Conjugate Gradient Fast Fourier Transform Method Research Articles

Analysis of Electromagnetic Scattering from Plasma Antenna Using CG-FFT Method

A gaseous plasma column as an efficient radiator of electromagnetic waves is well known. This paper presents the scattering analysis of a plasma antenna using the conjugate gradient fast Fourier transform (CG-FFT) method. Radar cross sections (RCS) of designed plasma antenna for different plasma parameters are computed mainly. Numerical results show that the plasma antenna with appropriate parameters can offer lower RCS than the metal one. It is evident from the observed scattering characteristics that the plasma antenna can be regarded as a rod of imperfect conductor with losses.

Application of the Spatial–Spectral CG-FFT Method for the Solution of Electromagnetic Scattering by Buried Flat Metallic Objects

The conjugate gradient fast Fourier transform (CG-FFT) method to analyze electromagnetic scattering by buried flat metallic objects of arbitrary shape and large size is presented. Due to the use of FFT in the spatial domain and spectral domain to handle a spatial-domain convolution, the electric field integral equation and scattered fields can be rapidly solved without evaluations of Sommerfeld integrals. The accuracy of this algorithm is better than that of the conventional CG-FFT method, and the CPU time required for this algorithm is reduced to a minimum, while memory cost is order of N (the total cell number) and computational complexity is of order N log N in each iteration

The CGFFT method with a discontinuous FFT algorithm

AbstractIn the conjugate gradient–fast Fourier transform (CGFFT) method, the FFT is used to evaluate the convolution integrals. When the function to be transformed has discontinuities, the accuracy of the FFT results, and thus the CGFFT results, will degrade. In this letter, an efficient FFT algorithm is developed for discontinuous functions with both uniform and nonuniform sampled data, with O(Np+N log N) complexity, where N is the number of sampling points and p is the interpolation order. The algorithm is incorporated into the CGFFT method. Numerical results for slabs demonstrate the efficiency and accuracy of the new FFT and CGFFT algorithms. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 47–49, 2001.

The hybrid extended Born approximation and CG-FFT method for electromagnetic induction problems

The authors propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier transform (CG-FFT) method to improve the efficiency of numerical solution of electromagnetic induction problems. This combination improves the solution efficiency in two ways. First, using the FFT in the extended Born approximation decreases the computational cost of the conventional EBA method from O(N/sup 2/) to O(N log/sub 2/ N) arithmetic operations, where N is the number of unknowns in the problem. This approach, referred to as the FFT-EBA method, applies to problems with a fairly large contrast. Secondly, using the EBA as a partial preconditioner for the CG-FFT method increases the convergence speed of the conventional CG-FFT method. This second approach, referred to as the EBA-CGFFT method, is in principle applicable to all problems with a homogeneous background, but is particularly efficient for problems with a higher contrast. Numerical experiments suggest that the combination of these two methods is more accurate and more efficient for electromagnetic induction problems.

Application of preconditioned CG-FFT technique to method of lines for analysis of the infinite-plane metallic grating

In this paper, both the fast Fourier transform (FFT) and the preconditioned CG technique are first introduced into the method lines (MOL) to further enhance the computational efficiency of this semianalytic method. Electromagnetic wave scattering by an infinite-plane metallic grating is used as examples to describe its implementation. For an arbitrary incident wave, the Helmholtz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by the FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution involving the computational complexity O(N log N). The banded diagonal impedance matrix is selected as a preconditioner to speed up the convergence rate of the CG algorithm. Our numerical results show that the PCG–FFT method converges to an accurate solution in a much smaller CPU time. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 24: 170–175, 2000.

