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JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research

Part of: Partial differential equations, boundary value problems Computer aspects of numerical algorithms Numerical linear algebra

Published online by Cambridge University Press:  07 September 2017

Xiaoqiang Yue ,
Xiaowen Xu  and
Shi Shu
Xiaoqiang Yue
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
Xiaowen Xu
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Shi Shu*
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
*
*Corresponding author. Email address:[email protected] (S. Shu)
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Abstract

We present a JASMIN-based two-dimensional parallel implementation of an adaptive combined preconditioner for the solution of linear problems arising in the finite volume discretisation of one-group and multi-group radiation diffusion equations. We first propose the attribute of patch-correlation for cells of a two-dimensional monolayer piecewise rectangular structured grid without any suspensions based on the patch hierarchy of JASMIN, classify and reorder these cells via their attributes, and derive the conversion of cell-permutations. Using two cell-permutations, we then construct some parallel incomplete LU factorisation and substitution algorithms, to provide our parallel -GMRES solver with the help of the default BoomerAMG in the HYPRE library. Numerical results demonstrate that our proposed parallel incomplete LU preconditioner (ILU) is of higher efficiency than the counterpart in the Euclid library, and that the proposed parallel -GMRES solver is more robust and more efficient than the default BoomerAMG-GMRES solver.

Keywords

Radiation diffusion equationscombined preconditioneradaptive technologyparallel computingJASMIN

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65N55: Multigrid methods; domain decomposition 65Y05: Parallel computation 65Z05: Applications to physics
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 3 , August 2017 , pp. 495 - 507
Copyright
Copyright © Global-Science Press 2017 

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