An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

Year:    2015

Communications in Computational Physics, Vol. 18 (2015), Iss. 5 : pp. 1313–1335

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 ($B_{co}$ and $\widetilde{B}_{co}$), 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 $B^α_{co}$ involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that $B^α_{co}$-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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.091014.060315a

Communications in Computational Physics, Vol. 18 (2015), Iss. 5 : pp. 1313–1335

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords: