An Investigation of Multi-Layer Scheme for Grid Refinement Methods

Leina Wu, Tsun-Zee Mai

Abstract: Grid Refinement Method has been developed to solve linear systems developed from partial differential equations along with iterative methods. A multi-layer scheme in the Grid Refinement Method is developed and presented in the paper. Accuracy and efficiency of the multi-layer scheme is investigated for comparison with the solutions obtained by uniform grid and the two layer scheme approach.

Keywords: Grid Refinement Method, linear system, partial differential equation, iterative methods, stopping procedure, Successive Over Relaxation Method, matrix decomposition, Dirichlet boundary conditions