Fast solvers with block-diagonal preconditioners for linear FEM-BEM coupling

The purpose of this paper is to present optimal preconditioned iterative methods to solve indefinite linear systems of equations arising from symmetric coupling of finite elements and boundary elements [14]. This is a block-diagonal preconditioner together with a conjugate residual method (PCR) and a preconditioned inner-outer iteration (PIO). We prove the efficiency of these methods by showing that the number of iterations to preserve a given accuracy is bounded independently of the number of unknowns. Numerical examples underline the efficiency of these methods.