Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.

Numerical Techniques in Electromagnetics, Second Edition

A vector H-field formulation is developed for electromagnetic wave propagation for a wide range of guided-wave problems. It is capable of solving microwave or optical waveguide problems with arbitrarily anisotropic materials. We have introduced infinite elements to extend the region of explicit field representation to infirdly, to consider open-type waveguides more accurately. Computed results are given for a variety of optical planar guides, image lines, and waveguides containing skew anisotropic dielectic.

Finite-Element Analysis of Optical and Microwave Waveguide Problems

This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.

Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

This paper presents a review of finite element open boundary techniques for the computation of static and quasistatic electromagnetic fields. The underlying assumptions and ideas behind these techniques are outlined and explained. The advantages and shortcomings of each technique are discussed. The goal of this review is to aid those working on numerical solutions of open boundary problems using the finite element method to gain perspectives on the variety of techniques presently available or being developed. This review is also intended to facilitate the communication of numerical techniques between the low-frequency field computation community and those in the high-frequency community.

A review of finite element open boundary techniques for static and quasi-static electromagnetic field problems

The method of infinite elements is briefly reviewed. New more logical and general formulations of infinite elements are presented. The simplicity of the programming is emphasized. Results are given for elasticity and potential problems. Future extensions are discussed.

More on infinite elements

Electric- and magnetic-field problems with boundaries at infinity are treated in finite-element terms by constructing an element to model an extremely large annulus surrounding the region of interest. A simple recursion technique is employed to generate the matrix representing the annular region. All nodes are eliminated from the external element except those on its inner surface, so that the final matrix is no larger than that required to describe the region of interest only. The method is simpler to program and requires less computing effort than boundary-integral techniques. It has been tested by solving several 2-dimensional magnetostatic and electrostatic problems and comparing the results with analytic solutions. The method can be applied to any 2-dimensional field problem bounded by a large empty region in which the field satisfies Laplace's equation.

C. J. Carpenter

Papers

Exterior finite elements for 2-dimensional field problems with open boundaries

Phase velocity equalization in microstrip couplers by partial dielectric overlays