Analytical regularization of the Dirichlet diffraction problem for screen of revolution

Sergey B. Panin, Paul D. Smith, Elena D. Vinogradova, Yury A. Tuchkin, Sergey S. Vinogradov

    Research output: Contribution to journalArticle

    Abstract

    A rigorous and numerically efficient approach, based on the Analytical Regularization Method, has been developed for the Dirichlet scalar diffraction problem of a smooth arbitrarily shaped open screen of revolution. The initial integral equation of the first kind is transformed so that the integral kernel is decomposed into a singular canonical part and a smooth remainder. Then the technique of dual series equations involving Jacoby polynomials reduces the problem to the infinite system of linear algebraic equations of the second kind. This provides desired solution accuracy depending on the truncation number alone. The numerical tests are presented for an open prolate spheroid and some open screens obtained by the revolution of the “Cassini Oval” and ”Pascal Lima¸con” curves. A high accuracy, efficiency and potential of the approach are shown.
    Original languageEnglish
    Pages (from-to)289-308
    Number of pages20
    JournalInternational electronic journal of pure and applied mathematics
    Volume3
    Issue number4
    Publication statusPublished - 2011

    Keywords

    • analytical regularization
    • scalar wave diffraction
    • open arbitrarily shaped screen of revolution
    • Dirichlet problem

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