Parallel Algebraic Multigrid Solvers for Composite Discontinuous Galerkin Discretization of the Cardiac EMI Model in Heterogeneous Media

Abstract

In this paper, we develop and numerically study algebraic multigrid (AMG) preconditioners for the cardiac EMI (Extracellular space, cell Membrane, and Intracellular space) model, a recent and biophysically detailed framework for cardiac electrophysiology. The EMI model addresses the limitations of traditional homogenized cardiac models and leverages contemporary computational power to enable high-resolution simulations at the cellular scale. Using a composite Discontinuous Galerkin (DG) discretization, we introduce an AMG-EMI solver for the three dimensional EMI model. Our investigation includes the AMG-EMI scalability performance, both weak and strong, and evaluates its numerical robustness under ischemic conditions, addressing the challenges of heterogeneous media. Numerical tests exploit state-of-the-art pre-exascale supercomputers with hybrid CPU–GPU architectures. The results indicate better scalability performance of the AMG-EMI solver on CPUs compared to GPUs. However, the best solution times achieved using GPUs are up to 40x faster than those obtained on CPUs.