The GMRES solver for the interpolating meshless local Petrov–Galerkin method applied to heat conduction. Issue 2 (5th July 2021)

• Record Type: Journal Article
• Authors: Singh, Abhishek Kumar; Singh, Krishna Mohan
• Is Part Of: Engineering computations. Volume 39:Issue 2(2022)
• Page Start: 493
• Page End: 522
• Publication Date: 2021-07-05
• Subjects: Interpolating MLS -- GMRES -- BiCGSTAB -- Heat conduction -- Meshless method; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-01-2021-0067
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The work presents a novel implementation of the generalized minimum residual (GMRES) solver in conjunction with the interpolating meshless local Petrov–Galerkin (MLPG) method to solve steady-state heat conduction in 2-D as well as in 3-D domains. Design/methodology/approach: The restarted version of the GMRES solver (with and without preconditioner) is applied to solve an asymmetric system of equations, arising due to the interpolating MLPG formulation. Its performance is compared with the biconjugate gradient stabilized (BiCGSTAB) solver on the basis of computation time and convergence behaviour. Jacobi and successive over-relaxation (SOR) methods are used as the preconditioners in both the solvers. Findings: The results show that the GMRES solver outperforms the BiCGSTAB solver in terms of smoothness of convergence behaviour, while performs slightly better than the BiCGSTAB method in terms of Central processing Unit (CPU) time. Originality/value: MLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods such as GMRES and BiCGSTAB methods are required for its solution for large-scale problems. This work presents the use of GMRES solver with the MLPG method for the very first time.