Numerical simulation of electrocardiograms M. Boulakia, M.A. Fern´ andez, J-F. Gerbeau, and N. Zemzemi Abstract This chapter presents a concise overview of various mathematical and nu- merical problems raised by the simulation of electrocardiograms (ECGs). A model for the propagation of the electrical activation in the heart and in the torso is pro- posed. Some of its mathematical properties are analyzed. This model is not aimed at reproducing the complex phenomena taking place at the microscopic level. It has been devised to produce realistic healthy ECGs, and some pathological ones, with a reasonable level of complexity. It relies on various assumptions that are carefully discussed through their impact on the ECGs. The coupling between the heart and the torso is a critical numerical issue which is addressed. In particular efficient cou- pling strategies based on explicit algorithms are presented and analyzed. The chapter ends with some preliminary results of a reduced order model based on the Proper Orthogonal Decomposition (POD) method. Muriel Boulakia Universit´ e Pierre et Marie Curie-Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions 75005 Paris, France e-mail: boulakia@ann.jussieu.fr Miguel A. Fern´ andez INRIA Paris-Rocquencourt, 78153 Le Chesnay Cedex, France e-mail: miguel.fernandez@inria.fr Jean-Fr´ ed´ eric Gerbeau INRIA Paris-Rocquencourt, 78153 Le Chesnay Cedex, France e-mail: jean-frederic.gerbeau@inria.fr Nejib Zemzemi INRIA Paris-Rocquencourt and Laboratoire de math´ ematiques d’Orsay, Universit´ e Paris 11. Current affiliation: University of Oxford, Computing laboratory, Oxford OX1 3QD, UK. e-mail: nejib.zemzemi@comlab.ox.ac.uk 1