Andrew F. Peterson

Improvements in the accuracy, computational cost, and reliability of computational techniques for high-frequency electromagnetics (including antennas, microwave devices and radar scattering applications) can be achieved through the use of 'high-order' techniques. This book outlines these techniques by presenting high-order basis functions, explaining their use, and illustrating their performance. The specific basis functions under consideration were developed by the authors, and include scalar and vector functions for use with equations such as the vector Helmholtz equation and the electric field integral equation. The book starts by considering the approximation of scalar functions, and explores the error in some of those representations. Singular functions (those that are unbounded) are also considered, since these often arise in practical EM problems. The authors then discuss the approximation of vector functions, and summarize the various classes of vector basis functions that have been used by the professional community. Following this, they present higher-order basis functions for the most common cell shapes used in finite element analysis procedures. Finally, they consider some of the implementation details associated with the use of these functions for integral equation/method of moments formulations and differential equation/finite element method approaches. This book provides an essential introduction to these techniques for researchers, graduate students and practicing professionals in the discipline of computational electromagnetics.

The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Vector basis functions of the divergence-conforming and curl-conforming types are explained, and specific interpolatory and hierarchical basis functions are reviewed. Procedures for mapping these basis functions from a reference domain to a curved cell, while preserving the desired continuity properties on curved cells, are discussed in detail. For illustration, results are presented for examples that employ divergence-conforming basis functions with the EFIE and curl-conforming basis functions with the MFIE. The intended audience includes electromagnetic engineers with some previous familiarity with numerical techniques.

Electrical Engineering Computational Methods for Electromagnetics A volume in the IEEE/OUP Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified and coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures. Topics covered include:*Two- and three-dimensional integral equation/method-of-moments formulations*Open-region finite-element formulations based on the scalar and vector Helmholtz equations*Finite difference time-domain methods*Direct and iterative algorithms for the solution of linear systems*Error analysis and the convergence behavior of numerical results*Radiation boundary conditions*Acceleration methods for periodic Green’s functions*Vector finite elementsDetail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries. About the IEEE/OUP Series on Electromagnetic Wave Theory Formerly the IEEE Press Series on Electromagnetic Waves, this joint series between IEEE Press and Oxford University Press offers outstanding coverage of the field, with new titles as well as reprintings and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.