a 'sleeper', receiving only modest attention for 50 years before emerging as a cornerstone of communications engineering in more recent times. Roughly one in six of Walsh's 281 publications are included, photographically reproduced. Reproduction is excellent except for one paper from 1918. The book also reproduces three brief papers about Walsh and his work, by W. E. Sewell, D. V. Widder and Morris Marden. The first two were written for a special issue of the SIAM Journal celebrating Walsh's 70th birthday; the third is an obituary.

Matrix iterative analysis (2nd edn), by Richard S. Varga. Springer Series in Computational Mathematics 27. Pp. 358. £55. 2000. ISBN 3 540 66321 5 (Springer Verlag).

A vector H -field finite-element method has been used for the solution of optical waveguide problems. The permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless. To extend the domain of the field representation, infinite elements have been introduced. To eliminate spurious solutions and to improve eigenvectors, a penalty function method has been introduced. To show the validity and usefulness of this formulation, computed results are illustrated for step channel waveguide, diffused channel waveguide, anisotropic channel waveguide, and channel waveguide directional couplers.

Finite-element solution of integrated optical waveguides

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

The finite element method is a well-established method for the solution of a wide range of guided wave problems. One drawback associated with the powerful vector formulation is the appearance of spurious or nonphysical solutions. A penalty function method has been introduced to the finite element formulation, to reduce or eliminate spurious solutions. It also improves the quality of the physical field solutions. The method has been applied for the solution of metallic homogeneous and inhomogeneous guides, and integrated optics guides.

Penalty Function Improvement of Waveguide Solution by Finite Elements

The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics. Nevertheless, computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides. Although our primary interest is with the computational methods, there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and, in addition, are of interest in themselves. These results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds. Some of the more powerful techniques available are illustrated by applying them to a model problem.

/pdf/eigenvalues-of-the-laplacian-in-two-dimensions-21xy0ib3p2.pdf

Eigenvalues of the Laplacian in Two Dimensions

Improving the modified Gauss-Seidel method for Z-matrices

Dispersion characteristics for open-typed dielectric waveguide structures operated at millimeter-and submillimeter-wave frequencies are calculated by a finite-element iterative procedure with a given criterion on the maximum field strength at the virtual boundary. Numerical results for a rectangular dielectric image guide are presented and compared with results from other methods. The strip dielectric guide and the insulated image guide with finite- or infinite-width substrates are also analyzed.

Analysis of Open-Type Dielectric Waveguides by the Finite-Element Iterative Method

We extend the modified Gauss-Seidel method introduced by A. D. Gunawardena et al. Some numerical examples show that our method is able to improve the rate of convergence compared to the modified Gauss-Seidel method.

Hiroshi Niki

Papers

Improving the modified Gauss-Seidel method for Z-matrices

Analysis of Open-Type Dielectric Waveguides by the Finite-Element Iterative Method

Adaptive gauss-seidel method for linear systems

A comparison theorem for the iterative method with the preconditioner (I + S max )

Accelerated iterative method for Z-matrices