A Domain Decomposition Method for Boundary Integral Equations Using a Transmission Condition Based on the Near-Zone Couplings

A domain decomposition method (DDM) for the solution of boundary integral equations for impenetrable objects is presented. The approach uses a transmission condition which is based on the near-range couplings. In order to obtain close approximations of the global solution on the subdomains, the comparatively strong near-zone interactions are taken into account to avoid unphysical reflections from the domain interfaces. The algorithm can be accelerated by fast integral solvers such as the multilevel fast multipole method (MLFMM) by creating local subtrees, which coincide with the different computing domains. This concept is embedded in an inner-outer iterative solution algorithm in which the DDM acts as a preconditioner in the inner iterations. By introducing small overlap regions, the convergence of the iterative solver is further improved. This results in a very robust DDM which can be integrated into existing codes with reasonable effort and which is suited for parallelization. Numerical results for various open and closed objects demonstrate the effectiveness and the excellent performance of the proposed DDM for the solution of electromagnetic radiation and scattering problems.