Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method

Authors:
Ben-Wen Li;Shuai Tian;Ya-Song Sun;Zhang-Mao Hu
Affiliations:
Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004, China;Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004, China;Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004, China;Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004, China
Venue:
Journal of Computational Physics
Year:
2010

Citing 5
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Abstract

The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates method.