Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies

Borup, D.T.; Gandhi, O.P.; Sarkar, Tapan K.

doi:10.1109/tap.1986.1143871

Cited by 298 publications

(93 citation statements)

References 7 publications

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“…At last, the spatial domain dyadic Green's function can be represented in series of spherical waves via Sommerfeld identity in (5).…”

Section: Two-level Discrete Complex Image Methods and Discussionmentioning

confidence: 99%

“…It can find various applications in geophysics exploring [1], unexploded objects characterizing, and microwave integrated circuit analyzing, etc. This structure can be efficiently and rigorously analyzed by the method of moments (MoM) [2][3][4] and fast algorithms based on MoM, such as the conjugate gradient fast Fourier transform method [5], the adaptive integral method [6], the fast multipole method [7]. Either for the conventional MoM or fast algorithms, dyadic Green's function for layered media should be computed.…”

Section: Introductionmentioning

confidence: 99%

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Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

Zhuang¹,

Zhang²,

Hu³

et al. 2008

PIER

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Abstract-Discrete complex image method is introduced to get a closed-form dyadic Green's function by a sum of spherical waves. However, the simulation result by the traditional discrete complex image method is only valid in near-field for several wavelengths. In this paper, we analyze the form of spectral domain dyadic Green's function in the whole k ρ plane and the variety of valid range of simulation results by different sampling paths in two-level discrete complex image method. Consequently, for dyadic Green's function, surface wave pole contribution both in spectral domain and spatial domain is clarified. We introduce the automatic incorporation of surface wave poles in discrete complex image method without extracting surface wave poles. The contribution of surface wave poles in spectral domain and spatial domain dyadic Green's function is further confirmed in the new method. Besides, this method can represent dyadic Green's function by spherical waves in the layer where the source and field points are. So it satisfies the splitting requirement and consequently reduces the computational complexity dramatically especially for objects with large scale inẑ direction.

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“…At last, the spatial domain dyadic Green's function can be represented in series of spherical waves via Sommerfeld identity in (5).…”

Section: Two-level Discrete Complex Image Methods and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

Zhuang¹,

Zhang²,

Hu³

et al. 2008

PIER

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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%

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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“…There exist a lot of fast integral equation methods that can be used to enhance the efficiency of the solution, for instance, FMM [12,[19][20][21], CGFFT [22,23], Pre-corrected FFT [24], SMCG [25], AIM [26], IceCube [27], IMLMQRF [11,28], and MLGFIM [1,2] and so on. In them, 1) FMM is the fastest method with O(N ) complexity for quasistatic problems; 2) SMCG, CGFFT, Pre-corrected FFT, SMCG, and AIM are FFT based methods with O(N log N ) complexity; 3) Ice Cube and IMLMQRF are the methods based on matrix compression technique, i.e., QR factorization, matrix merging, and matrix column and row sampling techniques; 4) MLGFIM is based on a hierarchical structure that is similar to FMM but using the Green's function matrix interpolation method with QR factorization technique.…”

Section: Introductionmentioning

confidence: 99%

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

Wang¹,

Zhao²

2008

PIER

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Abstract-In this paper, a fast integral equation method is developed for extracting the inductances in RF ICs, RF MEMs, IC packages, and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) [1,2] with the volume integral equation discretized using Volume Loop (VL) basis functions. In it, instead of using the filaments model to simulate the currents flowing in the inductors, we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line, the spiral inductors, the bump, and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

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Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies

Cited by 298 publications

References 7 publications

Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

Floating Interpolation Stencil Topology-Based Ie-FFT Algorithm

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

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