HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS  

作　　者：苑维然 陈璞 刘凯欣 

机构地区：[1]LTCS & Department of Mechanics and Aerospace Engineering,Peking University,Beijing 100871,P.R.China [2]LTCS & Department of Mechanics and Aerospace Engineering,Peking University,Beijing 100871,P.R.China Engineering Research Institute,Peking University,Beijing 100871,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2006年第10期1339-1348,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 10232040, 10572002 and 10572003)

摘　　要：A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.

关 键 词：sparse matrices linear equations meshless methods high performance computation 

分 类 号：O241.6[理学—计算数学]