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.

翻译：心脏电生理数值模拟是科学计算中极具挑战性的问题。双域系统是心脏生物电活动的最完整数学模型，包含两个反应扩散型偏微分方程（椭圆型与抛物型），用于描述电兴奋在心肌组织中的传播。这两个偏微分方程与描述心肌膜离子电流的刚性常微分方程组耦合。为降低心脏电生理数值模拟的计算成本，开发针对该计算挑战性模型离散化所得线性系统的高效可扩展预处理器至关重要。本文以双域系统为模型问题，对PETSc库中两种广泛应用的代数多重网格（AMG）预处理器实现进行基准测试，并研究特定参数校准对性能的影响。我们在现代高性能计算架构上开展分析，在多核与多GPU环境下进行可扩展性测试。结果表明，针对本文问题，虽然CPU验证了可扩展性，但GPU因在求解时间上表现最优而成为最佳选择。