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

In aerosol science today light scattering simulations are regarded as an indispensable tool to develop new particle characterization techniques or in solving inverse light scattering problems. Light scattering theories and related computational methods have evolved rapidly during the past decade such that scattering computations for wavelength sized nonspherical scatterers can be easily performed. This significant progress has resulted from rapid advances in computational algorithms developed in this field and from improved computer hardware. In this paper a review of the recent progress of light scattering theories and available computational programs is presented. We will focus on exact theories and will not cover approximate methods such as geometrical optics. Short outlines of the various theories are given alongside with informations on their capabilities and restrictions.

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Light scattering theories and computer codes

A version of the finite-difference time-domain method adapted to the needs of S-matrix calculations of microwave two-dimensional circuits is presented. The analysis is conducted by simulating the wave propagation in the circuit terminated by matched loads and excited by a matched pulse source. Various aspects of the method's accuracy are investigated. Practical computer implementation of the method is discussed, and an example of its application to an arbitrarily shaped microstrip circuit is presented. It is shown that the method in the proposed form is an effective tool of circuit analysis in engineering applications. The method is compared to two other methods used for a similar purpose, namely the contour integral method and the transmission-line matrix method. >

Analysis of arbitrarily shaped two-dimensional microwave circuits by finite-difference time-domain method

A finite-difference time-domain (FD-TD) formulation is described. It is shown that the finite-difference time-domain formulation is equivalent to the symmetrical condensed node model used in the transmission line matrix (TLM) method. The TLM method can be formulated exactly in a finite-difference form in terms of total field quantities. It is shown that, due to a better field resolution and fulfilment of continuity conditions, the FD-TD formulation or its TLM equivalent model give better convergence and accuracy than the traditional FD-TD method. This is illustrated by numerical results pertaining to a finned waveguide. >

A new finite-difference time-domain formulation and its equivalence with the TLM symmetrical condensed node

The general dispersion relations are derived for the 2-D TLM shunt and series meshes and the 3-D TLM expanded and condensed node meshes. Implicit in the resulting dispersion relations are both their physical and spurious modal solutions. It is demonstrated that of the four schemes, only the 3-D expanded node mesh is free of detrimental spurious solutions. >

Generalized dispersion analysis and spurious modes of 2-D and 3-D TLM formulations

It is shown that if the expanded node three-dimensional TLM method is operated in a certain way, then it can be numerically equivalent to a finite-difference method. Some comments are made on comparisons between the two approaches.

On the Relationship Between TLM and Finite-Difference Methods for Maxwell's Equations (Short Paper)

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On the Relationship Between TLM and Finite-Difference Methods for Maxwell's Equations (Short Paper)