Multilevel Schwarz preconditioners for the Bidomain system and applications to electrocardiology

Mathematical modeling and computer simulation has become in recent years an important support to experimental studies, for investigating the bioelectrical activity in cardiac tissue. The most complete mathematical model of electrocardiology is the Bidomain model, a degenerate parabolic system of nonlinear reaction-diffusion equations, coupled with a system of ordinary differential equations. In this work, Multilevel Schwarz preconditioners for the Bidomain system are introduced, analyzed and studied numerically on Linux clusters. We then apply the parallel solver implementing the Multilevel Schwarz methods to the study of myocardial ischemia, one of the major problems in electrocardiology.