V.V.S. Prakash

Efficient generation of method of moments matrices using the characteristic function method

We present a new, fast, and efficient technique for computing the MoM matrix elements from Rao-Wilton-Glisson (RWG) bases, one that does not require evaluating the usual surface integrals involving the expansion and testing functions. The matrix elements are represented in terms of characteristic functions (CFs), which can be expressed in a closed canonical form. These universal CFs make matrix generation more efficient and faster than the conventional triangular facet interaction scheme. The proposed technique can be applied for any subsectional basis functions other the RWG if the size of the basis function is small enough compared to the wavelength and the distance between the source and the testing basis functions is beyond a nominal distance. The proposed approach is validated for several canonical geometries, and the accuracy of the generated matrix elements, as well as the radar cross-section (RCS) has been verified.

RCS computation over a frequency band using the characteristic basis and model order reduction method

In many practical applications, it is desirable to analyze the radar scattering from an object over a wide frequency band. Earlier attempts to achieving a fast frequency sweep involved the computation of higher order moments of the MoM matrix, which requires considerable fill time for each frequency point when the number of unknowns is large. In this paper, we present an approach for constructing a set of universal basis functions that can be used over the entire frequency band of interest. The use of this universal basis set obviates the need to factorize the block sub-matrices at each frequency, and results in considerable time saving. The numerical accuracy and the computational advantage of the proposed technique are illustrated by studying the problem of plane wave scattering from a PEC plate over a wide frequency band.

Analysis of large finite frequency selective surfaces embedded in dielectric layers

This paper presents an efficient approach for the analysis of large finite multiple frequency selective surfaces (FSSs) embedded in dielectric layers. Numerical results are presented for two typical test cases and are validated by using an element-by-element MoM approach. The proposed approach can handle arbitrarily large arrays, and offers significant savings in computational time without compromising accuracy. For practical radomes comprising thousands of elements, the use of the direct MoM technique would be totally impractical, owing to an enormous burden imposed on computational time and memory. However, the proposed approach does not suffer from this limitation, since the computational time required by this method is virtually independent of the number of elements in the finite structure.

Multi-frontal preconditioners for iterative solvers

The integral equation formulation for the solution of Maxwells equations leads to a dense system of complex equations. Direct solution of these equations using LU factorization becomes unwieldy as the size of the scatterer increase in terms of wavelength. Iterative solvers, such as those based on Krylov projection methods, offer an alternative approach for solving large system of equations. Most often, the iterative methods are used in combination with some kind of preconditioning to improve the condition number of the system matrix A in order to achieve accelerated convergence. This paper discusses the application of multi-frontal preconditioners (MFPs) for the Krylov projection methods for an efficient solution of the dense system of linear equations. The MFP uses a combined unifrontal/multi-frontal approach to handle arbitrary sparsity patterns and enables a general fill-in reduction. The paper specifically focuses on the efficient solution of complex general systems, without making any assumptions regarding the positive definiteness of the operators. Performances of several popular Krylov projection methods are presented to demonstrate the computational efficiency of the present method, using the MFP.

Analysis of interaction between microwave antennas and frequency selective surface (FSS) radomes

The interaction between the microwave antenna and the FSS is analyzed by using a modified plane wave spectrum approach. The analysis of the antenna is carried out by using CFDTD technique in order to obtain its aperture fields which are in turn used as an excitation for the FSS. Both the aperture electric and magnetic fields of the antenna are used in deriving the spectrum. The original truncated FSS problem has been transformed into an equivalent one that renders it far more manageable to treat than its original version. This is especially true for large radomes, comprising hundreds, if not thousands of elements. The proposed method is validated by comparison with measurement. The method is completely general and can handle various types of microwave antennas, FSS elements of different shapes, and FSS radomes with arbitrary boundary truncations.

An improved iterative solution for method of moments problems in electromagnetics

The MoM formulation of Maxwells equations leads to a large dense system of complex equations. An efficient approach is presented for the solution of large dense systems of linear equations arising in the integral equation formulation of electromagnetic problems. A three-step process is introduced in which the condition number of the matrix is first improved by equilibration, and then further enhanced by preconditioning. The initial guess for the iterative solution is generated by using an extrapolation technique. It is shown that the proposed approach considerably improves the computational efficiency of iterative solvers, e.g., CGNR and GMRES, even for poorly conditioned MoM matrices with a relatively small number of unknowns.

Analysis of a Vivaldi phased array antenna using the conformal finite difference time domain (CFDTD) method

A pattern multiplication technique for analyzing large finite phased array antennas, which employs the active element distribution computed from the CFDTD, is presented in this paper. Numerically rigorous simulations of the Vivaldi array antenna demonstrate the validity of the proposed technique, even for a relatively small 7x7 array. The accuracy of the technique can be further enhanced by combining the active element pattern of the center element with those of a few representative edge elements, and this topic will be the subject of future investigation.

Efficient RCS computation for multiple incident angles using the FMM/MNM technique

We extend the MNM (Markov and Maxwell) technique, originally developed for frequency sweeping in the context of RCS computation, to speed up the iterative solution of MoM matrix equations with multiple right hand sides, corresponding to different angles of incidence. We show that the use of this technique can reduce computation time while preserving the accuracy of the solution. The MNM itself places little additional computational burden on the iteration process and usually requires less than the time required for a single iteration in the CG (conjugate gradient) process. The time-saving realized over the zero initial guess can be significant, especially when the angular increment is small, which is needed to capture rapid variations of the RCS, typically associated with large or complex scatterers.

Radiation from finite microstrip patch arrays using infinite array approach

A DFT-based technique is presented for efficient analysis of large finite phased array antennas that can handle arbitrary complex excitations of the individual elements. Numerical results are presented to demonstrate the versatility of the present approach for handling non-uniform excitations. The results of the study are reported for a representative example of a 7 /spl times/ 7 microstrip patch array, and good agreement has been found between the results derived by the DFT technique and the conventional MoM-based approach. For practical array antennas comprising of hundreds if not thousands of elements, it is not possible to use the direct MoM approach because of the extremely heavy burden on the computational time and the memory size, which can be estimated by extrapolating the corresponding requirements for the relatively small case of 7 /spl times/ 7 array reported here. In contrast to this, the proposed approach does not suffer from this limitation, since its computational complexity is almost independent of the number of elements in the finite structure.

Interpolatory basis for two-dimensional scattering problems

The problem of scattering from two-dimensional bodies continue to attract the attention of researchers, and a major focus of the research has been the reduction of the computational time. In the method of moments (MoM) formulation of the 2D scattering problem, the unknown currents are expanded in suitable basis functions and this is followed by a testing procedure. Pulse expansion and point matching is one of the preferred methods because it is both simple and computationally efficient. This method may present a bottleneck due to the singular nature of the kernel. In this paper, both the TE and TM scattering from two-dimensional conducting bodies are investigated by using interpolatory basis functions which help to circumvent this problem. Using this functions results in simplified and accurate expressions for the matrix elements in the CFIE, with out employing higher-order basis to handle the singular kernels. This approach has the simplicity of the collocation technique and yet yields an efficient solution for the surface currents. Scattering from square PEC cylinder is a model test case to see if the singular nature of the current at the 90/spl deg/ corners is indeed reproduced in the solution for the TMz illumination. Numerical results for TEz and TMz polarization have been derived and compared with those available in the literature.