Accelerated Group Krylov Algorithms In 2D Elliptic Partial Differential Equation

摘要

The Modified Explicit Decoupled Group (MEDG) iterative method [3] was recently formulated using a combination of the rotated five-point finite difference approximation grid stencil together with the five-point centred difference approximation on the h and 2h grid stencils and was shown to have a better convergence rate than the existing explicit group schemes of the same family. In this paper, we investigate the applicability of this discretisation scheme with a left-right splitting preconditioner combined with specific Krylov subspace acceleration techniques as a way to further improve the convergence rate of this iterative scheme. Numerical experimentations in solving a 2-D elliptic partial differential equation (PDE) will be conducted and discussed. Comparisons with other existing explicit group schemes will be presented.