Speed-up of the volumetric method of moments for the approximate RCS of large arbitrary-shaped dielectric targets

Moreno, Javier; Somolinos, Álvaro; Romero, Gustavo; Gónzalez, Iván; Cátedra, M.F.

doi:10.1016/j.cpc.2017.04.002

Cited by 1 publication

(7 citation statements)

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“…In these cases, the problems can be formulated in terms of electrical field integral equation (EFIE) when the volume is modelled by volumetric electrical equivalent currents. This approach is implemented in [16], where the volumes are meshed regularly but the metallic surfaces can be meshed arbitrarily. In order to increase the efficiency in [16], the Toeplitz symmetry is used to avoid the re-computation of the near-field terms of the MLFMM impedance matrix, taking advantage of the invariance of these terms when the relative distance between subdomains does not change.…”

Section: Introductionmentioning

confidence: 99%

“…This approach is implemented in [16], where the volumes are meshed regularly but the metallic surfaces can be meshed arbitrarily. In order to increase the efficiency in [16], the Toeplitz symmetry is used to avoid the re-computation of the near-field terms of the MLFMM impedance matrix, taking advantage of the invariance of these terms when the relative distance between subdomains does not change. The sparse approximate inverse (SAI) [17][18][19] is also included in [16], considering the approximate inverse of this near-field impedance.…”

Section: Introductionmentioning

confidence: 99%

“…In order to increase the efficiency in [16], the Toeplitz symmetry is used to avoid the re-computation of the near-field terms of the MLFMM impedance matrix, taking advantage of the invariance of these terms when the relative distance between subdomains does not change. The sparse approximate inverse (SAI) [17][18][19] is also included in [16], considering the approximate inverse of this near-field impedance. Additionally, [16] introduced advanced meshing strategies to treat dielectric bodies modeled by closed surfaces defined in terms of non-uniform rational bi-spline (NURB) surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…The sparse approximate inverse (SAI) [17][18][19] is also included in [16], considering the approximate inverse of this near-field impedance. Additionally, [16] introduced advanced meshing strategies to treat dielectric bodies modeled by closed surfaces defined in terms of non-uniform rational bi-spline (NURB) surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed formulation is validated by comparing the results of the monostatic and bistatic RCS, computed for several dielectric boxes, with the results obtained using other approaches. The memory usage and CPU load times are compared considering the MLFMM of [16], where the rigorous matrix was calculated and used in the iterative process of attaining the solution, illustrating how the new technique leads to significant improvements. As in reference [16], the proposed approach permits the analysis of volumetric bodies with metallic surfaces and does not need the huge matrices of [12][13][14] for representing the discretized Green function of a size eight times bigger than the discretized full volume of the problem.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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Section: Introductionmentioning

confidence: 99%