Dual-primal methods for the cardiac bidomain model

The cardiac Bidomain model consists in a reaction-diffusion system of partial differential equations which is often discretized by low-order finite elements in space and implicit-explicit methods in time; the resulting linear systems are very ill-conditioned and they must be solved at each time step of a cardiac beat simulation. In this paper we will construct and analyze Balancing Domain Decomposition by Constraints and Finite Element Tearing and Interconnecting Dual-Primal methods for the Bidomain operator. Proven theoretical estimates show that the proposed methods are scalable, quasi-optimal and robust with respect to possible coefficient discontinuities of the Bidomain operator and the time step. The results of extensive parallel numerical tests in three dimensions confirm the convergence rates predicted by the theory; large numerical simulations up to 400 millions of degrees of freedom on 27K cores of BlueGene/Q are also provided.