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An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

Part of: Partial differential equations, boundary value problems Numerical linear algebra

Published online by Cambridge University Press:  23 November 2015

Xiaoqiang Yue ,
Shi Shu ,
Xiao wen Xu  and
Zhiyang Zhou
Xiaoqiang Yue
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, P.R. China
Shi Shu*
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, P.R. China
Xiao wen Xu
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China
Zhiyang Zhou
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, P.R. China
*
*Corresponding author. Email addresses: yuexq@xtu.edu.cn (X. Yue), shushi@xtu.edu.cn (S. Shu), xwxu@iapcm.ac.cn (X. Xu), peghoty@163.com (Z. Zhou)
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Abstract

The paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

Keywords

Radiation diffusion equationscombined preconditioneradaptive preconditioningconvergence analysis

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F15: Eigenvalues, eigenvectors 65N55: Multigrid methods; domain decomposition 65Z05: Applications to physics
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 5 , November 2015 , pp. 1313 - 1335
Copyright
Copyright © Global-Science Press 2015 

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