Parallel nonlinear solvers in computational cardiac electrophysiology *

Abstract

This investigation focuses on nonlinear solvers for the Bidomain model, a nonlinear system of parabolic reaction-diffusion equations describing the bioelectrical activity of the myocardium. Staggered fully implicit time discretizations of the Bidomain finite element semi-discrete problem lead to nonlinear algebraic systems to be solved at each time step. This work compares several nonlinear solvers, such as inexact-Newton, quasi-Newton and nonlinear Generalized Minimal Residual methods, for the solution of these nonlinear systems. Parallel experiments show strong scalability and robustness of the resulting solver with respect to the number of degrees of freedom of the discrete problem. These preliminary results pave the way for further studies of nonlinear solvers for cardiac electrophysiology models that can attain better parallel efficiency than the standard Newton method.