A fast MoM solution for large arrays: Green's function interpolation with FFT

Fasenfest,; Capolino, Filippo; Wilton,; Jackson, David R.; Champagne,

doi:10.1109/lawp.2004.833713

Cited by 39 publications

(35 citation statements)

References 8 publications

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“…We will do this by modifying a technique developed by Fasenfest, which was originally used to study truncation effects of phased arrays [11]. Fasenfest's technique, the Green's Function Interpolation with a Fast Fourier Transform (GIFFT), depends on the fact that the elements of the phased array, although truncated, conform to a periodic lattice.…”

Section: Work Pertaining To Defectsmentioning

confidence: 99%

“…One such technique that belongs to the class of fast solvers for large periodic structures is the GIFFT algorithm, which is first discussed in [11]. This method is a modification of the Adaptive Integral Method (AIM) [13], which is a technique based on the projection of subdomain basis functions onto a rectangular grid.…”

Section: Description Of Gifftmentioning

confidence: 99%

“…Although GIFFT [11] was originally developed to handle strictly periodic structures, the technique has now been extended to efficiently handle a small number of distinct element types. Thus, in addition to reducing the computational burden associated with large periodic structures, GIFFT now permits modeling these structures with source and defect elements.…”

Section: Description Of Gifftmentioning

confidence: 99%

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Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Johnson¹,

Warne²,

Jorgenson³

et al. 2006

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In this LDRD we examine techniques to analyze the electromagnetic scattering from structures that are nearly periodic. Nearly periodic could mean that one of the structure's unit cells is different from all the others -a defect. It could also mean that the structure is truncated, or butted up against another periodic structure to form a seam. Straightforward electromagnetic analysis of these nearly periodic structures requires us to grid the entire structure, which would overwhelm today's computers and the computers in the foreseeable future. In this report we will examine various approximations that allow us to continue to exploit some aspects of the structure's periodicity and thereby reduce the number of unknowns required for analysis. We will use the Green's Function Interpolation with a Fast Fourier Transform (GIFFT) to examine isolated defects both in the form of a source dipole over a meta-material slab and as a rotated dipole in a finite array of dipoles. We will look at the numerically exact solution of a one-dimensional seam. In order to solve a two-dimensional seam, we formulate an efficient way to calculate the Green's function of a 1d array of point sources. We next formulate ways of calculating the far-field due to a seam and due to array truncation based on both array theory and high-frequency asymptotic methods. We compare the high-frequency and GIFFT results. Finally, we use GIFFT to solve a simple, two-dimensional seam problem.3

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Section: Work Pertaining To Defectsmentioning

confidence: 99%

Section: Description Of Gifftmentioning

confidence: 99%

Section: Description Of Gifftmentioning

confidence: 99%

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Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Johnson¹,

Warne²,

Jorgenson³

et al. 2006

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“…During the past several decades, many fast integral equation solvers have been developed to expedite the iterative solution of integral equation, such as conjugate gradient fast Fourier transform (CG-FFT) [3], multilevel fast multipole algorithm (MLFMA) [4,5], adaptive integral method (AIM) [6,7], precorrected fast Fourier transform (P-FFT) [8,9], Green's function interpolation with fast Fourier transform (GIFFT) [10], integral equation fast Fourier transform (IE-FFT) [11,12] and multilevel Green's function interpolation method (MLGFIM) [13]. The MLFMA has a low complexity of O(N log N ) for arbitrary geometry shape, but it is a kennel dependent method and also has a low frequency breakdown problem.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the AIM and P-FFT, the GIFFT and IE-FFT calculate matrix elements by mapping the Green's function onto interpolation functions defined on the Cartesian grids with equal step cell. The GIFFT approximates the Green's function over the interpolation grids as a sum of separable functions, is ideally suitable for solving array problems [10], while the IE-FFT simply interpolates the Green's function by Lagrange interpolation polynomials, calculates the interaction between nearby elements directly and expedites the interaction between far elements using FFT [11]. Different from the above methods, the MLGFIM uses multilevel discretization of the problem domain like MLFMA to realize the multilevel Green's function interpolation [13].…”

Section: Introductionmentioning

confidence: 99%

Floating Interpolation Stencil Topology-Based Ie-FFT Algorithm

Yin¹,

Hu²,

Nie³

et al. 2011

PIER M

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Abstract-The integral equation fast Fourier transform (IE-FFT)is a fast algorithm for 3D electromagnetic scattering and radiation problems based on the interpolation of the Green's function. In this paper, a novel floating interpolation stencil topology is used to improve the IE-FFT algorithm. Compared to the traditional interpolation stencil topology, it can further reduce the storage and CPU time for the IE-FFT algorithm. The reduction is especially significant for volume integral equations. Furthermore, the accuracy of the algorithm is still good though the near-interaction element numbers are reduced. Finally, some numerical results including perfectly electric conductors, dielectric objects, composite conducting and dielectric objects are given to demonstrate the performance of the present method.

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Fast Fourier Transforms in Electromagnetics

Guo

2014

Wiley Encyclopedia of Electrical and Electronics Engineering

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This Chapter review the fast Fourier transform (FFT) technique and its application to computational electromagnetics, especially to the fast solver algorithms including the Conjugate Gradient Fast Fourier Transform (CG‐FFT) method, Precorrected Fast Fourier Transform (pFFT) method, Adaptive Integral Method (AIM), Greens Function Interpolation with FFT (GI‐FFT) method and Integral Equations with FFT (IE‐FFT) method. The basic ideas used in the FFT applications are addressed while the brief introduction to integral equation method is conducted. The general formulation and procedure in the integral equation method, surface integral equations, volume integral equations, solutions to integral equations, and their implementations of fast Fourier transform algorithm are also briefed together with fast convolution using fast Fourier transform. Fast integral equation method developed based on fast Fourier transform are reviewed where conjugate gradient fast Fourier transform method, and precorrected fast Fourier transform method (where projection operators and interpolation operators are also highlighted), adaptive integral method, Greens function interpolation with FFT approach and integral equations with FFT method are also described. While the matching schemes for gradients of Green's functions are addressed, accuracy and complexity, memory requirement and computational cost, and error controls and estimations are also discussed.

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A fast MoM solution for large arrays: Green's function interpolation with FFT

Cited by 39 publications

References 8 publications

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Floating Interpolation Stencil Topology-Based Ie-FFT Algorithm

Fast Fourier Transforms in Electromagnetics

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