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Nowadays mathematical models are used to study the propagation of electrical waves in the heart and understand cardiac pathologies,such as arrhythmias,ventricular fibrillations,etc.These electrophysiological waves are usually modelled using reaction-diffusion partial differential equations(PDE)for the propagation in the myocardial tissue coupled with a system of stiff ordinary differential equations(ODE)representing the ionic activity at the cell level.The highly nonlinear nature of the system together with the complex geometry of the heart makes it essential to use efficient numerical methods for its solution.We will briefly present the mathematical model for cardiac propagation and introduce numerical methods to solve such equations.In particular,anisotropic mesh adaptation and time-stepping methods will be covered,and their performance will be illustrated with numerical test cases.We will also explain how we obtained a very detailed geometrical model of the heart from medical images,and how propagating electrical waves can be computed on such geometrical model.