Studies on Low Frequency Fast Multipole Algorithms

118 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.The low frequency breakdown problem of MLFMA is studied in the second part. A low frequency fast inhomogeneous plane wave algorithm (LF-FIPWA) is developed to overcome this issue with the transition region around 0.1 wavelength. Evanescent waves and propagating waves are both used to compensate for the accuracy lost in the conventional translation process. The scale invariance of LF-FIPWA is studied in detail to preserve the basic Laplace equation property. To improve the efficiency at low frequencies, a novel mixed-form fast multipole algorithm is introduced. The conversion between the multipoles at low frequencies and plane waves at midfrequencies is needed during the aggregation and disaggregation processes. Both dense and diagonal translations are used for one FMA matrix-vector multiplication. This method can effectively overcome the low frequency limitation of MLFMA.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD