Recursive algorithms for computational electromagnetics
Abstract
Efficient and fast recursive algorithms for both the spectraldomain and the spacedomain solutions of the electromagnetic scattering problems have been developed. These algorithms have less than O(N(sup 3)) computational complexities and less than O(N(sup 2)) memory requirements for arbitrary geometries of scatterers clustered together. Although the algorithms are discussed as they are applied to the electromagnetic scattering problems, their domains of applicability can be extended to other types of electromagnetic problems (e.g., guidance, resonance, and radiation) and also to other types of field and wave equations (e.g., acoustic, elastic, and Schrodinger). The applications of these algorithms to the conducting strip and patch geometries have been demonstrated. Dielectric and magnetic materials can also be incorporated into conductor geometries. Due to the availability of the spectral Green's function, spectraldomain algorithms can efficiently handle geometries consisting of an arbitrary number of infinitely thin, conducting strips and flat patches of any shape embedded in arbitrarily layered media, in which the layers are infinitely large in the transverse directions. On the other hand, the spacedomain algorithms presented in this dissertation are the recursive Tmatrix algorithms, and due to the nature of the Tmatrix formulations, they can easily handle geometries consisting of conductors, dielectrics and magnetic materials of finite size. Therefore, various problems defined in broad classes of geometries can be solved with these spectraldomain and spacedomain algorithms. A recursive implementation of the method of moments is also presented. This algorithm is based on the principle of inversion of a general matrix by partitioning. Since it is a recursive algorithm, and since each recursion step requires O(N(sup 2)) operations, it can efficiently solve the problems in which one has to modify or perturb some parts of a main body whose solution is already known. When solving the electromagnetic scattering problem, these algorithms give the fullwave solution without having to make any approximations. Being computational algorithms, they are 'exact' in the numerical sense. These algorithms also give the solution for all possible incident waves or 'righthand sides' at once, a property that is not shared by some other fast solution techniques such as the conjugategradient method. Futhermore, as opposed to some other formulation schemes such as the finiteelement method, these algorithms naturally incorporate the radiation condition at infinity; therefore, they can handle geometries in unbounded media.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT........32G
 Keywords:

 Algorithms;
 Computer Programs;
 Electromagnetic Radiation;
 Electromagnetic Scattering;
 Electromagnetism;
 Wave Equations;
 Waveguides;
 Dielectrics;
 Green'S Functions;
 Magnetic Materials;
 Communications and Radar