Solutions of New Potential Integral Equations Using MLFMA Based on the Approximate Stable Diagonalization

We present efficient solutions of recently developed potential integral equations (PIEs) using a low-frequency implementation of the multilevel fast multipole algorithm (MLFMA). PIEs enable accurate solutions of low-frequency problems involving small objects and/or small discretization elements with respect to wavelength. As the number of unknowns grows, however, PIEs need to be solved via fast algorithms, which are also tolerant to low-frequency breakdowns. Using an approximate diagonalization in MLFMA, we present a new implementation that can provide accurate, stable, and efficient solutions of low-frequency problems involving large numbers of unknowns. The effectiveness of the implementation is demonstrated on canonical problems.