The preconditioned GMRES method for systems of coupled FEM-BEM equations

We analyze the generalized minimal residual method (GMRES) as a solver for coupled finite element and boundary element equations. To accelerate the convergence of GMRES we apply a hierarchical basis block preconditioner for piecewise linear finite elements and piecewise constant boundary elements. It is shown that the number of iterations which is necessary to reach a given accuracy grows only poly-logarithmically with the number of unknowns. This revised version was published online in June 2006 with corrections to the Cover Date.