MLFMAMulti-Level Fast Multi-Pole Algorithm (integral equation solving algorithm)
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In the traditional fast algorithms, the matrix decompositions are only performed on the far-field groups especially for the physically related methods such as MLFMA. However, the mutual interactions between two different cells (off-diagonal blocks) are all computed by PSA in our implementation.
Ergul, "Parallel implementation of mlfma for homogeneous objects with various material properties," Progress in Electromagnetics Research, vol.
Writing for graduate students and researchers in the areas of computational electromagnetics, numerical analysis, and computer science, they cover basics, solutions of electromagnetic problems with surface integral equations, iterative solutions of electromagnetic problems with the multilevel fast multiple algorithm (MLFMA), the parallelization of MLFMA for solving large-scale electromagnetics problems, and applications such as photonic crystals and scattering from red blood cells.
In order to increase efficiency of the proposed scheme, the MLFMA is used to speed up the matrix vector product in Equations (6) and (12).
(1) The nonconformal VIE expanded by the SWG basis function in discontinued boundaries is explained in detail, and the solver is accelerated by MLFMA
Carin, "Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space," IEEE.
However, in order to analyze an electrically large object, such as an aircraft, the utilization of CBFM and MLFMA would be necessary.
It can be efficiently solved by using iterative solvers such as GMRES with the aid of MLFMA which significantly speeds up the matrix-vector multiplication of [P]{[E.sub.S]} and [Q]{[[bar.H].sub.S]}.
To alleviate this problem, a spherical harmonics expansion-based MLFMA (SE-MLFMA) for the dyadic form of surface integral equation (SIE) was proposed [6].
In this paper, we present a deep review of the effort we have made over the last years extending the SIE-MoM [21, 24-26] combined with the most recent advances in spectral acceleration techniques, based on the multilevel fast multipole algorithm (MLFMA) [27-29] and the fast Fourier transform (FFT) [30-32], for the simulation of realistic large-scale plasmonic systems.
Method of Moment (MoM) [4] is widely used numerical algorithm, which is adequately developed into fast algorithms, such as Generalized Forward-Backward Method (GFBM) [5, 6] and multilevel fast multipole algorithm (MLFMA) [7, 8].
The other class of algorithms performing rapid MoM solution of the IEs is the Multi-Level-Fast-Multipole- Algorithm (MLFMA) [2].