Fig. 3: Fast multipole method (FMM) implementations in electromagnetic scattering.
a Parallel graphics processing unit (GPU) and multilevel FMM model for an electrically large and complicated object71. a.i Schematic of the electrically large and complicated object of the ship model. a.ii VV-polarized bistatic radar cross-section of the large sphere diameter 3040 m from 0° to 180° generated from the parallel GPU and multilevel FMM (GPU-PMLFMA; red dashed line), PMLFMA (blue dashed line), and Mie series (black solid line). a.iii Speedup of the GPU-PMLFMA versus the number of unknowns of the ship model with the aggregation matrix and disaggregation matrix (Vs and Vf; red dashed line), translation matrix (T; blue dashed line), near-group impedance matrix (Znear; magenta dashed line), generalized minimal residual method (GMRES; cyan dashed line), and total speedup (black solid line). b Hybridization of the method of auxiliary sources (MAS) with the FMM75. b.i Schematic of a large, rectangular array of circular dielectric cylinders, stimulated either by a plane-wave electromagnetic field or an infinite line source running parallel to their axes. b.ii Comparison of the required execution times by the conventional MAS method (blue solid line) and the hybridization method (orange solid line) versus the number of unknowns. c FMM for large-scale electromagnetic metasurface31. c.i A two dimensional total E-field when the surface is normally illuminated by a Gaussian beam. c.ii Computational time requirements between the standard generalized sheet transition conditions of the integral equations (IE-GSTC; black dashed line) and the FMM IE-GSTC (black solid line) versus the surface length. c.iii Schematics of electrically large rooms scenario without (top) and with (bottom) metasurfaces.
