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

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
81/2025
Title:
A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology
Date:
Monday 22nd December 2025
Author(s):
Leimer Saglio, C. B.; Pagani, S.; Antonietti, P. F.
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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.