The Fast Multipole Method

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Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm (2003, background): “These operations can be carried using local schemes [ 11 ], [15].”
A wideband fast multipole method for the Helmholtz equation in three dimensions (2006, methodology): “In [16], the complete theory of such diagonal forms is developed, and full-scale FMMs for the Helmholtz and Maxwell’s equations are constructed in [28,33,12,13,15].”
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems (2007, background): “Initially one or two level versions were recommended which gave O(n3/2) or O(n4/3) algorithms [40, 41], but recently multilevel implementations were reported on, both in 2D and 3D, with complexity O(nloga n) for some small constant a (see [4, 19 , 37]).”
A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain (2008, methodology): “The results of Sections 5.2 and 5.3 are consistent with corresponding studies in [ 8 , 53] for electromagnetics, where particular the O(N3/2) complexity of the direct and inverse extrapolations is also”
Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents (2013, background): “Integration methods typically suffer from dense system matrices, but fast multipole acceleration considerably increases their speed [241].”