Real-Coefficient FGG-Fg-FFT for the Combined Field Integral Equation

Abstract

Abstract-This article proposes a new scheme of real-coefficient fitting both Green's function and its gradient with Fast Fourier Transform (RFGG-FG-FFT) for combined field integral equation (CFIE) to compute the conducting object's electromagnetic scattering, which improves original fitting both Green's function and its gradient with Fast Fourier Transform (FGG-FG-FFT) on efficiency. Firstly, based on Moore-Penrose generalized inverse, an equivalent form of fitting matrix equation is obtained containing the property of Green's function's integral proved by addition theorem. Based on this property, with truncated Green's function new fitting technique is presented for computing fitting coefficients with real value expression, which is different from complex value expression by the original fitting technique in FGG-FG-FFT. Numerical analysis of error shows that new fitting technique has the same accuracy, but only one half of sparse matrices' storage compared to the original fitting technique in FGG-FG-FFT. Finally, the new scheme combining FGG-FG-FFT and new fitting technique is constructed. Some examples show that the new scheme is accurate and effective compared to FGG-FG-FFT and p-FFT.

Rof for the Combined Field Integral Equation

“…Assume R m = r m + 0.05λ, λ is the wavelength in free space. {r t } Te 1 are testing points located on S m , which are chosen according to [12]. So Green's function and its gradient can be expressed as:…”

“…According to the interaction between basis functions, resultant impedance matrix can be split into two parts of near-field interaction and far-field interaction [12]:…”

“…Among the latter methods, Integral Equation with FFT (IE) [9] projects Green's function on Cartesian Grid nodes by Lagrange interpolation; however, computation precision is not high. Aiming at improving precision, Fitting Green's function's Gradient and Fitting Green's function with FFT (FGG) [11] is proposed utilizing fitting method, whose coefficients are expressed by complex values [12]. For transforming complex fitting coefficients into real coefficients, the authors proposed real-coefficient fitting method [12], which can reduce half storage requirement of fitting coefficient and accelerate solving process.…”

“…Aiming at improving precision, Fitting Green's function's Gradient and Fitting Green's function with FFT (FGG) [11] is proposed utilizing fitting method, whose coefficients are expressed by complex values [12]. For transforming complex fitting coefficients into real coefficients, the authors proposed real-coefficient fitting method [12], which can reduce half storage requirement of fitting coefficient and accelerate solving process. Usually, all of FFT-based algorithms need a cube-like grid enclosing source/field points, so that basis functions or Green's functions can be expressed by the linear combination of the ones on this cube-like grid.…”

“…Secondly, reduced order grid or the cross-shaped grid different from original grid is proposed to reduce the modified products' number concerning near-field coupling impedances. Reduced order grid is very suitable for fitting method [11,12] rather than Lagrange interpolation in IE due to low precision of the interpolation method. Thirdly, by combining new fitting method and reduced order grid, a new scheme of ROF is presented.…”