Speaker
Description
Accurate, scalable numerical simulations are crucial for studying large-scale brain electrophysiology. We propose a massively parallel, two-level non-overlapping Schwarz preconditioner for the efficient solution of the algebraic systems arising from high-order polytopal Discontinuous Galerkin (PolyDG) discretizations of brain electrophysiology models. The study focuses on the monodomain equation coupled with the Barreto-Cressman ionic model, which describes the evolution of the transmembrane potential and ionic concentration dynamics in neural tissue. Spatial discretization is performed using high-order PolyDG methods on polytopal meshes, resulting in a large linear system to be solved at each time step. These systems are typically severely ill-conditioned, especially when polygonal meshes and high polynomial degrees are employed. To address this issue, we design an additive Schwarz preconditioner based on a non-overlapping domain decomposition with an agglomerated coarse space. The approach combines independent local subdomain solvers with a global coarse correction.
Numerical experiments on sequences of nested polytopal meshes, modeling heterogeneous grey and white matter tissues, assess robustness with respect to mesh refinement, polynomial degree, and coarse-to-fine mesh ratios. The results show that the proposed preconditioner significantly lowers condition numbers and iteration counts compared to the unpreconditioned solver, while maintaining scalability for fixed coarse-to-fine ratios.