Low-frequency Fast Multipole Algorithm Research Articles

A Low-Frequency EFIE-MLFMA Solver Based on Approximate Diagonalization of Green’s Function

The low-frequency fast multipole algorithm (LFFMA) based on the approximate diagonalization of Green’s function for the electric field integral equation (EFIE) is proposed for open and complex structures with high accuracy. Moreover, the multiresolution preconditioner is employed to the mixed potential form of EFIE with RWG basis functions for stability. Herein, a triangle-grouping scheme is adopted for the scalar potential so that the accuracy of the LFFMA can be guaranteed. Furthermore, the computational resources can be reduced largely since part of the radiation pattern of vector potential can share one of the scalar potentials by taking advantage of some mathematical deductions.

Calderon multiplicative preconditioner based on curvilinear elements for fast analysis of electromagnetic scattering

In this study, an efficient Calderon multiplicative preconditioner (CMP) based on the curvilinear elements is proposed for preconditioning electric field integral equation (EFIE) for three-dimensional electromagnetic problems. The curvilinear CMP are constructed by the curvilinear Buffa–Christinansen (BC) basis functions and curvilinear Rao–Wilton–Glisson (CRWG) basis functions, both of which can be presented as a linear combination of CRWG basis functions acting on barycentrically refined triangular meshes. Therefore the implementation of the curvilinear CMP-preconditioned EFIE allows direct application to the existing method of moments (MoM) code using CRWG basis functions and can be combined with the multilevel fast multipole algorithm (MLFMA) for electrically large problems and low-frequency fast multipole algorithm (LF-FMA) for low-frequency problems. The Caldron identities of the curvilinear CMP can lead to the fast convergence rate of iterative solvers for EFIE solutions, independently of the discretisation density. The numerical results demonstrate that the curvilinear CMP scheme with both MLFMA and LF-FMA lead to significant reduction of both the iteration number and the CPU time of monostatic radar cross-section (RCS) calculation.

A memory saving fast A-EFIE solver for modeling low-frequency large-scale problems

We propose a new fast solver for solving the augmented electric field integral equation (A-EFIE), which realizes memory savings for modeling low-frequency large-scale problems, compared with the low-frequency fast multipole algorithm (LF-FMA). The A-EFIE has been proposed to avoid the imbalance between the vector potential and the scalar potential at low frequencies by adding the charge to the unknown list. The corresponding low frequency fast multipole algorithm (LF-FMA) was also developed for solving the A-EFIE. Instead of the factorization of the scalar Greenʼs function by using the scalar addition theorem in the LF-FMA, we adopt the vector addition theorem for the factorization of the dyadic Greenʼs function to develop a vector fast multipole algorithm (VFMA) for solving the A-EFIE. The storage of radiation and receiving patterns of the VFMA, which becomes the main part of the total storage with the increasing scale of problems, can be reduced by 25 percent compared with that of the LF-FMA, although the storage for vector translators, which is independent of the number of unknowns, is larger than that of the LF-FMA. At last, some numerical results show the validity of the VFMA for solving A-EFIE.

A mixed-form fast multipole algorithm

The fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies. Each can operate in their respective regimes, but are not tenable in the other regimes. The paper reports on a way to factorize the Green's function for fast algorithm using a mixed form. The low-frequency fast multipole algorithm (LF-FMA) will be used at low frequencies or the long-wavelength regime, and the multilevel fast multipole algorithm (MLFMA) will be used for the mid frequencies or the shorter-wavelength regime. For object modeling where both long-wavelength and wave physics are important, we propose a mixed-form fast multipole algorithm (MF-FMA). This algorithm has no low frequency break down, and it can work seamlessly from static (where circuit physics is important) to dynamic (where wave physics is important).