Analysis of a parallel Schwarz algorithm for elliptic problems

摘要

A parallel algorithm, which is derived directly from the Schwarz alternating algorithm with an overlapping domain decomposition, for solving boundary value problems of elliptic partial differential equations is analyzed. A new general analysis framework different from Lions' ones is established to describe the recursive relations of error functions between approximate solutions and the exact solution at the different iterative steps. Some abstract theories on convergence and convergent rate of the synchronously parallel algorithm are established under different conditions.