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High performance sparse solver for unsymmetrical linear equations with out-of-core strategies and its application on meshless methods

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Abstract

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.

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Authors and Affiliations

  1. LTCS & Department of Mechanics and Aerospace Engineering, Peking University, Beijing, 100871, P. R. China

    Yuan Wei-ran  (苑维然), Chen Pu Doctor  (陈璞) (Associate Professor) & Liu Kai-xin  (刘凯欣)

  2. Engineering Research Institute, Peking University, Beijing, 100871, P. R. China

    Liu Kai-xin  (刘凯欣)

Authors
  1. Yuan Wei-ran  (苑维然)
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  2. Chen Pu Doctor  (陈璞)
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  3. Liu Kai-xin  (刘凯欣)
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Corresponding author

Correspondence to Chen Pu Doctor  (陈璞).

Additional information

Communicated by YE Qing-kai

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

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Yuan, Wr., Chen, P. & Liu, Kx. High performance sparse solver for unsymmetrical linear equations with out-of-core strategies and its application on meshless methods. Appl Math Mech 27, 1339–1348 (2006). https://doi.org/10.1007/s10483-006-1006-1

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  • DOI: https://doi.org/10.1007/s10483-006-1006-1

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2000 Mathematics Subject Classification

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