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A Conservative Parallel Iteration Scheme for Nonlinear Diffusion Equations on Unstructured Meshes

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Numerical methods in complex analysis

Published online by Cambridge University Press:  02 November 2016

Yunlong Yu ,
Yanzhong Yao ,
Guangwei Yuan  and
Xingding Chen
Yunlong Yu*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
Yanzhong Yao*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
Guangwei Yuan*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
Xingding Chen*
Affiliation:
Department of Mathematics, College of Science, Beijing Technology and Business University, Beijing 100048, P.R. China
*
*Corresponding author. Email addresses:yu_yunlong@iapcm.ac.cn (Y. Yu), yao_yanzhong@iapcm.ac.cn (Y. Yao), yuan_guangwei@iapcm.ac.cn (G. Yuan), chenxd@th.btbu.edu.cn (X. Chen)
*Corresponding author. Email addresses:yu_yunlong@iapcm.ac.cn (Y. Yu), yao_yanzhong@iapcm.ac.cn (Y. Yao), yuan_guangwei@iapcm.ac.cn (G. Yuan), chenxd@th.btbu.edu.cn (X. Chen)
*Corresponding author. Email addresses:yu_yunlong@iapcm.ac.cn (Y. Yu), yao_yanzhong@iapcm.ac.cn (Y. Yao), yuan_guangwei@iapcm.ac.cn (G. Yuan), chenxd@th.btbu.edu.cn (X. Chen)
*Corresponding author. Email addresses:yu_yunlong@iapcm.ac.cn (Y. Yu), yao_yanzhong@iapcm.ac.cn (Y. Yao), yuan_guangwei@iapcm.ac.cn (G. Yuan), chenxd@th.btbu.edu.cn (X. Chen)

Abstract

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In this paper, a conservative parallel iteration scheme is constructed to solve nonlinear diffusion equations on unstructured polygonal meshes. The design is based on two main ingredients: the first is that the parallelized domain decomposition is embedded into the nonlinear iteration; the second is that prediction and correction steps are applied at subdomain interfaces in the parallelized domain decomposition method. A new prediction approach is proposed to obtain an efficient conservative parallel finite volume scheme. The numerical experiments show that our parallel scheme is second-order accurate, unconditionally stable, conservative and has linear parallel speed-up.

Keywords

Diffusion equationsconservationparallel schemeunstructured mesh

MSC classification

Secondary: 65M08: Finite volume methods 65E05: Numerical methods in complex analysis (potential theory, etc.)

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 5 , November 2016 , pp. 1405 - 1423
Copyright
Copyright © Global-Science Press 2016 

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