On preconditioned BiCGSTAB solver for MLPG method applied to heat conduction in complex geometry

Meshless local Petrov-Galerkin (MLPG) method is a promising meshfree method for continuum problems in complex domains, especially for large deformation, moving boundary and phase change problems. For large-scale problems, iterative methods for solving the discretized equations are more suitable than direct methods. Krylov subspace solvers of conjugate gradient type are the most preferred iterative solvers. The convergence rate of these methods depends on preconditioner used. Recently, proposed schedule relaxation Jacobi (SRJ) method can be used as a stand-alone solver and as a preconditioner. In the present work, the SRJ method is tested as a stand-alone solver and as a preconditioner for BiCGSTAB solver in the MLPG method, and its performance has been compared with successive overrelaxation (k) preconditioner. Two-dimensional linear steady-state heat conduction in complex shape geometry has been used as the model test problem.