Hristos T. Anastassiu

Aspects of the Method of Auxiliary Sources (MAS) in computational electromagnetics

The method of auxiliary sources (MAS) is a numerical technique, alternative to the standard surface integral-equation formulation, suitable for solving elliptic boundary-value problems appearing in electromagnetic scattering analysis, antenna modeling, waveguide structures, etc. This paper provides an overview of MAS as applied to computational electromagnetics. The fundamentals of MAS are presented and its advantages over the method of moments are highlighted, while special emphasis is given to a number of advanced issues. Moreover, a selection of recent developments in the method is presented, with a detailed description of several challenging topics. Finally, the potential applicability of the method to a broader range of problems is contemplated.

A review of electromagnetic scattering analysis for inlets, cavities, and open ducts

This paper is a review of all methods that have been used in the literature for the solution of a very important and challenging set of problems, namely electromagnetic scattering from inlets, cavities, and open ducts. The techniques examined have been grouped together according to their fundamental principles, so that easy and direct comparisons among them are facilitated. The complexity and difficulty of the problems are clearly inferred from the very long list of references, which includes several very recent articles. The purpose of the paper is to highlight the advantages and limitations of the techniques invoked, draw useful conclusions, and trigger initiatives for future improved approaches to the topic.

Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary condition (SIBC)

A novel combination of the method of auxiliary sources (MAS) and the standard impedance boundary condition (SIBC) is employed in the analysis of transverse magnetic (TM) plane wave scattering from infinite, coated, perfectly conducting cylinders with square cross sections. The scatterer is initially modeled by a SIBC surface and the scattering mechanism is subsequently analyzed via MAS. Although SIBC as well as MAS possess theoretical limitations with regard to an edge, the numerical results show that the MAS/SIBC method provides results of high accuracy for a range of structures with edges. The SIBC modeling of coated conductors with edges has previously been investigated in the literature and thus, this work focuses on comparing MAS and the method of moments (MoM) for SIBC surfaces (MoM/SIBC). A detailed complexity analysis shows that the MAS/SIBC method is, under certain conditions, more efficient than the MoM/SIBC method, proving that the proposed novel combination is a powerful and advantageous computational tool.

Electromagnetic scattering from simple jet engine models

The mode-matching (MM) technique is employed for the evaluation of the radar cross section (RCS) of structures that simulate a jet engine inlet. The geometry consists of a perfectly conducting cylindrical inlet terminated by an array of blades mounted on a cylindrical hub. Comparisons of numerical results with actual measurements are presented for the first time.

Accuracy analysis and optimization of the method of auxiliary sources (MAS) for scattering by a circular cylinder

This paper presents a rigorous accuracy analysis of the method of auxiliary sources (MAS), when applied to scattering problems. A benchmark, canonical geometry, consisting of a perfectly conducting, infinite, circular cylinder, is chosen for clarity and simplicity. For this particular structure it is shown that the MAS square matrix can be inverted analytically, yielding exact mathematical expressions for the discretization error and the condition number of the pertinent linear system. It is also demonstrated that the error increases very abruptly for source locations associated with the characteristic eigenvalues of the scattering geometry, precisely as predicted in theory. Various plots depict comparisons between analytical and computational data for the boundary condition error, and all occurring discrepancies are fully explained. Among several important results of the analysis, the fundamental MAS question concerning the optimal location of the auxiliary sources is thoroughly investigated and resolved on the grounds of error minimization.

Scattering from planar structures containing small features using the adaptive integral method (AIM)

Fast integral equation algorithms such as the adaptive integral method (AIM) have been demonstrated to reduce memory and execution time associated with moment-method solutions for arbitrarily shaped three-dimensional (3-D) geometries. In this paper, we examine the efficiency of AIM in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas. Such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns. AIM with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries. In the latter part of the paper, we demonstrate the application of AIM in connection with a finite-element boundary-integral formulation for cavity-backed antennas.

An improved accuracy version of the method of auxiliary sources for computational electromagnetics

The method of auxiliary sources (MAS) is normally applicable to electromagnetic problems involving structures of significant thickness, so that an adequately large distance between source and collocation points is guaranteed. For thin or open geometries the accuracy of the method is depleted, due to numerical instabilities caused by the highly singular terms of the dyadic Greens function (DGF). In this paper a modified MAS (MMAS) is developed to circumvent this particular difficulty. Higher order terms of the DGF are numerically calculated by introducing a canonical grid, where derivatives can be accurately computed via a discrete scheme, unlike standard MAS, where the DGF analytical, problematic expression is invoked instead. This procedure is equivalent to the involvement of auxiliary currents and charges in the solution, instead of the elementary source fields used in standard MAS.

ERROR ESTIMATION OF THE METHOD OF AUXILIARY SOURCES (MAS) FOR SCATTERING FROM AN IMPEDANCE CIRCULAR CYLINDER

The purpose of this paper is a rigorous error estimation of the Method of Auxiliary Sources (MAS),when the latter is applied to electromagnetic scattering from a circular,coated,perfectly conducting cylinder,assumed to satisfy the Standard Impedance Boundary Condition (SIBC). The MAS matrix is inverted analytically, via eigenvalue analysis,and an exact expression for the discretization error in the boundary condition is derived. Furthermore,an analytical formula for the condition number of the linear system is also extracted, in addition to an asymptotic estimate for large scatterers,explaining the irregular behavior of the computational error resulting from numerical matrix inversion. Finally,the optimal location of the auxiliary sources is determined,on the grounds of error minimization.

Scattering from relatively flat surfaces using the adaptive integral method

The adaptive integral method is applied to electromagnetic scattering from relatively flat, perfectly conducting surfaces. It is demonstrated that for nearly flat scatterers, as is the case with corrugated geometries and rough surfaces, the memory requirements and complexity of the technique are extremely low. Furthermore, for such geometries the algorithm can be effectively parallelized without excessive effort. Several numerical results are included, proving the accuracy and computational efficiency of the method.

The mode matching technique for electromagnetic scattering by cylindrical waveguides with canonical terminations

The Mode Matching Technique is employed for the evaluation of the Radar Cross-Section (RCS) of cylindrical inlets terminated by a perfectly conducting cylindrical hub or a cylindrical array of grooves that may be straight or curved. In the case of curved grooves, the geometry is analyzed via the generalized transmission line theory and a closed form solution is given for the first time. The method is formally exact, and yields accurate RCS patterns for geometries that have not been previously investigated. Analytical expressions are derived for the coupling factors between the various modes and RCS results are presented which may be used as a reference in validating other, more general numerical techniques.