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.

A comparative study of scalable multilevel preconditioners for cardiac mechanics / N.A. Barnafi, L.F. Pavarino, S. Scacchi. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 492:(2023), pp. 112421.1-112421.24. [10.1016/j.jcp.2023.112421]

A comparative study of scalable multilevel preconditioners for cardiac mechanics

N.A. Barnafi
Primo
;
S. Scacchi
Ultimo
2023

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.
Algebraic multigrid; Cardiac mechanics; Domain decomposition; HPC
Settore MAT/08 - Analisi Numerica
   Modeling the heart across the scales: from cardiac cells to the whole organ
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   2017AXL54F_003
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1019418
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