language: en

THE DOMAIN REDUCTION METHOD: HIGH WAY REDUCTION IN THREE DIMENSIONS AND CONVERGENCE WITH INEXACT SOLVERS *

CRAIG C. DOUGLAS AND JAN MANDEL

Abstract. We study a method for parallel solution of elliptic partial differential equations which decomposes the problem into a number of independent subproblems on subspaces of the underlying solution space. Using symmetries of the domain, we obtain up to 64 such subproblems for a 3 dimensional cube and the method reduces to a direct solver. In the general case, or when the subproblems are solved only approximately, the method becomes an iterative method or can be used as a preconditioner. Bounds on the resulting convergence factors and condition numbers are given.

1. Introduction.