  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.
