Application of the additive Schwarz method to large scale Poisson problems

✍ Scribed by Singh, K. M. ;Williams, J. J. R.

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 138 KB
• Volume: 20
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/cnm.660

✦ Synopsis

Abstract

This paper presents an application of the additive Schwarz method to large scale Poisson problems on parallel computers. Domain decomposition in rectangular blocks with matching grids on a structured rectangular mesh has been used together with a stepwise approximation to approximate sloping sides and complicated geometric features. A seven‐point stencil based on central difference scheme has been used for the discretization of the Laplacian for both interior and boundary grid points, and this results in a symmetric linear algebraic system for any type of boundary conditions. The preconditioned conjugate gradient method has been used as an accelerator for the additive Schwarz method, and three different methods have been assessed for the solution of subdomain problems. Numerical experiments have been performed to determine the most suitable set of subdomain solvers and the optimal accuracy of subdomain solutions; to assess the effect of different decompositions of the problem domain; and to evaluate the parallel performance of the additive Schwarz preconditioner. Application to a practical problem involving complicated geometry is presented which establishes the efficiency and robustness of the method. Copyright © 2004 John Wiley & Sons, Ltd.