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.
@article{arxiv.1806.04164,
title = {Solutions of New Potential Integral Equations Using MLFMA Based on the Approximate Stable Diagonalization},
author = {Ugur Meric Gur and Ozgur Ergul},
journal= {arXiv preprint arXiv:1806.04164},
year = {2018}
}