Fast analysis of scattering by arbitrarily shaped three‐dimensional objects using the precorrected‐FFT method

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

doi:10.1002/mop.10488

Cited by 39 publications

(23 citation statements)

References 7 publications

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“…The actual speed-up achieved by the P-FFT has already been demonstrated in [18] and is beyond the scope of this paper. The first example is a spherical radome of inner radius 0.9λ 0 and outer radius 1.0λ 0 .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The precorrected-FFT (P-FFT) method is a fast method associated with O(N 3/2 log N ) or less complexity. It was originally proposed by Philips and White [16,17] to solve the electrostatic integral equations associated with capacitance extraction problems and was recently extended by the present authors to the analysis of scattering by large conducting objects [18,19] and microstrip antenna arrays [20]. Like other fast algorithms, the P-FFT method also works on approximating the far-zone interactions.…”

Section: Precorrected-fft Methodsmentioning

confidence: 99%

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Fast Analysis of Electromagnetic Transmission Through Arbitrarily Shaped Airborne Radomes Using Precorrected-FFT Method

Nie¹,

Yuan²,

Li³

et al. 2005

PIER

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Abstract-A fast technique based on the Poggio, Miller, Chang, Harrington and Wu (PMCHW) formulation and the precorrected-FFT method is presented for accurate and efficient analysis of electromagnetic transmission through dielectric radomes of arbitrary shape (including airborne radomes). The method of moments is applied to solve the integral equations in which the surfaces of the radomes are modeled using surface triangular patches and the integral equations are converted into a linear system in terms of the equivalent electric and magnetic surface currents. Next, the precorrected-FFT method, a fast approach associated with O(N 1.5 log N ) or less complexity, is used to eliminate the requirement of generating and storing the square impedance matrix and to speed up the matrix-vector product in each iteration of the iterative solution. Numerical results are presented to validate the implementation and illustrate the accuracy of the method.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Precorrected-fft Methodsmentioning

confidence: 99%

Fast Analysis of Electromagnetic Transmission Through Arbitrarily Shaped Airborne Radomes Using Precorrected-FFT Method

Nie¹,

Yuan²,

Li³

et al. 2005

PIER

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“…The precorrected-FFT (pFFT) method was proposed to solve the Laplace equation for static problem of analyzing very large scale integrated circuits [17,18]. The pFFT method has then extended to solve the vectorial Helmholtz equations for electromagnetic scattering problems [19] and it has been applied successively to the solution of the SIE formulation for large conducting objects [20][21][22], and mixed conducting-dielectric objects [23,24].…”

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

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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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Fast analysis of scattering by arbitrarily shaped three‐dimensional objects using the precorrected‐FFT method

Cited by 39 publications

References 7 publications

Fast Analysis of Electromagnetic Transmission Through Arbitrarily Shaped Airborne Radomes Using Precorrected-FFT Method

Fast Analysis of Electromagnetic Transmission Through Arbitrarily Shaped Airborne Radomes Using Precorrected-FFT Method

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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