MP-RAS: A Multi-Parallel Restricted Additive Schwarz Preconditioner for Cardiac Electrophysiology Simulation

In this paper, we present a multi-parallel restricted additive Schwarz (MP-RAS) preconditioner construction method for cardiac electrophysiology simulation. This method is designed to address the need for solving large-scale linear systems in realistic cardiac electrophysiology simulations and can provide a more efficient computational tool for patient-specific electrical propagation modeling, arrhythmia studies, and the evaluation of ablation strategies. The proposed preconditioner is suitable for the finite element simulation of the anisotropic cardiac monodomain model. In particular, we construct the subdomains based on Morton code sorting, build submatrices by indices and decompose the formula for parallel computing. Given that the computing of each subdomain is relatively independent, the iteration can be extended to N-parallel. Numerical experiments indicate that for matrices of the same size and under the same number of partitions, Morton code sorting is at least 105 times faster than METIS, while the memory usages are reduced by 12∼32%. The iteration number is reduced by approximately two times compared with the Jacobi and block Jacobi preconditioned conjugate gradient (PCG) method. Comparative experiments with other solvers further demonstrate that the MP-RAS solver is highly efficient for solving this parabolic partial differential equation and have strong parallel scalability.