Accurate Computation of Mathieu Functions

This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Introduction.- Mathieu Functions.- Observed Accuracy Using Traditional and Tuned Methods.- Recommended Algorithm for Mathieu Function Computation.- Electromagnetic Scattering from Conducting Elliptic Cylinders.- Electromagnetic Scattering from an Infinite Conducting Strip.- References.- Authors' Biographies.

Andrew F. Peterson received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from the University of Illinois, Urbana-Champaign in 1982, 1983, and 1986 respectively. Since 1989, he has been a member of the faculty of the School of Electrical and Computer Engineering at the Georgia Institute of Technology, where he is now Professor and Associate Chair for Faculty Development. He teaches electromagnetic field theory and computational electromagnetics, and conducts research in the development of computational techniques for electromagnetic scattering, microwave devices, and electronic packaging applications Malcolm M. Bibby received the B.Eng. and Ph.D. degrees in Electrical Engineering from the University of Liverpool, England in 1962 and 1965, respectively. He also holds an MBA from the University of Chicago, U.S.A. His career includes both engineering and management. He was president of LXE Inc., a manufacturer of wireless data communications products from 1983 to 1994. ereafter he was president of NDI, a manufacturer of hardened hand-held computers, for five years. He is currently an Adjunct Professor in ECE at Georgia Tech. His interests lie in the field of high accuracy computational electromagnetics.