Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

Handle URI:
http://hdl.handle.net/10754/561071
Title:
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Authors:
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano ( 0000-0002-0435-0433 )
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.
KAUST Department:
Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics 2015 Computer Methods in Applied Mechanics and Engineering
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
18-Jul-2015
DOI:
10.1016/j.cma.2015.07.009
Type:
Article
ISSN:
00457825
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0045782515002212
Appears in Collections:
Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPavarino, L.F.en
dc.contributor.authorScacchi, S.en
dc.contributor.authorZampini, Stefanoen
dc.date.accessioned2015-07-27T12:30:21Zen
dc.date.available2015-07-27T12:30:21Zen
dc.date.issued2015-07-18en
dc.identifier.citationNewton-Krylov-BDDC solvers for nonlinear cardiac mechanics 2015 Computer Methods in Applied Mechanics and Engineeringen
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2015.07.009en
dc.identifier.urihttp://hdl.handle.net/10754/561071en
dc.description.abstractThe 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.en
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0045782515002212en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 18 July 2015. DOI:10.1016/j.cma.2015.07.009en
dc.titleNewton-Krylov-BDDC solvers for nonlinear cardiac mechanicsen
dc.typeArticleen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.eprint.versionPost-printen
dc.contributor.institutionDipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italyen
kaust.authorZampini, Stefanoen
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