Balancing domain decomposition for mixed finite elements

Lawrence C. Cowsar and Mary F. Wheeler

Rice University, Houston, Texas

Jan Mandel

University of Colorado at Denver


Abstract

The rate of convergence of a substructuring domain decomposition method imploying the balancing preconditioner of Mandel is analyzed for the mixed finite element discretization of second order elliptic equations. Quasi-optimal bounds on the condition number involving two logarithms of the ratio of the size of the subdomains to the size of mesh are derived in both two and three dimensions and for elements of arbitrary order. The key component of the analysis is a new equivalence of norm induced by the bilinear form on the interface to the H^{1/2}-norm of an interpolant of the interface data. Computational examples from a message passing parallel implementation on an INTEL i860 machine are presented that show the method to be both efficient and scalable, as well as, robust with respect to discontinuities in coefficients.