Analysis of a parallel Schwarz algorithm for elliptic problems

A parallel algorithm, which is derived directly from the Schwarz alternatin g algorithm with an overlapping domain decomposition, for solving boundary value problems of elliptic partial differential equations is analyzed. A ne w general analysis framework different from Lions' ones is established to d escribe the recursive relations of error functions between approximate solu tions and the exact solution at the different iterative steps. Some abstrac t theories on convergence and convergent rate of the synchronously parallel algorithm are established under different conditions. (C) 2000 Elsevier Sc ience Inc. All rights reserved.