Fast Computation by MLFMM-FFT with NURBS in Large Volumetric Dielectric Structures

Abstract

A refinement for the computation of the rigorous part of the multi-level fast multipole method (MLFMM) of analyzing volumetric objects is presented. A scheme based on the fast Fourier technique (FFT) is proposed with the objective of reducing the computational resources required to accurately analyze large homogeneous and non-homogeneous dielectric volumes. In order to reduce the memory requirements, the storage of the near-field terms of the method of moments (MoM) matrix is performed only for the positions corresponding to a parallelepiped with the size of the level 1 block of the MLFMM, computed with the vacuum permittivity, taking advantage of the Toeplitz symmetry present in regular hexahedral meshes. The FFT avoids applying the near-field MoM matrix in the iterative solution process. The application of this approach results in huge improvements in terms of memory usage, but also a speeds up the iterative solution process because the use of three-dimensional (3D) FFTs is very efficient for computing convolutions when the number of unknowns of the problems becomes very large as happens in volumetric problems. We also propose a new approach for the numerical treatment of the transition of the dielectric permittivity between different dielectrics or between a dielectric and a free space. To validate the computation technique, the radar cross section (RCS) of several dielectric bodies is computed using the classical MLFMM approach and it is compared with the presented FFT-based-MLFMM solution. The results demonstrate that the efficient memory and computation time usage of the proposed approach.

Enhancement of Electromagnetic Scattering Computation Acceleration Using LSTM Neural Networks

“…In terms of computing RCS using artificial neural networks, Rui Weng et al implemented a computational model for the RCS of a deformed S-shaped cavity using artificial neural networks [13]. These studies demonstrate the significant potential of neural network applications in accelerating electromagnetic simulation calculations [14,[18][19][20][21][22].…”

Efficient EM Scattering Modeling from Metal Targets Coated with Anisotropic Thin Layers

“…In the microwave frequency range where radar operates, common targets such as missiles and aircraft, featuring anisotropic material coatings and complex geometries, often exhibit electrically large-scale scattering characteristics. When dealing with such electrically large metallic targets, the efficiency of full-wave EM simulations often diminishes with increasing problem scales [13][14][15][16][17][18]. Highfrequency approximation methods based on approximation theories, while not matching the computational accuracy of full-wave techniques, have garnered attention due to their rapid computation and minimal resource requirements in various engineering applications.…”

RCS Estimation of Singly Curved Dielectric Shell Structure with PMCHWT Method and Experimental Verification

“…The radar cross-section (RCS) of a system can be estimated from the measurements in a near-field or far-field condition [1]. On the other hand, the computational electromagnetic technologies have been widely utilized to make the process of RCS estimation more manageable, as far as possible [2][3][4][5][6]. In many practical situations, measurement is not possible, especially for electrically large objects.…”

“…In recent studies, many efficient MoM-based algorithms have been proposed as a solution for large-scale problems. In many commercial and industrial approaches, the multi-level-based MoM solutions have proved their effectiveness at handling large-scale problems [3,9,10]. Even further, the fast multi-pole method (FMM) [11] and characteristic basis function method(CBFM) [12,13] can be combined with the multi-level algorithms.…”