A comparison of Algebraic Multigrid Bidomain solvers on hybrid CPU-GPU architectures

TL;DR

This paper benchmarks Algebraic Multigrid preconditioners for the Bidomain model of cardiac electrophysiology on hybrid CPU-GPU architectures, demonstrating GPU superiority in solution time despite CPU scalability.

Contribution

It provides a comparative analysis of AMG solvers on modern HPC architectures for cardiac bioelectrical simulations, highlighting GPU efficiency.

Findings

GPUs outperform CPUs in solution time for the Bidomain system

Scalability is confirmed on multi-core CPUs

Performance benchmarks guide efficient solver selection on hybrid architectures

Abstract

The numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a parabolic partial differential equation (PDE), of reaction-diffusion type, describing the spread of electrical excitation in the cardiac tissue. The two PDEs are coupled with a stiff system of ordinary differential equations (ODEs), representing ionic currents through the cardiac membrane. Developing efficient and scalable preconditioners for the linear systems arising from the discretization of such computationally challenging model is crucial in order to reduce the computational costs required by the numerical simulations of cardiac electrophysiology. In this work, focusing on the Bidomain system as a model problem, we have benchmarked two popular implementations of the Algebraic Multigrid (AMG) preconditioner embedded in the PETSc library and we have studied the performance on the calibration of specific parameters. We have conducted our analysis on modern HPC architectures, performing scalability tests on multi-core and multi-GPUs setttings. The results have shown that, for our problem, although scalability is verified on CPUs, GPUs are the optimal choice, since they yield the best performance in terms of solution time.