Subspace Orthogonalization for Substructuring Preconditioners for Non-self-adjoint Elliptic Problems

Abstract

For non-self-adjoint elliptic boundary value problems which are preconditioned by a substructuring method, i.e., nonoverlapping domain decomposition, we introduce and study the concept of subspace orthogonalization. In subspace orthogonalization variants of Krylov methods, the computation of inner products and vector updates, and the storage of basis elements is restricted to a (presumably small) subspace, in this case the edge and vertex unknowns with respect to the partitioning into subdomains. We discuss the convergence properties of these iteration schemes and compare them with Krylov methods applied to the full preconditioned system.