Parallel Coupled and Uncoupled Multilevel Solvers for the Bidomain Model of Electrocardiology

Abstract

We study two parallel coupled and uncoupled multilevel solvers for the cardiac Bidomain model, describing the bioelectric activity of the cardiac tissue and consisting of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations, describing the ionic currents through the cellular membrane. The uncoupled solver is based on splitting the parabolic PDE from the elliptic PDE at each time step. The resulting discrete linear systems are solved by Multilevel Additive Schwarz methods. Three-dimensional parallel numerical tests on a BlueGene cluster show that the uncoupled multilevel technique is as scalable as the coupled one, but it is more efficient because it has a faster convergence rate. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about 1.5 times faster than the coupled approach.