A novel asymptotic extraction technique for the efficient evaluation of a class of double Sommerfeld integrals

Authors:
Michael P. Spowart;Edward F. Kuester
Affiliations:
National Center for Atmospheric Research, Boulder, Colorado;Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colorado
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
Cited 0

Integrals and series of special functions

Integrals and series of special functions
Numerical computation of the incomplete Lipschitz-Hankel integral Jeo(a, z)

Journal of Computational Physics
Numerical computation of 2D Sommerfeld integrals—decomposition of the angular integral

Journal of Computational Physics
Numerical computation of 2D Sommerfeld integrals—a novel asymptotic extraction technique

Journal of Computational Physics

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Abstract

When the Galerkin method of moments (MoM) is used in the numerical analysis of microwave microstrip networks, elements of a network impedance matrix are required. Two dimensional (2D) Sommerfeld (spectral) integrals must be evaluated in such cases. When semi-infinite circuit feed lines are used, certain specific types of Sommerfeld integrals arise whose integrands oscillate rapidly and present serious numerical difficulties for their evaluation. In this paper, a novel, accurate, and much more efficient asymptotic extraction technique (AET) is developed that involves extracting an inner asymptotic angular integral, which is then evaluated analytically before evaluating the outer integral numerically.