The solution of Helmholtz equation in elliptical domains (Short Papers)

Summary form only given, as follows. The propagation of electromagnetic (EM) waves in hollow, perfectly conducting waveguides has been studied recently by J.G. Kretzschmar ["Wave propagation in hollow conducting elliptical waveguides," ibid., vol. MTT-18, pp. 547-554, Sept. 1970] in an excellent paper. Extensive numerical data are presented for the cutoff wavelength on 19 successive modes. The paper is also of interest in other fields of applied sciences, since in the case of TM modes the problem is mathematically equivalent to that of an elliptical cylinder, subject to a sudden temperature change at the outer surface of the cylinder [E.T. Kirkpatrick & W.F. Stokey, "Transient heat conduction in elliptica plates and cylinders," J. Heat Transfer, Trans. ASME, pp. 54-60, Feb. 1959]. The numerical evaluation of the solution requires the zeros of ordinary and modified Mathieu functions and the calculation of integrals involving the functions. Kirkpatrick and Stokey\´s paper describes also the evaluation of the temperature equation by the use of a digital computer giving results for ellipses having eccentricities of 0.60, 0.70, 0.80, and 0.90. Kretzschmar uses a Bessel-function product-series approach, while Kirkpatrick and Stokey make use of a hyperbolic function series. It should also be pointed out that only the even TM0mp(m = 0, 2, 4 ... , p = 1, 2, ... ) in Kretzschmar have their equivalent in Kirkpatrick.