Andreas; Pettersen, Kristin Ytterstad & Aagesen, Finn Arve (2004). Nyttig nysgjerrighet : Fagplan for informasjons- og kommunikasjonsteknologi (IKT).
• Bounaim, Aicha; Holm, Sverre; Chen, Wen; Ødegård, Åsmund; Tveito, Aslak & Thomenius, Kai (2003). FETD simulation of wave propagation modeling the Cari breast sonography.
• Chen, W; Bounaim, A; Cai, Xing; Holm, S; Tveito, Aslak & Ødegård, Åsmund (2003). Mathematical and numerical modeling of medical ultrasound wave propagation.
• Chen, Wen; Bounaim, Aicha; Holm, Sverre; Ødegård, Åsmund; Cai, Xing & Tveito, Aslak (2003). Mathematical and numerical modeling of medical ultrasound wave propagation: an abstract of our project progress.
• Lines, Glenn Terje; Nielsen, Bjørn Fredrik; Tveito, Aslak; Sundnes, Joakim; Grøttum, Per; Cai, Xing & Mardal, Kent-Andre (2003). Computing the electrical activity in the human heart.
• Tveito, Aslak; Lines, Glenn Terje; Nielsen, Bjørn Fredrik; Sundnes, Joakim; Grøttum, Per; Cai, Xing & Mardal, Kent-Andre (2003). Computing the heart.
• Tveito, Aslak; Lines, Glenn Terje; Sundnes, Joakim; Nielsen, Bjørn Fredrik; Grøttum, Per; Cai, Xing & Mardal, Kent-Andre (2003). Computing the electrical activity in the human heart.
• Lines, Glenn Terje; Sundnes, Joakim; Tveito, Aslak; Cai, Xing; Mardal, Kent-Andre & Bruaset, Are Magnus (2002). Diffpack simulation of the electrical activity in the heart.
• Nielsen, Bjørn Fredrik & Tveito, Aslak (2002). Preconditioning by inverting the Laplacian; an analysis of the eigenvalues. Research report at the Simula Research Laboratory. 0.
• Bounaim, Aicha; Holm, Sverre; Chen, Wen; Ødegård, Åsmund & Tveito, Aslak (2002). Simulation of the CARI technique for breast tumor detecting using ultrasound wave propagation.
• Chen, Wen; Holm, Sverre; Bounaim, Aicha; Ødegård, Åsmund & Tveito, Aslak (2002). Frequency decomposition time-domain model of broadband frequency-dependent absorption.
• Lines, Glenn Terje; Sundnes, Joakim & Tveito, Aslak (2002). A Domain Embedding Strategy for Solving the Bidomain Equations on Complicated Geometries. Show summary

  Simulations with the bidomain equations are often solved on simple geometries due to the complexity introduced by using more realistic boundaries. In this paper we propose a method where all the calculations are carried out on squares and boxes even when the tissue boundaries are complex. This is achieved by domain inbedding and proper extension of the conductivity tensors in the model.

• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2002). A second order scheme for solving the bidomain and forward problem.
• Lines, Glenn Terje; Cai, Xing & Tveito, Aslak (2001). A parallel solution of the bidomain equations modeling the electrical activity of the heart.
• Nielsen, Bjørn Fredrik; Tveito, Aslak & Skavhaug, Ola (2001). Numerical Solution of American Option Problems Using Penalty Methods.
• Sundnes, Joakim; Lines, Glenn Terje; Mardal, Kent-Andre & Tveito, Aslak (2001). On numerical techniques for the bidomain model.
• Ingebrigtsen, Linda; Tveito, Aslak; Langtangen, Hans Petter & Bounaim, Aicha (2001). Moving Mesh Techniques for Fluid Flow Simulations. Show summary

  Our aim is to develop a numerical simulator enabling an analysis of the relation between the stiffness of the wall and pressure gradients in the left heart during diastole. In order to develop such a simulator, we need to solve the incompressible Navier-Stokes equations on a moving domain. Hence, the purpose of this study is to compare three moving grid methods for the Navier-Stokes equations. The methods are compared on a test problem where we have an analytical solution, thus allowing a comparison of the CPU-effort vs. the error for the three methods.

• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2001). Efficient solution of ordinary differential equations modeling electrical activity in cardiac cell.
• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2001). ODE-solvers for a stiff system arising in the modeling of the electrical activity in the heart.
• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2000). A penalty scheme for solving American option problems.
• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2000). Penalty methods for the numerical solution of American multi-asset option problems. Preprint series (Universitetet i Oslo. Matematisk institutt). 289.
• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2000). Penalty methods for the numerical solution of American option problems.
• Lines, Glenn Terje; Cai, Xing & Tveito, Aslak (2000). A parallel solution of the bidomain equations modeling the electrical activity of the heart. Show summary

  A combined model for the electrical activity of the heart and the body is presented. An approach for solving the resulting 3D numerical problem in parallel is discussed. The algorithm is implemented on a Linux PC cluster using Diffpack and an MPI library. An acceptable speed-up is achieved. Several features typical for the propagation of electrical signal in the heart is found in the computed solution.

• Nielsen, Bjørn Fredrik; Skavhaug, Ola & Tveito, Aslak (2000). Penalty and front-fixing methods for the numerical solution of American option problems.
• Schroll, H. J. & Tveito, Aslak (2000). Local existence and Stability for a Hyperbolic-Elliptic System Modeling Two-Phase Reservoir Flow.
• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2000). An investigation of different solvers for stiff ODE systems.
• Sundnes, Joakim; Lines, Glenn Terje & Tveito, Aslak (2000). Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.
• Ødegård, Åsmund; Fox, Paul D.; Holm, Sverre & Tveito, Aslak (2000). Finite Element Modelling of Pulsed Bessel Beams and X--Waves using Diffpack.
• Ødegård, Åsmund; Fox, Paul D.; Holm, Sverre & Tveito, Aslak (2000). Finite element simulations of acoustic fields with Diffpack.
• Cai, Xing; Bruaset, Are Magnus; Langtangen, Hans Petter; Lines, Glenn Terje; Samuelson, K; Chen, W; Tveito, Aslak & Zumbusch, G (1998). Performance Modeling of PDE Solvers.
• Bruaset, Are Magnus; Cai, Xing; Langtangen, Hans Petter; Lines, Glenn Terje; Samuelsson, Klas; Shen, Wen; Tveito, Aslak & Zumbush, G. (1998). CPU-measurements of some numerical PDE simulations.

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