An agglomeration-based multigrid solver for the discontinuous Galerkin discretization of cardiac electrophysiology

TL;DR

This paper introduces a new agglomeration-based multilevel preconditioner to improve the efficiency of solvers for the discontinuous Galerkin discretization of cardiac electrophysiology models, demonstrating strong scalability and effectiveness.

Contribution

It develops a novel multilevel preconditioner using agglomeration on polytopic grids, enhancing solver convergence for cardiac electrophysiology simulations.

Findings

Strong solver effectiveness demonstrated in 2D and 3D experiments.

Favorable scalability with polynomial degree and number of multigrid levels.

Applicable to realistic unstructured geometries in cardiac models.

Abstract

This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in cardiac electrophysiology. The proposed approach exploits general polytopic grids at coarser levels, obtained through the agglomeration of elements from an initial, potentially fine, mesh. By leveraging a robust and efficient agglomeration strategy, we construct a nested hierarchy of grids suitable for multilevel solver frameworks. The effectiveness and performance of the methodology are assessed through a series of numerical experiments on two- and three-dimensional domains, involving different ionic models and realistic unstructured geometries. The results demonstrate strong solver effectiveness and favorable scalability with respect to both the polynomial degree of the discretization and the number of levels selected in the multigrid preconditioner.