A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology

TL;DR

This paper introduces a massively parallel non-overlapping Schwarz preconditioner for high-order PolyDG discretizations of brain electrophysiology models, significantly improving solver efficiency and scalability for large-scale simulations.

Contribution

It develops a novel additive Schwarz preconditioner tailored for PolyDG methods applied to brain electrophysiology models, enhancing parallel solver performance.

Findings

Robustness across discretization parameters

Significant reduction in iteration counts

Effective for large-scale parallel simulations

Abstract

We investigate non-overlapping Schwarz preconditioners for the algebraic systems stemming from high-order discretizations of the coupled monodomain and Barreto-Cressman models, with applications to brain electrophysiology. The spatial discretization is based on a high-order Polytopal Discontinuous Galerkin (PolyDG) method, coupled with the Crank-Nicolson time discretization scheme with explicit extrapolation of the ion term. To improve solver efficiency, we consider additive Schwarz preconditioners within the PolyDG framework, which combines (massively parallel) local subdomain solvers with a coarse-grid correction. Numerical experiments demonstrate robustness with respect to the discretization parameters, as well as a significant reduction in iteration counts compared to the unpreconditioned solver. These features make the proposed approach well-suited for parallel large-scale simulations in brain electrophysiology.