Solutions of New Potential Integral Equations Using MLFMA Based on the Approximate Stable Diagonalization
This work addresses the need for fast solvers for low-frequency electromagnetic problems with many unknowns, but the results are demonstrated only on canonical problems, making it an incremental contribution.
The authors developed a low-frequency MLFMA implementation using approximate stable diagonalization to solve potential integral equations (PIEs) for low-frequency electromagnetic problems, enabling accurate and efficient solutions for large numbers of unknowns.
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.