2018/06/11 by Gur, Ugur Meric, Ergul, Ozgur
#Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Numerical Analysis (math.NA) #and Science (cs.CE)
paper · doi:10.48550/arxiv.1806.04164
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.