Convergence of a Balancing Domain Decomposition by Constraints and Energy Minimization

Dedicated to Professor Ivo Marek on the occasion of his 70th birthday. A convergence theory is presented for a substructuring preconditioner based on constrained energy minimization concepts. The preconditioner is formulated as an Additive Schwarz method and analyzed 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 usual form C(1 + log2(H/h)) are obtained under the standard assumptions of substructuring theory. Computational results demonstrating the performance of method are included