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

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Main Authors: Saglio, Caterina B. Leimer, Pagani, Stefano, Antonietti, Paola F.
Format: Preprint
Published: 2025
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author Saglio, Caterina B. Leimer
Pagani, Stefano
Antonietti, Paola F.
author_facet Saglio, Caterina B. Leimer
Pagani, Stefano
Antonietti, Paola F.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_19536
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology
Saglio, Caterina B. Leimer
Pagani, Stefano
Antonietti, Paola F.
Numerical Analysis
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.
title A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology
topic Numerical Analysis
url https://arxiv.org/abs/2512.19536