GMRES Solver for MLPG Method Applied to Heat Conduction

Abstract

Abstract In recent years, meshless local Petrov-Galerkin (MLPG) method has emerged as the promising choice for solving variety of scientific and engineering problems. MLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods (such as GMRES and BiCGSTAB methods) are more competent than the direct solvers for solving a general linear system of larger size (order of millions or billions). This paper presents the use of GMRES solver with MLPG method for the very first time. The restarted version of the GMRES method is applied in connection with the interpolating MLPG method, to solve steady-state heat conduction in three-dimensional regular geometry. The performance of GMRES solver (with and without preconditioner) has been compared with the preconditioned BiCGSTAB method in terms of computation time and convergence behaviour. Jacobi and successive over-relaxation methods have been used as preconditioners in both the solvers. The results show that GMRES solver takes about 18 to 20% less CPU time than the BiCGSTAB solver along with better convergence behaviour.