Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

S. Ovtchinnikov; F. Dobrian; X. C. Cai; D. E. Keyes

doi:10.1016/j.jcp.2007.02.027

Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

S. Ovtchinnikov, F. Dobrian, X. C. Cai^*, D. E. Keyes

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

A parallel, fully coupled, nonlinearly implicit Newton-Krylov-Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.

Original language	English (US)
Pages (from-to)	1919-1936
Number of pages	18
Journal	Journal of Computational Physics
Volume	225
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2007.02.027
State	Published - Aug 10 2007
Externally published	Yes

Keywords

Fully implicit
Magnetohydrodynamics
Newton-Krylov
Parallel computing
Restricted additive Schwarz preconditioner

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2007.02.027

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title = "Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems",

abstract = "A parallel, fully coupled, nonlinearly implicit Newton-Krylov-Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.",

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AU - Ovtchinnikov, S.

AU - Dobrian, F.

AU - Cai, X. C.

AU - Keyes, D. E.

PY - 2007/8/10

Y1 - 2007/8/10

N2 - A parallel, fully coupled, nonlinearly implicit Newton-Krylov-Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.

AB - A parallel, fully coupled, nonlinearly implicit Newton-Krylov-Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.

KW - Fully implicit

KW - Magnetohydrodynamics

KW - Newton-Krylov

KW - Parallel computing

KW - Restricted additive Schwarz preconditioner

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SN - 0021-9991

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SP - 1919

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

Abstract

Keywords

ASJC Scopus subject areas

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