Volume 7, Issue 3
JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research

Xiaoqiang Yue, Xiaowen Xu & Shi Shu

East Asian J. Appl. Math., 7 (2017), pp. 495-507.

Published online: 2018-02

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  • Abstract

We present a JASMIN-based two-dimensional parallel implementation of an adaptive combined preconditioner B α co 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 B α co -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 B α co -GMRES solver is more robust and more efficient than the default BoomerAMG-GMRES solver

  • Keywords

Radiation diffusion equations, combined preconditioner, adaptive technology, parallel computing, JASMIN.

  • AMS Subject Headings

65F10, 65N55, 65Y05, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-495, author = {}, title = {JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {495--507}, abstract = {

We present a JASMIN-based two-dimensional parallel implementation of an adaptive combined preconditioner B α co 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 B α co -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 B α co -GMRES solver is more robust and more efficient than the default BoomerAMG-GMRES solver

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.061116.230417a}, url = {http://global-sci.org/intro/article_detail/eajam/10761.html} }
TY - JOUR T1 - JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research JO - East Asian Journal on Applied Mathematics VL - 3 SP - 495 EP - 507 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.061116.230417a UR - https://global-sci.org/intro/article_detail/eajam/10761.html KW - Radiation diffusion equations, combined preconditioner, adaptive technology, parallel computing, JASMIN. AB -

We present a JASMIN-based two-dimensional parallel implementation of an adaptive combined preconditioner B α co 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 B α co -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 B α co -GMRES solver is more robust and more efficient than the default BoomerAMG-GMRES solver

Xiaoqiang Yue, Xiaowen Xu & Shi Shu. (2020). JASMIN-based Two-dimensional Adaptive Combined Preconditioner for Radiation Diffusion Equations in Inertial Fusion Research. East Asian Journal on Applied Mathematics. 7 (3). 495-507. doi:10.4208/eajam.061116.230417a
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