Publications

B. F. Nielsen and Kent-A. Mardal. Analysis of the Minimal Residual Method applied to ill-posed optimality systems, Submitted to journal for publication, 2012.

B. F. Nielsen and Kent-A. Mardal. The Minimal Residual Method applied to ill-posed optimality systems; eigenvalues and convergence properties, Presented at the workshop "Numerical Methods for Optimal Control and Inverse Problems", Munich, Germany, 2012.

M. Burger and B. F. Nielsen. Funding: Deutscher Akademischer Austauschdienst Programme des Projektbezogenen Personenaustauschs DAADppp Mobility Programme Germany–Norway, Circulation, 125 (18), 2012.

Kent-A. Mardal and B. F. Nielsen. Efficient preconditioning of optimality systems, Precond 11 , 2011.

A. Tveito, H. P. Langtangen, B. F. Nielsen, and X. Cai. Elements of Scientific Computing, Springer, 2010.

M. Burger, Kent-A. Mardal, and B. F. Nielsen. Stability analysis of the inverse transmembrane potential problem in electrocardiography, Inverse Problems 26(10), 2010.

B. F. Nielsen and Kent-A. Mardal. Efficient preconditioners for optimality systems arising in connection with inverse problems, SIAM Journal on Control and Optimization 48(8), 2010.

Kent-A. Mardal and B. F. Nielsen. An operator theoretical approach to preconditioning optimality systems, Talk at European Multi-Grid Conference, EMG, 2010, 2010.

B. F. Nielsen, O. M. Lysaker, and P. Grøttum. Theoretical and practical aspects of the inverse ischemia problem, Presented at Karlsruhe Institute of Technology, Germany, 2010.

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.

T. S. Ruud, B. F. Nielsen, O. M. Lysaker, and J. Sundnes. A Computationally Efficient Method for Determining the Size and Location of Myocardial Ischemia, IEEE Transactions on Biomedical Engineering 56(2):263-272, 2009.

A. A. Vázquez and B. F. Nielsen. The multigrid algorithm applied to a degenerate equation; a convergence analysis, Journal of Computational and Applied Mathematics 225(1):251-267, 2009.

J. B. Haga, H. P. Langtangen, B. F. Nielsen, and H. Osnes. On the performance of an algebraic multigrid preconditioner for the pressure equation with highly discontinuous media, In: Proceedings of MekIT'09, ed. by B. Skallerud and H. I. Andersson, pp. 191-204, NTNU, Tapir, 2009.

O. M. Lysaker, B. F. Nielsen, P. Grøttum, K. Haugaa, J. G. Fjeld, and A. Abildgaard. Mathematical Based Imaging of Regional Ischemia, In: World Congress on Medical Physics and Biomedical Engineering, ed. by Olaf Dössel and Wolfgang C. Schlegel, vol. 25(2), pp. 98-101, Springer, 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 Tveito, Tveito and Bruaset, Are Magnus and Lysne, Olav. Springer, Heidelberg, chap. 22, pp. 287-319, 2009.

M. Burger and B. F. Nielsen. Preconditioning in Inverse Problems, Minisymposium at the Applied Inverse Problems conference, Vienna, Austria, 2009.

J. B. Haga, H. P. Langtangen, B. F. Nielsen, and H. Osnes. On the Perfermance of an Algebraic Multigrid Preconditioner for the Pressure Equationwith Highly Discontinuous Media, Talk at MekIT'09: Fifth National Conference on Computational Mechanics, Trondheim, May 26-27, 2009.

O. M. Lysaker, B. F. Nielsen, P. Grøttum, K. Haugaa, J. G. Fjeld, and A. Abildgaard. Mathematical Based Imaging of Regional Ischemia, Presented at the WORLD CONGRESS 2009, Medical physics and biomedical engineering, 2009.

B. F. Nielsen. Recent contributions to the inverse problem of electrocardiography, Minisymposium at the Applied Inverse Problems conference, Vienna, Austria, 2009.

B. F. Nielsen and Kent-A. Mardal. An operator theoretical approach to preconditioning optimality systems, Presented at the Applied Inverse Problems conference, Vienna, Austria, 2009.

B. F. Nielsen, O. M. Lysaker, P. Grøttum, K. Haugaa, J. G. Fjeld, and A. Abildgaard. The inverse ischemia problem; mathematical models and validation, Presented at the Applied Inverse Problems conference, Vienna, Austria, 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.

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.

O. M. Lysaker, B. F. Nielsen, P. Grøttum, A. Abildgaard, J. Fjeld, and K. Haugaa. Computer simulations for identifying ischemic heart disease; a validation study, Presented at the BBG-MedViz seminar at the Department of Mathematics, University of Bergen , 2008.

O. M. Lysaker, B. F. Nielsen, P. Grøttum, A. Abildgaard, J. Fjeld, and K. Haugaa. Theoretical and practical aspects of the inverse problem of electrocardiography, Presented at the Fourth International Conference "Inverse Problems: Modeling and Simulation", Turkey, 2008.

Kent-A. Mardal, B. F. Nielsen, and M. S. Alnæs. Two Steps Towards Automating Efficient Solution of Inverse Problems, Invited Talk at the FEniCS 08 Workshop, March 5-7,Baton Rouge, Louisiana, 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.

B. F. Nielsen, O. 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.

A. Schroll, A. M. Bruaset, and B. F. Nielsen. Automatic Calibration of Depositional Models: An Inverse Problems Approach, In: book of abstracts, 33rd Intl. Geoogical Congress, Oslo, 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. 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, X. Cai, and O. M. Lysaker. On the possibility for computing the transmembrane potential in the heart with a one shot method; an inverse problem, Mathematical Biosciences 210(2):523--553, 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.

O. M. Lysaker and B. F. Nielsen. PDE methods for identifying ischemic heart disease, Presented at the 6th International Congress on Industrial and Applied Mathematics, 2007.

B. F. Nielsen. Inverse solutions for assesing myocardial ischemia, Talk at CBC, Seminar on Electrophysiology Modeling, Simula, 2007.

B. F. Nielsen, O. M. Lysaker, and M. Larson. Can inverse problems tell you the condition of your heart?, Zurich Intelligencer; International Congress on Industrial and Applied Mathematics (ICIAM), Springer-Verlag, 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, 2006.

O. M. Lysaker and B. F. Nielsen. Towards a level set framework for infarction modeling: An inverse problem, International Journal of Numerical Analysis and Modeling 3(4):377-394, 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.

O. M. Lysaker, C. Tarrou, A. Abildgaard, and B. F. Nielsen. On the Use of Computers to Simulate Cardiac Functions, In: The 24th International EuroPACS Conference, chap. Clinical Experiences, pp. 1-4, EuroPACS, 2006.

B. F. Nielsen, O. M. Lysaker, C. Tarrou, J. Sundnes, X. Cai, and Kent-A. Mardal. On the use of the bidomain equations for computing the transmembrane potential throughout the heart wall: An inverse problem, In: Computers in Cardiology 2006, ed. by A. Murray, pp. 797-800, Computers in Cardiology, 2006.

O. M. Lysaker, C. Tarrou, A. Abildgaard, and B. F. Nielsen. On the Use of Computers to Simulate Cardiac Functions, Presented at the 24th International EuroPACS Conference, Trondheim, 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.

B. F. Nielsen, O. M. Lysaker, C. Tarrou, J. Sundnes, X. Cai, and Kent-A. Mardal. On the use of the bidomain equations for computing the transmembrane potential throughout the heart wall: An inverse problem, Presented at the Computers in Cardiology conference in Valencia, Spain, 2006.

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.