Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE Formulations

An efficient parallel algorithm for solving linear and nonlinear exterior boundary value problems arising, e.g., in magnetostatics is presented. It is based upon the domaindecomposition-(DD)-coupling of Finite Element and Galerkin Boundary Element Methods which results in a unified variational formulation. In this way, e.g., magnetic field problems in an unbounded domain with Sommerfeld's radiation condition can be modelled correctly. The problem of a nonsymmetric system matrix due to Galerkin-BEM is overcome by transforming it into a symmetric but indefinite matrix and applying Bramble/Pasciak's CG for indefinite systems. For preconditioning, the main ideas of recent DD research are being applied. Test computations on a multiprocessor system were performed for two problems of practical interest including a nonlinear example.