Publications

A. Tveito, G. T. Lines, R. Artebrant, O. Skavhaug, and M. Maleckar. Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts, Submitted to journal for publication, 2010.

A. Tveito, and R. Winther. Introduction to Partial Differential Equations; A Computational Approach, Springer-Verlag (second edition)(ISBN: 978-3-540-88704-1), 2009.

A. Tveito, H. P. Langtangen, B. F. Nielsen, and X. Cai. Elements of Scientific Computing, Springer (submitted), 2009.

A. Tveito, A. M. Bruaset, and O. Lysne. Simula Research Laboratory — by thinking constantly about it, Springer, Heidelberg(ISBN: ISBN 978-3-642-01155-9), 2009.

R. Artebrant, A. Tveito, and G. T. Lines. A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells, Accepted for publication in Mathematical Biosciences and Engineering , 2009.

M. Hanslien, R. Artebrant, J. Sundnes, and A. Tveito. An unconditionally stable second order method for the Luo-Rudy 1 model used in simulations of defibrillation, International journal of numerical analysis and modeling 6(4):627-641, 2009.

M. Hanslien, R. Artebrant, A. Tveito, G. T. Lines, and X. Cai. Stability of two time-integrators for the Aliev-Panfilov system, Submitted to journal for publication, 2009.

G. T. Lines, S. Linge, M. MacLachlan, and A. Tveito. Synchronizing Computer Simulations with Measurement Data for a Case of Atrial Flutter, Annals of Biomedical Engineering 37(7):1287-1293, 2009.

S. Linge, J. Sundnes, M. Hanslien, G. T. Lines, and A. Tveito. Numerical solution of the bidomain equations, Philosophical Transactions of the Royal Society A 367(1895):1931-1951, 2009.

B. F. Nielsen, X. Cai, J. Sundnes, and A. Tveito. Towards a computational method for imaging the extracellular potassium concentration during regional ischemia, Mathematical Biosciences 220(2):118-130, 2009.

B. F. Nielsen, A. Tveito, and W. Hackbusch. Preconditioning by inverting the Laplacian; an analysis of the eigenvalues, IMA Journal of Numerical Analysis 29(1):24-42, 2009.

J. Sundnes, R. Artebrant, O. Skavhaug, and A. Tveito. A second order algorithm for solving dynamic cell membrane equations, IEEE Transactions on Biomedical Engineering 56(10):2546-2548, 2009.

A. Tveito, and G. T. Lines. A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells, Mathematical Biosciences 217(2):167-173, 2009.

A. Tveito, G. T. Lines, P. Li, and A. McCulloch. Computing Advantageous Properties of a Drug Targeting the Long-QT (LQT3) Syndrome, Submitted to journal for publication, 2009.

A. Tveito, O. Skavhaug, G. T. Lines, and R. Artebrant. A software system for analyzing the stability of steady-state solutions of mathematical models of the electrical activity in the heart, Submitted to journal for publication, 2009.

B. F. Nielsen, O. M. Lysaker, P. Grøttum, Kent-A. Mardal, A. Tveito, C. Tarrou, K. Haugaa, A. Abildgaard, and J. G. Fjeld. Can ECG recordings and mathematics tell the condition of your heart?, In: Simula Research Laboratory - by thinking constantly about it, ed. by Aslak Tveito, Are Magnus Bruaset, Olav Lysne. Springer, Heidelberg, chap. 22, pp. 287-319. (ISBN: 978-3-642-01156-6), 2009.

G. T. Lines, A. Tveito, and P. Li. Antiarrhythmic Drug Identifaction, 2009.

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, K. Haugaa, A. Abildgaard, J. G. Fjeld, and M. Burger. Modelling, mathematical properties and validation of the inverse ischemia problem, Presented at the Bidomain Workshop, Graz, Austria, 2009.

S. O. Linge, G. T. Lines, J. Sundnes, and A. Tveito. On the frequency of automaticity during ischemia in simulations based on stochastic perturbations of the Luo-Rudy 1 model, Computers in biology and medicine 38( ):1218-1227, 2008.

B. F. Nielsen, O. Skavhaug, and A. Tveito. Penalty methods for the numerical solution of American multi-asset option problems, Journal of Computational and Applied Mathematics 222(1):3-16, 2008.

A. Tveito, and G. T. Lines. A condition for setting off ectopic waves in computational models of excitable cells, Mathematical Biosciences 213(2):141-150, 2008.

B. F. Nielsen, M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld, and K. Hermann Haugaa. The inverse problem of identifying ischemic heart disease, Presented at the annual meeting of European Cardiac Simulation Group, Bologna, Italy, 2008.

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld, and K. H. Haugaa. On the use of computer simulations for identifying ischemic heart disease; theoretical and practical aspects, Presented at the workshop "Mathematics in Medicine/Biology", Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, 2008.

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld, and K. H. Haugaa. Theoretical and practical aspects of the inverse problem of electrocardiography, Presented at Institut für Mathematik und Wissenschaftliches Rechnen, Karl Franzes Universität in Graz, Austria. Also presented at Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Germany, 2008.

X. Cai, B. F. Nielsen, and A. Tveito. A note on the efficiency of the Conjugate Gradient method for a class of time-dependent problems, Numerical Linear Algebra with Applications 14(5):459--467, 2007.

M. Hanslien, J. Sundnes, and A. Tveito. An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation, Mathematical Biosciences 208(2):375--392, 2007.

