Two novel parallel Newton-Krylov balancing domain decomposition by constraints (BDDC) and dual-primal finite element tearing and interconnecting (FETI-DP) solvers with deluxe scaling are constructed, analyzed, and tested numerically for implicit time discretizations of the three-dimensional bidomain system of equations. This model represents the most advanced math-ematical description of the cardiac bioelectrical activity, and it consists of a degenerate system of two nonlinear reaction-diffusion partial differential equations (PDEs), coupled with a stiff system of ordinary differential equations (ODEs). A finite element discretization in space and a segregated im-plicit discretization in time, based on decoupling the PDEs from the ODEs, yields at each time step the solution of a nonlinear algebraic system. The Jacobian linear system at each Newton iteration is solved by a Krylov method, accelerated by BDDC or FETI-DP preconditioners, both augmented with the recently introduced deluxe scaling of the dual variables. A polylogarithmic convergence rate bound is proven for the resulting parallel Bidomain solvers. Extensive numerical experiments on Linux clusters up to two thousand processors confirm the theoretical estimates, showing that the proposed parallel solvers are scalable and quasi-optimal.

PARALLEL NEWTON-KRYLOV BDDC AND FETI-DP DELUXE SOLVERS FOR IMPLICIT TIME DISCRETIZATIONS OF THE CARDIAC BIDOMAIN EQUATIONS / N.M.M. Huynh, L.F. Pavarino, S. Scacchi. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 44:2(2022), pp. 224-249. [10.1137/20M1353848]

PARALLEL NEWTON-KRYLOV BDDC AND FETI-DP DELUXE SOLVERS FOR IMPLICIT TIME DISCRETIZATIONS OF THE CARDIAC BIDOMAIN EQUATIONS

N.M.M. Huynh
;
L.F. Pavarino;S. Scacchi
2022

Abstract

Two novel parallel Newton-Krylov balancing domain decomposition by constraints (BDDC) and dual-primal finite element tearing and interconnecting (FETI-DP) solvers with deluxe scaling are constructed, analyzed, and tested numerically for implicit time discretizations of the three-dimensional bidomain system of equations. This model represents the most advanced math-ematical description of the cardiac bioelectrical activity, and it consists of a degenerate system of two nonlinear reaction-diffusion partial differential equations (PDEs), coupled with a stiff system of ordinary differential equations (ODEs). A finite element discretization in space and a segregated im-plicit discretization in time, based on decoupling the PDEs from the ODEs, yields at each time step the solution of a nonlinear algebraic system. The Jacobian linear system at each Newton iteration is solved by a Krylov method, accelerated by BDDC or FETI-DP preconditioners, both augmented with the recently introduced deluxe scaling of the dual variables. A polylogarithmic convergence rate bound is proven for the resulting parallel Bidomain solvers. Extensive numerical experiments on Linux clusters up to two thousand processors confirm the theoretical estimates, showing that the proposed parallel solvers are scalable and quasi-optimal.
bidomain system; deluxe scaling; domain decomposition; FETI-DP and BDDC preconditioners
Settore MAT/08 - Analisi Numerica
PRIN201719SSCAC_01 - Modeling the heart across the scales: from cardiac cells to the whole organ - SCACCHI, SIMONE - PRIN2017 - PRIN bando 2017 - 2019
Article (author)
File in questo prodotto:
File Dimensione Formato  
huynhPS_2022.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 2.51 MB
Formato Adobe PDF
2.51 MB Adobe PDF Visualizza/Apri
20m1353848.pdf

accesso aperto

Tipologia: Publisher's version/PDF
Dimensione 2.44 MB
Formato Adobe PDF
2.44 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/944029
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 3
social impact