Flexible GMRES solver for interpolating MLPG analysis of heat conduction

Abstract

This article evaluates the performance of flexible generalized minimum residual (FGMRES) solver in meshless local Petrov–Galerkin (MLPG) analysis of heat conduction. Interpolating MLPG formulation has been used for the meshless discretization, resulting in an asymmetric algebraic equation system. FGMRES is a variant of GMRES, which allows the preconditioner to vary from step to step. Also, the GMRES solver can be used as a preconditioner. The FGMRES method has been used with Jacobi, SOR(k), and GMRES preconditioners for MLPG analysis of heat conduction in two-dimensional and three-dimensional geometries. The performance of the FGMRES solver is compared with the restarted GMRES solver (and BiCGSTAB solver in 3-D complex geometry). Jacobi and SOR(k) preconditioners are used in the restarted GMRES and BICGSTAB solvers. Results demonstrate that the FGMRES solver performs better than the GMRES and BiCGSTAB solvers, except for two-dimensional complex geometry.