A comparative study of scalable multilevel preconditioners for cardiac mechanics

TL;DR

This study compares the performance of BDDC and AMG preconditioners in large-scale cardiac mechanics simulations, highlighting their efficiency and scalability on high-performance computing clusters.

Contribution

It provides a detailed performance comparison of BDDC and AMG preconditioners for cardiac mechanics, including parameter tuning and scalability analysis.

Findings

BDDC and AMG show different strengths depending on mesh type and problem size.

Scalability tests demonstrate effective parallel performance up to 1024 processors.

Parameter choices significantly impact preconditioner efficiency.

Abstract

In this work, we provide a performance comparison between the Balancing Domain Decomposition by Constraints (BDDC) and the Algebraic Multigrid (AMG) preconditioners for cardiac mechanics on both structured and unstructured finite element meshes. The mechanical behavior of myocardium can be described by the equations of three-dimensional finite elasticity, which are discretized by finite elements in space and yield the solution of a large scale nonlinear algebraic system. This problem is solved by a Newton-Krylov method, where the solution of the Jacobian linear system is accelerated by BDDC/AMG preconditioners. We thoroughly explore the main parameters of the BDDC preconditioner in order to make the comparison fair. We focus on: the performance of different direct solvers for the local and coarse problems of the BDDC algorithm; the impact of the different choices of BDDC primal degrees of freedom; and the influence of the finite element degree. Scalability tests are performed on Linux clusters up to 1024 processors, and we conclude with a performance study on a realistic electromechanical simulation.