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www.adv-radio-sci.net/4/11/2006/
doi:10.5194/ars-4-11-2006
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Numerical quadrature for the approximation of singular oscillating integrals appearing in boundary integral equations
Professur für Theoretische Elektrotechnik und Numerische Feldberechnung, Helmut-Schmidt-Universität Universität der Bundeswehr Hamburg, PO. Box 700 822, 22 008 Hamburg, Germany Bundeswehr Hamburg, PO. Box 700 822, D-22 008 Hamburg, German
Abstract. Boundary Integral Equation formulations can be used to describe electromagnetic shielding problems. Yet, this approach frequently leads to integrals which contain a singularity and an oscillating part. Those integrals are difficult to handle when integrated naivly using standard integration techniques, and in some cases even a very high number of integration nodes will not lead to precise results. We present a method for the numerical quadrature of an integral with a logarithmic singularity and a cosine oscillator: a modified Filon-Lobatto quadrature for the oscillating parts and an integral transformation based on the error function for the singularity. Since this integral can be solved analytically, we are in a position to verify the results of our investigations, with a focus on precision and computation time.
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Citation: Fichte, L. O., Lange, S., and Clemens, M.: Numerical quadrature for the approximation of singular oscillating integrals appearing in boundary integral equations, Adv. Radio Sci., 4, 11-15, doi:10.5194/ars-4-11-2006, 2006. Bibtex EndNote Reference Manager XML
