Convergence of a balancing domain decomposition by constraints and energy minimization

Abstract

Abstract A convergence theory is presented for a substructuring preconditioner based on constrained energy minimization concepts. The substructure spaces consist of local functions with zero values of the constraints, while the coarse space consists of minimal energy functions with the constraint values continuous across substructure interfaces. In applications, the constraints include values at corners and optionally averages on edges and faces. The preconditioner is reformulated as an additive Schwarz method and analysed by building on existing results for balancing domain decomposition. The main result is a bound on the condition number based on inequalities involving the matrices of the preconditioner. Estimates of the form C (1+log 2 (H/h)) are obtained under the standard assumptions of substructuring theory. Computational results demonstrating the performance of method are included. Published in 2003 by John Wiley & Sons, Ltd.