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

摘要

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.