A Fast Combined Field Volume Integral Equation Solution to EM Scattering by 3-D Dielectric Objects of Arbitrary Permittivity and Permeability

Nie, Xiao-Chun; Yuan, Naichang; Li, Le‐Wei; Gan, Yeow-Beng; Yeo, Tat‐Soon

doi:10.1109/tap.2006.869927

Cited by 33 publications

(17 citation statements)

References 18 publications

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“…In the AIM, a scheme based on matching the multiple moments of the irregularly distributed sources and the grid sources is used [18]. In the PFFT, we use the free space Green's function and construct the projection operators by matching the scalar or vector potentials produced by the original source distributions and those produced by the grid sources at some pre-selected test points [19], [20]. From (8) and (9), we can see that the different order derivative matrices have different Green's functions, and even for the same , the Green's functions for the current sources in (9a) and charge sources in (9b) are also different.…”

Section: Pre-corrected Fft/adaptive Integral Methodsmentioning

confidence: 99%

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Fast Analysis of RCS Over a Frequency Band Using Pre-Corrected FFT/AIM and Asymptotic Waveform Evaluation Technique

Nie

Yuan

et al. 2008

IEEE Trans. Antennas Propagat.

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The pre-corrected fast Fourier transform (PFFT)/ adaptive integral method (AIM) is combined with the asymptotic waveform evaluation (AWE) technique to present fast RCS calculation for arbitrarily shaped three-dimensional PEC objects over a frequency band. The electric field integral equation (EFIE) is used to formulate the problem and the method of moments (MoM) is employed to solve the integral equation. By using the AWE method, the unknown equivalent current is expanded into a Taylor series around a frequency in the desired frequency band. Then, instead of solving the equivalent current at each frequency point, it is only necessary to solve for the coefficients of the Taylor series (called "moments") at each expansion point. Since the number of the expansion points is usually much smaller than that of the frequency points, the AWE can achieve fast frequency sweeping. To facilitate the analysis of large problems, in this paper, all the full matrices are stored in a sparse form and the PFFT/AIM method is employed to accelerate all the matrix-vector products on both sides of the matrix equation for the moments. Further, the incomplete LU preconditioner is used at each expansion point to improve the convergence behaviour of the matrix equation for the moments. The present method can deal with much larger problems than the conventional MoM-AWE method since the PFFT/AIM achieves considerable reduction in memory requirement and computation time. Numerical results will be presented to show the efficiency and capability of the method.Index Terms-Adaptive integral method (AIM), asymptotic waveform evaluation (AWE), method of moments (MoM), pre-corrected fast Fourier transform (PFFT) method, radar cross section (RCS).

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Section: Pre-corrected Fft/adaptive Integral Methodsmentioning

confidence: 99%

“…Numerical examples, including RCS from a plate, cube, sphere and a cylinder over a frequency band will be presented and compared with the solutions of the PFFT accelerated MoM and Mie series. The PFFT-MoM has been verified in [19], [20] and its solutions are used as references since all examples in this paper are too large for the traditional MoM.…”

mentioning

confidence: 99%

Fast Analysis of RCS Over a Frequency Band Using Pre-Corrected FFT/AIM and Asymptotic Waveform Evaluation Technique

Nie

Yuan

et al. 2008

IEEE Trans. Antennas Propagat.

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“…Recently it was extended to the analysis of inhomogeneous dielectric objects by using the VIE formulation [25,26], the hybrid volume surface integral equation for the analysis of composite conducting and dielectric objects, and various antenna analysis [27][28][29][30]. Although the pFFT method is very similar to the AIM, they were originated differently in different areas, but almost at the same time; most importantly, they have different mapping schemes, which thus differentiates the two approaches.…”

Section: Introductionmentioning

confidence: 99%

Ased-Aim Analysis of Scattering by Large-Scale Finite Periodic Arrays

Li¹,

Li²,

Yeo³

2009

PIER B

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Abstract-In this paper, the Adaptive Integral Method (AIM) has been extended to characterizing electromagnetic scattering by large scale finite periodic arrays with each cell comprising of either dielectric or metallic objects, by utilizing accurate sub-entire-domain (ASED) basis function. The solution process can be carried out in two steps. In the first step, a small problem is solved in order to construct ASED basis functions to be implemented for the second step. When dielectric materials are involved in the cell which results in a large number of unknowns for the small problem, the AIM can be used to accelerate the solution process and reduce the memory requirement. In the second step, the entire problem is solved using the ASED basis function constructed in the first step. The AIM can be enhanced with the ASED basis function implemented to solve the entire problem more efficiently. When calculating the near interaction impedance matrix, computation time can be significantly reduced by using the near impedance matrix in the first step. The complexity analysis shows that the computational time is O(N 0 log N 0 ) + O(M log M ) and memory requirement is O(N 0 ) + O(M ), where N 0 denotes the number of cells and M stands for the number of elements in one cell. The results calculated respectively by the ASED-AIM and the existing AIM are then compared and an excellent agreement has been observed, which demonstrates the accuracy of the proposed method. In the meantime, memory and computational time requirements have been considerably reduced using the ASED-AIM as compared to the existing AIM. Finally, an example with over 10 million unknowns is given to demonstrate the efficiency of the proposed method.

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“…It was later extended further to solve Helmholtz equations in electromagnetic problems in radio frequency [9 10]. The precorrected-FFT method has been further developed by Yuan et al [11] analyzing scattering by, and radiation of, large microstrip antenna arrays; and by Nie et al [9,10,12] solving scattering problems of arbitrarily shaped objects based on the surface integral equations and volume integral equations [13][14][15]. As a further application, a high performance phased antenna array is designed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Design and Analysis of Phased Antenna Array With Low Sidelobe by Fast Algorithm

Yuan¹,

Yuan²,

Li³

et al. 2008

PIER

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Abstract-In this paper, a high performance phased antenna array is designed. Compared with the traditional ones, this antenna array has a lower sidelobe characteristic of down to −16 dB. At different scanning angles, the comparison between calculated and measured results of S-parameters and E-and H-plane antenna patterns is made and a very good agreement is found. Moreover, the precorrected fast Fourier transform method is employed to accelerate the entire computational process to reduce significantly both the memory requirement and computational time, but to increase the design accuracy and optimization efficiency.

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A Fast Combined Field Volume Integral Equation Solution to EM Scattering by 3-D Dielectric Objects of Arbitrary Permittivity and Permeability

Cited by 33 publications

References 18 publications

Fast Analysis of RCS Over a Frequency Band Using Pre-Corrected FFT/AIM and Asymptotic Waveform Evaluation Technique

Fast Analysis of RCS Over a Frequency Band Using Pre-Corrected FFT/AIM and Asymptotic Waveform Evaluation Technique

Ased-Aim Analysis of Scattering by Large-Scale Finite Periodic Arrays

Design and Analysis of Phased Antenna Array With Low Sidelobe by Fast Algorithm

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