Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods.

Integral Equation Methods for Electromagnetic and Elastic Waves

An overview is given over some of the most widely used numerical techniques for solving the electromagnetic scattering problem that start from rigorous electromagnetic theory. In particular, the theoretical foundations of the separation of variables method, the finite-difference time-domain method, the finite-element method, the method of lines, the point matching method, the method of moments, the discrete dipole approximation, and the null-field method (or extended boundary condition method) are reviewed, and the advantages and disadvantages of the different methods are discussed. Aspects concerning the T matrix formulation and the surface Green's function formulation of the electromagnetic scattering problem are addressed.

Numerical methods in electromagnetic scattering theory

We have developed an algorithm for computing the magnetotelluric response of three‐dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of Maxwell’s equations rather than the differential forms. This formulation does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second‐order vector diffusion equation. Rather, one must determine how averages are to be computed. Side boundary values for the H fields are obtained from putting two‐dimensional (2-D) slices of the model into a larger‐scale 2-D model and solving for the fields at the 3-D boundary positions. To solve the 3-D system of equations, we propagate an impedance matrix, which relates all the horizontal E fields in a layer to all the horizontal H fields in that same layer, up through the earth model. Applying a plane‐wave source condition and the side boundary H field values allows us to solve for the unknown fields within the model. The r...

Three-dimensional magnetotelluric modeling using difference equations­ Theory and comparisons to integral equation solutions

This work deals with the influence the presence of a person has on the performance of antennas for hand-held portable telephones. It is shown how input impedance, far-field radiation pattern, radiation efficiency, and the magnitude of the near field are affected by the presence of the human body. The investigations have been carried out by applying the finite-difference time-domain (FDTD) technique to a model of the telephone with a lambda /4 monopole antenna and a simple hand-head model of the operator. Results from this configuration are compared with results for the telephone box and antenna alone. Measurements have been performed to verify the results obtained by simulations. The results show that a shadow effect in the far-field pattern occurs in the direction of the person and that the radiation pattern, including polarization, changes considerably from the telephone with the antenna alone. The impedance results show a change in resonance frequency when the telephone is placed next to a person. Results for radiation efficiency show that close to half of the energy is absorbed by hand and head. On average a system loss of 3-4 dB should be included in a link budget, and there is considerable fading, even in a radio-anechoic chamber, when persons move around in a natural manner. >

Effects on portable antennas of the presence of a person

Numerical modeling of materials processing in microwave furnaces

Finite element and finite difference methods in electromagnetic scattering

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Finite element and finite difference methods in electromagnetic scattering