Floating Interpolation Stencil Topology-Based Ie-FFT Algorithm

Yin, Jianpeng; Hu, Jun; Nie, Zaiping; Feng, Xiaobing; He, Shiquan

doi:10.2528/pierm10103104

Cited by 5 publications

(9 citation statements)

References 20 publications

(24 reference statements)

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“…can be approximately written as (20) Substituting (20) into (18), we can have (21) where is a sparse matrix. The detailed steps for acquiring are similar to those in the next subsection.…”

Section: A the Center Difference Quotient Scheme (Cdqs)mentioning

confidence: 99%

“…The expression (20) has implicitly given us an approach that the Green's function's values at the nodes within a box can be used to fit the gradient of the Green's function. We are now going to transform the discrete Gradient function in (18) into the discrete Green's function.…”

Section: B the Two-step Fitting Scheme (Tsfs)mentioning

confidence: 99%

“…The authors interpolated the Green's function onto the nodes of a uniform Cartesian grid by Lagrange polynomials and provided a realization of the IE-in-FFT with this line of thought for the electric field integral equation (EFIE). Further researches on the IE-FFT for the EFIE can be found in [19], [20]. Shortly after [18], a version of the IE-FFT for the combined field integral equation (CFIE) was proposed in [21], being followed by our version with higher accuracy in [22].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

Xie

Zhou

Wang

et al. 2013

IEEE Trans. Antennas Propagat.

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In this paper, a novel realization of the Integral Equation in combination with the fast Fourier transform for the CFIE is established by Fitting both the Green's function and its Gradient onto the nodes of a uniform Cartesian grid. The new method has been compared with several existing popular FFT-based methods, including the AIM, the IE-FFT, and the p-FFT. The accuracy of the proposed method is significantly higher than other FFT-based methods, and the method is not sensitive to both the grid spacing and the expansion order. The outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions. Therefore, when the higher order basis functions would be adopted in the method of moments, only one fitting procedure for the Green's function and its gradient on a basis function support is needed to meet all of basis functions defined on this support. Some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method.

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“…can be approximately written as (20) Substituting (20) into (18), we can have (21) where is a sparse matrix. The detailed steps for acquiring are similar to those in the next subsection.…”

Section: A the Center Difference Quotient Scheme (Cdqs)mentioning

confidence: 99%

Section: B the Two-step Fitting Scheme (Tsfs)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

Xie

Zhou

Wang

et al. 2013

IEEE Trans. Antennas Propagat.

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“…7 Nevertheless, due to the singular nature of the GF, parts of G that are associated with near interactions produce inaccurate results and this effect has to be corrected by means of corrections applied to the NF matrix Z near . 32,39 To alleviate any ambiguity, we define the NF interactions as (1) those occurring between the currents inside a box and themselves (2) those occurring between the currents inside a box and currents residing in its immediate neighboring boxes. The definition is easily generalized to include boxes not just in the immediate but also farther neighborhood.…”

Section: Comparison To Ie-fftmentioning

confidence: 99%

Array Integral Equation-Fast Fourier Transform Solver for Simulation of Supercells and Aperiodic Penetrable Metamaterials

Ansari-Oghol-Beig¹,

Mosallaei²

2015

j comput theor nanosci

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A hybrid surface integral equation solver based on the hierarchical matrix, the integral equation fast Fourier transform method and the equivalent surface method is developed for simulation of (pseudo-) periodic optical metamaterial problems. The solver is typically suitable for problems with (1) large periodic supercell or aperiodic cell arrays, (2) dominance of near field interactions, (3) presence of deep subwavelength features and (4) high geometry surface to volume ratio. An integral equation accelerator is introduced which uses a four to six level block Toeplitz matrix structure which naturally maps to the pseudo-periodic structure of metamaterial array problems, eliminates the need for the correction process encountered in fast Fourier transform-based methods and leads to substantial recycling of near field matrices. Novel metamaterial designs such as a supercell metamaterials, an aperiodic metasurfaces an a surface Luneburg lens are presented and solved, verifying the efficiency and accuracy of the presented model.

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“…The traditional fast algorithms of MoM include three categories: methods based on the addition theorem [2][3][4], methods based on Fast Fourier Transformation (the FFT-based methods) [5][6][7], and the methods based on matrix-compression algorithm [8][9][10]. Due to its high universality, the FFT-based methods are widely used and studied in depth [11,12].…”

Section: Introductionmentioning

confidence: 99%

A Novel Scheme with FG-FFT for Analysis of Electromagnetic Scattering from Large Objects

Xie

Pang

et al. 2017

International Journal of Antennas and Propagation

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The replacement values to the singularity of fitting Green's function are intensively researched in Fitting Green's function Fast Fourier Transformation (FG-FFT). As is shown in the research, the accuracy of fitting Green's function of near element is affected by different replacement values. The experiments show that an appropriate replacement value can improve the accuracy of fitting Green's function of near element, and it is called the optimal replacement value in this paper. In the case of application of the proposed scheme to FG-FFT, the number of the near correction elements is significantly reduced. Therefore, the optimal replacement scheme can dramatically reduce the memory requirement and computing time in FG-FFT. The experiments show that, compared with traditional random replacement schemes, the optimal replacement scheme can reduce the number of the near correction elements by about 55%∼60% and greatly improve the computational efficiency of FG-FFT.

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Floating Interpolation Stencil Topology-Based Ie-FFT Algorithm

Cited by 5 publications

References 20 publications

A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

Array Integral Equation-Fast Fourier Transform Solver for Simulation of Supercells and Aperiodic Penetrable Metamaterials

A Novel Scheme with FG-FFT for Analysis of Electromagnetic Scattering from Large Objects

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