Hierarchical basis preconditioners and their application to the PMWCHT integral equation

We present an analysis of the application of (general) hierarchical basis preconditioners developed for preconditioning the electric field integral equation (EFIE) to the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation on simply and multiply-connected geometries. First, we discuss the correct choice of the rescaling factors for the solenoidal and non-solenoidal hierarchical bases. Then we consider the harmonic subspace that appears on multiply-connected domains: it turns out that differently from the combined field integral equation (CFIE), the global loops must not be rescaled in frequency. The numerical results confirm the theoretically predicted results.