domain decomposition methods with small overlap for qnqn2 spectral elements：随着qnqn2光谱元素小的重叠区域分解方法_.pdf

Applied Numerical Mathematics 33 (2000) 463–470 Domain decomposition methods with small overlap for spectral elements 2 Luca F. Pavarino 1 Department of Mathematics, Università di Milano, Via Saldini 50, 20133 Milano, Italy Abstract An indefinite overlapping Schwarz method is introduced and studied for Stokes problems discretized with spectral elements. This results in a parallel and scalable preconditioner for the iterative solution of the 2 discrete system of equations. The preconditioner is based on the solution of local Stokes problems on overlapping subregions and a coarse Stokes problem with elements. The efficiency of the method is based on using a 2 0 nodal basis and quadrature rules associated with Gauss–Lobatto–Legendre nodes. As for -version finite elements, a small overlap between subregions seems to be the most efficient choice.  2000 IMACS. Published by Elsevier Science B.V. All rights reserved. Keywords: Domain decomposition; Spectral elements 1. Introduction An indefinite overlapping Schwarz method was introduced by Klawonn and Pavarino [9] for -version mixed finite elements discretizations of saddle point problems. In this paper, this method is extended to spectral elements, using the nodal basis for spectral elements associated with Gauss– 2 Lobatto–Legendre (GLL) nodes. For simplicity, we focus here on the Stokes problem. The method proposed is based on the solution of local Stokes problems on overlapping subregions and a coarse Stokes problem with elements. The overlapping subregions are built by extending the boundary