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A Lions Domain Decomposition Algorithm for Radiation Diffusion Equations on Non-matching Grids

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

Published online by Cambridge University Press:  10 November 2015

Li Yin ,
Jiming Wu  and
Zihuan Dai
Li Yin*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
Jiming Wu
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
Zihuan Dai
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
*
*Corresponding author. Email address: yinli_kitty 122@sina.com (L. Yin), wu_jiming@iapcm.ac.cn (J. Wu), dai_zihuan@iapcm.ac. cn (Z. Dai)
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Abstract

We develop a Lions domain decomposition algorithm based on a cell functional minimization scheme on non-matching multi-block grids for nonlinear radiation diffusion equations, which are described by the coupled radiation diffusion equations of electron, ion and photon temperatures. The L2 orthogonal projection is applied in the Robin transmission condition of non-matching surfaces. Numerical results show that the algorithm keeps the optimal accuracy on the whole computational domain, is robust enough on distorted meshes and curved surfaces, and the convergence rate does not depend on Robin coefficients. It is a practical and attractive algorithm in applying to the two-dimensional three-temperature energy equations of Z-pinch implosion simulation.

Keywords

Lions domain decompositionradiation diffusion equationsnon-matching gridsSchwarz algorithm

MSC classification

Secondary: 65M06: Finite difference methods 65M55: Multigrid methods; domain decomposition
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 4 , November 2015 , pp. 530 - 548
Copyright
Copyright © Global-Science Press 2015 

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