Splitting strategies for preconditioned explicit group schemes

Abstract

Combining iterative methods with appropriate preconditioners is a worthwhile effort in improving the performances of the methods since the reliability of these methods have been shown to improve by the use of appropriate preconditioning techniques. However, the hardest issue is to find the suitable preconditioners which are computationally inexpensive and easy to solve for the group methods. The aim of this paper is to study the performance of the Explicit Group (EG) method (Evans & Yousif 1986) preconditioned by a specific ‘splitting’ approach in solving the two dimensional elliptic partial differential equation. Our goal in this work is to investigate whether the performance of this group method is affected by this preconditioner. The experimental work performed is reported and discussed.