Newton–Krylov-BDDC solvers for nonlinear cardiac mechanics

Pavarino, Luca F.; Scacchi, Simone; Zampini, Stefano

doi:10.1016/j.cma.2015.07.009

Cited by 25 publications

(14 citation statements)

References 67 publications

(109 reference statements)

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“…Previous versions of the PCBDDC code also have been applied to the spectral element discretization of almost incompressible elasticity in three dimensions [67] and within the isogeometric analysis framework [13,14]. Finally, a Newton-Krylov-BDDC approach has been recently proposed for nonlinear mechanical models of cardiac tissue deformation [68].…”

Section: Numerical Resultsmentioning

confidence: 99%

PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

Zampini¹

2016

SIAM J. Sci. Comput.

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Abstract. A class of preconditioners based on balancing domain decomposition by constraints methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc). The algorithm and the underlying nonoverlapping domain decomposition framework are described with a specific focus on their current implementation in the library. Available user customizations are also presented, together with an experimental interface to the finite element tearing and interconnecting dual-primal methods within PETSc. Large-scale parallel numerical results are provided for the latest version of the code, which is able to tackle symmetric positive definite problems with highly heterogeneous distributions of the coefficients. Current limitations and future extensions of the preconditioner class are also discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

Zampini¹

2016

SIAM J. Sci. Comput.

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“…Preconditioning for cardiac electromechanical solvers is an active field of research, see Pavarino et al and Franzone et al In this work, the block Gauss‐Seidel preconditioning strategy proposed in Deparis et al in the context of fluid‐structure interaction problems (FaCSI preconditioning), and then extended in for cardiac electromechanical problems with the monodomain model, is further extended for the Jacobian matrix in Equation 22, with the modifications required by the extra blocks

{scriptA}_{boldV U_{e}}

{scriptA}_{U_{e} boldV}

and

{scriptA}_{U_{e}}

, coming from the bidomain model.…”

Section: Numerical Approximationmentioning

confidence: 99%

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

Landajuela

Vergara

Gerbi

et al. 2018

Numer Methods Biomed Eng

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In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

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“…Across a broad range of structural mechanics applications, the demand for more accurate, complex and reliable numerical simulations is increasing exponentially. In this context, the Finite Element Method (FEM) remains the most widely used approach and the number of new extremely challenging applications is countless, e.g., modeling of fractal formation in macroscopic elasto-plasticity in three-dimensional bodies [1], simulation of cardiac mechanics [2], submarine landslides [3], stir welding processes [4], concrete gravity dam [5], just to name some recent applications. In all the problems mentioned above, the underlying partial differential equations (PDEs) are discretized to approximate the continuous solution in an algebraic system of equations of the form:…”

Section: Introductionmentioning

confidence: 99%

A robust adaptive algebraic multigrid linear solver for structural mechanics

Franceschini

Magri

Mazzucco

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.

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Newton–Krylov-BDDC solvers for nonlinear cardiac mechanics

Cited by 25 publications

References 67 publications

PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

A robust adaptive algebraic multigrid linear solver for structural mechanics

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