  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.
