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Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Parabolic equations and systems

Published online by Cambridge University Press:  28 July 2017

Qiya Hu  and
Lin Zhao
Qiya Hu*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientic/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing, China
Lin Zhao*
Affiliation:
Huada Empyrean Software Co., Ltd, China Electronics Corporation, Beijing
*
*Corresponding author. Email addresses:hqy@lsec.cc.ac.cn (Q. Hu), zhaolin@lsec.cc.ac.cn (L. Zhao)
*Corresponding author. Email addresses:hqy@lsec.cc.ac.cn (Q. Hu), zhaolin@lsec.cc.ac.cn (L. Zhao)
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Abstract

In this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.

Keywords

2D-3T heat conduction equationsdiscontinuous Galerkin methoddomain decomposition preconditioneriterative numbers

MSC classification

Secondary: 35K51: Initial-boundary value problems for second-order parabolic systems 35K55: Nonlinear parabolic equations 65M55: Multigrid methods; domain decomposition 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 1069 - 1100
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

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