An integral equation-fast Fourier transform-based hybrid method for analysis of wire-surface configurations on electrically large platforms

2008 ◽  
Vol 51 (2) ◽  
pp. 486-490 ◽  
Author(s):  
Xiang An ◽  
Zhi-Qing Lü
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Hybrid Method ◽  
Wire Surface

Iterative magnetic forward modeling for high susceptibility based on integral equation and Gauss-fast Fourier transform

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. J1-J13 ◽  
Author(s):  
Fang Ouyang ◽  
Longwei Chen
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Extreme Case ◽  
Computational Time ◽  
Acceptable Result ◽  
Iterative Computation ◽  
Wide Range ◽  
Numerical Precision ◽  
Complex Target

Self-demagnetization due to strongly magnetic bodies can seriously affect the interpretation of magnetic anomalies. Conventional numerical methods often neglect the self-demagnetization effects and limit their use to low susceptibilities ([Formula: see text]). We have developed a novel iterative method based on the integral equation and the Gauss-fast Fourier transform (FFT) technique for calculating the magnetic field from finite bodies of high magnetic susceptibility and arbitrary shapes. The method uses a segmented model consisting of prismatic voxels to approximate a complex target region. In each voxel, the magnetization is assumed to be constant, so that the integral equation in the spatial domain can reduce to a simple form with lots of merit in numerical calculation after the 2D Fourier transform. Moreover, a contraction operator is derived to ensure the convergence of the iterative calculation, and the Gauss-FFT technique is applied to reduce numerical errors due to edge effects. Our modeling results indicate that this new iterative scheme performs well in a wide range of magnetic susceptibilities (1–1000 SI). For lower susceptibilities ([Formula: see text]), the iterative algorithm converges rapidly and indicates very good correlation with the analytical solutions. At higher susceptibilities ([Formula: see text]), our method still performs well, but the numerical accuracy improves with a relatively slow speed. In the extreme case ([Formula: see text]), an acceptable result is also obtained after sufficient iterative computation. A further improvement in the numerical precision can be achieved by increasing the number of prismatic voxels, but at the same time, the computational time increases linearly with the size of the voxels.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document