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

Abstract

In this paper we propose a direct so- lution 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 unsymmet- ric matrix, is unsymmetric in its numerical val- ues, but nearly symmetric in its nonzero distri- bution of upper and lower triangular portions. MLPG employs trial and test functions in differ- ent 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 factor- ization method and can be implemented without great effort by porting a symmetric matrix fac- torization code. Besides, a blocked out-of-core strategy is also developed to expand the solution scale. The proposed approach convincingly in- creases the efficiency of MLPG, as we demon- strate.