A wideband fast integral equation solver combining multilevel fast multipole and multilevel Green's function interpolation method with fast Fourier transform acceleration

2011 ◽  
Author(s):  
Dennis T. Schobert ◽  
Thomas F. Eibert
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Green’S Function ◽  
Green's Function ◽  
Interpolation Method ◽  
Fast Multipole

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.

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

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