scholarly journals Fitting Green’s Function FFT Acceleration Applied to Anisotropic Dielectric Scattering Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Shu-Wen Chen ◽  
Feng Lu ◽  
Yao Ma
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Volume Integral ◽  
Scattering Problems ◽  
Volume Integral Equation ◽  
Anisotropic Dielectric

A volume integral equation based fast algorithm using the Fast Fourier Transform of fitting Green’s function (FG-FFT) is proposed in this paper for analysis of electromagnetic scattering from 3D anisotropic dielectric objects. For the anisotropic VIE model, geometric discretization is still implemented by tetrahedron cells and the Schaubert-Wilton-Glisson (SWG) basis functions are also used to represent the electric flux density vectors. Compared with other Fast Fourier Transform based fast methods, using fitting Green’s function technique has higher accuracy and can be applied to a relatively coarse grid, so the Fast Fourier Transform of fitting Green’s function is selected to accelerate anisotropic dielectric model of volume integral equation for solving electromagnetic scattering problems. Besides, the near-field matrix elements in this method are used to construct preconditioner, which has been proved to be effective. At last, several representative numerical experiments proved the validity and efficiency of the proposed method.

Green’s Function Integral Equation Methods for Electromagnetic Scattering Problems

2018 ◽  
pp. 197-250
Author(s):  
Andrei V. Lavrinenko ◽  
Jesper Lægsgaard ◽  
Niels Gregersen ◽  
Frank Schmidt ◽  
Thomas Søndergaard
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Scattering Problems ◽  
Integral Equation Methods

The efficient implementation of IE-FFT algorithm with combined field integral equation for solving electromagnetic scattering problems

2020 ◽  
pp. 1-7
Author(s):  
Seung Mo Seo
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Cartesian Grid ◽  
Memory Storage ◽  
Scattering Problems ◽  
Cpu Time ◽  
Interaction Terms ◽  
Field Integral

Abstract An integral equation-fast Fourier transform (IE-FFT) algorithm is applied to the electromagnetic solutions of the combined field integral equation (CFIE) for scattering problems by an arbitrary-shaped three-dimensional perfect electric conducting object. The IE-FFT with CFIE uses a Cartesian grid for known Green's function to considerably reduce memory storage and speed up CPU time for both matrix fill-in and matrix vector multiplication when used with a generalized minimal residual method. The uniform interpolation of the Green's function on an equally spaced Cartesian grid allows a global FFT for field interaction terms. However, the near interaction terms do not take care for the singularity of the Green's function and should be adequately corrected. The IE-FFT with CFIE does not always require a suitable preconditioner for electrically large problems. It is shown that the complexity of the IE-FFT with CFIE is found to be approximately O(N1.5) and O(N1.5log N) for memory and CPU time, respectively.

scholarly journals VIE-FG-FFT for Analyzing EM Scattering from Inhomogeneous Nonmagnetic Dielectric Objects

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shu-Wen Chen ◽  
Hou-Xing Zhou ◽  
Wei Hong ◽  
Jia-Ye Xie
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Cartesian Grid ◽  
Volume Integral ◽  
Grid Spacing ◽  
Em Scattering ◽  
Volume Integral Equation ◽  
Numerical Examples ◽  
Dielectric Objects

A new realization of the volume integral equation (VIE) in combination with the fast Fourier transform (FFT) is established by fitting Green’s function (FG) onto the nodes of a uniform Cartesian grid for analyzing EM scattering from inhomogeneous nonmagnetic dielectric objects. The accuracy of the proposed method is the same as that of the P-FFT and higher than that of the AIM and the IE-FFT especially when increasing the grid spacing size. Besides, the preprocessing time of the proposed method is obviously less than that of the P-FFT for inhomogeneous nonmagnetic dielectric objects. Numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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