Application of Adaptive Integral Method To Scattering and Radiation Analysis of Arbitrarily Shaped Planar Structures

The adaptive integral method (AIM) is applied to the scattering and radiation analysis of arbitrarily shaped planar structures. The method extends the well-known conjugate gradient fast Fourier transform (CGFFT) method to the triangular subdomain discretization, which has a much better geometry modeling capability than the rectangular subdomain discretization employed in the traditional CGFFT method. The resulting algorithm has a memory requirement proportional to O(N) and the operation count for the matrix-vector multiplication proportional to O(N log N). Numerical results are presented to demonstrate the efficiency and accuracy of this method.

2-D validation of a formulation for the analysis of 3-D bodies that are periodic in one direction and finite sized in the others

A numerical scheme to analyze three-dimensional bodies that are periodic in one direction (z) and finite sized in the other ones (x, y) is presented. The geometry and material composition of the body can be arbitrary. A new formulation using the conjugate gradient-fast Fourier transform method (CG-FFT) has been developed. The formulation is based on the discretization and resolution of the electric field integral equation (EFIE) in both the real and spectral domains and leads to an efficient and accurate numerical procedure. Results are presented for RCS, equivalent currents and fields inside 3-D periodic structures (infinitely long cylinders with arbitrary shape and material composition). These results are compared with analytical solutions and the agreement is found to be good.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of microstrip S-parameters using a CG-FFT scheme

Several open microstrip structures have been analyzed by using the conjugate gradient fast Fourier transform (CGFFT) method to solve the electric field integral equation (EFIE). The analysis of the microstrip structure provides equivalent electric currents on the conducting patches. Extensive computation is performed in the spectral domain. Windowing techniques are used to improve the accuracy of the method. New models for the microstrip feed and load have been developed in combination with the CGFFT method. Results for the S-parameters are compared with the results of other methods and with measurements. The method appears to be accurate and computationally efficient.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Biconjugate Gradient FFT Solution for Scattering by Planar Plates

ABSTRACT An efficient numerical solution of the scattering by planar perfectly conducting or resistive plates is presented. The electric field integral equation is discretized using roof–top subdo–main functions as testing and expansion basis and the resulting system is solved via the biconjugate gradient (BiCG) method in conjunction with the fast Fourier transform (FFT). Unlike other formulations employed in conjunction with the conjugate gradient FFT (CG–FFT) method, in this formulation the derivatives associated with the dyadic Green's function are transferred to the testing and expansion basis, thus reducing the singularity of the kernel. This leads to substantial improvements in the convergence of the solution as demonstrated by the included results.

A Combined Finite Element-Boundary Element Formulation for Solution of Two-Dimensional Problems via CGFFT

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Spectral domain analysis of conducting patches of arbitrary geometry in multilayer media using the CG-FFT method

A conjugate gradient-fast Fourier transform (CG-FFT) scheme for analyzing finite, flat, metallic patches in multilayer structures is presented. Rooftop and razor-blade functions are considered as basis and testing functions, respectively. An equivalent periodic problem in both domains (real and spectral) is obtained and solved. Aliasing problems are avoided by performing a window on the Green's function. The spectral domain periodicity makes it feasible to take into account almost all the harmonics and to reduce the ripple in the computed current distributions. Nearly all the operations are performed in the spectral domain, including Green's function computations. Several results of convergence rates, current distributions and radar cross-section (RCS) values are given and compare favorably with measurements or results obtained by other methods. >

A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform

A numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described. The RCS is obtained by solving the electric-field integral equation (EFIE) using the conjugate gradient-fast Fourier transform method (CG-FFT). The choice of a suitable set of basis and testing functions to discretize the EFIE leads to a very accurate and computationaly efficient CG-FFT procedure. This accuracy is checked by comparison with RCS measurements or predictions by other methods. As compared to the moment method, this CG-FFT scheme avoids the storage of large matrices and reduces the computer time by orders of magnitude. >

On the Formulation and Implementation of a Conjugate Gradient FFT Method

Criteria are established for choosing the best way to formulate and implement a conjugate gradient FFT (fast Fourier transform) method. Also, the issues of speed and convergence are addressed in co...