M. C. MacLachlan, J. Sundnes, O. Skavhaug, O. M. Lysaker, B. F. Nielsen, and A. Tveito. A linear system of partial differential equations modeling the resting potential of a heart with regional ischemia, Mathematical Biosciences 210(1):238--252, 2007.

Kent-A. Mardal, B. F. Nielsen, X. Cai, and A. Tveito. An order optimal solver for the discretized Bidomain equations, Numerical Linear Algebra with Applications 14(2):83--98, 2007.

B. F. Nielsen, O. M. Lysaker, and A. Tveito. On the use of the resting potential and level set methods for identifying ischemic heart disease; an inverse problem, Journal of Computational Physics 220(2):772--790, 2007.

B. F. Nielsen, T. S. Ruud, G. T. Lines, and A. Tveito. Optimal Monodomain approximations of the Bidomain equations, Applied Mathematics and Computation 184(2):276--290, 2007.

A. Schroll, G. T. Lines, and A. Tveito. On the Accuracy of Operator Splitting as Applied to Discretized Reaction Diffusion Systems, International Journal of Computer Mathematics 84(6):871 - 885, 2007.

J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, Kent-A. Mardal, and A. Tveito. Computing the electrical activity in the heart, Springer-Verlag(ISBN: 3-540-33432-7 ), 2006.

A. M. Bruaset, and A. Tveito. Numerical Solution of Partial Differential Equations on Parallel Computers, Springer(ISBN: 3-540-29076-1), 2006.

M. Hanslien, K. H. Karlsen, and A. Tveito. On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity, Int J of Num Anal and Mod 3(4):395-412, 2006.

M. C. MacLachlan, B. F. Nielsen, O. M. Lysaker, and A. Tveito. Computing the size and location of myocardial ischemia using measurements of ST-segment shift, IEEE Transactions on Biomedical Engineering 53(6):1024--1031, 2006.

J. Sundnes, B. F. Nielsen, Kent-A. Mardal, X. Cai, G. T. Lines, and A. Tveito. On the computational complexity of the bidomain and the monodomain models of electrophysiology, Annals of biomedical engineering 34(7):1088-1097, 2006.

C. Tarrou, O. M. Lysaker, X. Cai, Kent-A. Mardal, C. Tarrou, T. S. Ruud, M. MacLachlan, and A. Tveito. Identifying Ischemic Heart Disease in Terms of ECG Recordings and an Inverse Problem for the Bidomain Equations; Modeling and Experiments, In: The Third International Conference "Inverse Problems: Modeling and Simulation", ed. by K. Kunisch, S. I. Kabanikhin, A. Hasanov, H. T. Banks, pp. 138--140, Literat{\"u}r Yayincilik Ltd. (ISBN: 975-04-0381-9), 2006.

M. Hanslien, J. Sundnes, and A. Tveito. Simulations of reentrant arrhythmias in the heart, and defibrillation as a treatment, Presented at NADA, KTH, Sweeden, 2006.

M. Hanslien, J. Sundnes, G. T. Lines, and A. Tveito. Simulating electrical activity in the heart, Presented at St Jude Medical, Stockholm, Sweeden, 2006.

B. F. Nielsen, O. M. Lysaker, X. Cai, Kent-A. Mardal, C. Tarrou, M. MacLachlan, J. Sundnes, G. T. Lines, and A. Tveito. Computational issues in heart modeling, Presented at the Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, 2006.

M. Hanslien, K. H. Karlsen, and A. Tveito. A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model, BIT 45(4):725 - 741, 2005.

J. Sundnes, G. T. Lines, and A. Tveito. An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso, Mathematical biosciences 194(2):233--248, 2005.

B. F. Nielsen, O. M. Lysaker, C. Tarrou, A. Abildgaard, M. MacLachlan, and A. Tveito. On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease, In: Computers in Cardiology 2005, Lyon, France, September 25-28, ed. by A. Murray, pp. 1005--1008, IEEE, 2005.

O. M. Lysaker, B. F. Nielsen, A. Tveito, G. T. Lines, J. Sundnes, and C. Tarrou. Kan man simulere et hjerteslag?, LAMIS - SOMMERKURS "Matematikk – med røtter og vinger ", Asker, 2005.

Kent-A. Mardal, B. F. Nielsen, and A. Tveito. Preconditioners for Elliptic Problems with Variable Coefficients, Presented at the SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, France, 2005.

B. F. Nielsen, O. M. Lysaker, M. MacLachlan, and A. Tveito. On the use of level set techniques for identifying heart infarctions, Presented at the Level Set Methods for Direct and Inverse Problems workshop in Linz, Austria, 2005.

B. F. Nielsen, O. M. Lysaker, C. Tarrou, M. MacLachlan, A. Abildgaard, and A. Tveito. On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease, Presented at the Computers in Cardiology conference in Lyon, France, 2005.

B. F. Nielsen, O. M. Lysaker, C. Tarrou, M. MacLachlan, A. Abildgaard, and A. Tveito. Kan vi identifisere hjerteinfarkt ved hjelp av datamaskiner?, Presented at the BeMatA seminar (Norwegian Research Council), Hurdal, 2005.

J. Sundnes, M. Hanslien, and A. Tveito. An unconditionally stable numerical method for the Luo-Rudy I model used in defibrillation, Presented at Tulane University, New Orleans, 2005.

X. Cai, G. Lines, and A. Tveito. Parallel Solution of the Bidomain Equations with High Resolutions, In: Parallel Computing: Software Technology, Algorithms, Architectures & Applications, ed. by G. R. Joubert and W. E. Nagel and F. J. Peters and W. V. Walter. Elsevier Science, pp. 837--844, 2004.