The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction-relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics / L.F. Pavarino, S. Scacchi, S. Zampini. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - 295(2015), pp. 562-580. [10.1016/j.cma.2015.07.009]

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

L.F. Pavarino
;
S. Scacchi
Secondo
;
S. Zampini
Ultimo
2015

Abstract

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction-relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
BDDC preconditioners; Cardiac contraction and relaxation; Cardiac electro-mechanical coupling; Domain decomposition methods; Finite elasticity; Finite element methods; Computer Science Applications1707 Computer Vision and Pattern Recognition; Computational Mechanics; Mechanics of Materials; Mechanical Engineering; Physics and Astronomy (all)
Settore MAT/08 - Analisi Numerica
2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/349288
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