Open Access

ARTICLE

A New Quasi-Unsymmetric Sparse Linear Systems Solver for Meshless Local Petrov-Galerkin Method (MLPG)

Weiran Yuan¹, Pu Chen^1,2, Kaishin Liu^1,3

1 State Key Laboratory for Turbulence and Complex Systems and College of Engineering, Peking University, Beijing 100871, P.R. China
2 Corresponding author. E-mail: chenpu@pku.edu.cn
3 Engineering Research Institute, Peking University, Beijing 100871, P.R. China

Computer Modeling in Engineering & Sciences 2007, 17(2), 115-134. https://doi.org/10.3970/cmes.2007.017.115

Abstract

In this paper we propose a direct solution method for the quasi-unsymmetric sparse matrix (QUSM) arising in the Meshless Local Petrov-Galerkin method (MLPG). QUSM, which is conventionally treated as a general unsymmetric matrix, is unsymmetric in its numerical values, but nearly symmetric in its nonzero distribution of upper and lower triangular portions. MLPG employs trial and test functions in different functional spaces in the local domain weak form of governing equations. Consequently the stiffness matrix of the resultant linear system is a QUSM. The new solver for QUSM conducts a two-level unrolling technique for LDU factorization method and can be implemented without great effort by porting a symmetric matrix factorization code. Besides, a blocked out-of-core strategy is also developed to expand the solution scale. The proposed approach convincingly increases the efficiency of MLPG, as we demonstrate.

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Keywords

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