Open shells of revolution: Method of analytical regularisation

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

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

    Abstract

    Based on the idea of an analytical regularisation a mathematically rigorous and numerically efficient approach is proposed to solve the potential problem for open arbitrary shaped shell of revolution with Dirichlet boundary condition. The initial integral equation is reduced to a form admitting decomposition of the integral kernel into the sum of the Green's function for a sphere, which includes all the singularities of the reformulated problem, and a smooth remainder. An effective calculation technique for the coefficients of the Fourier expansion of the remainder was obtained. Using the analytical regularisation, the problem is equivalently reduced to an infinite system of linear algebraic equations of the second kind. Such equations can be effectively and efficiently solved by standard numerical methods. The convergence improvement of the series describing the surface charge is implemented.

    Original languageEnglish
    Title of host publicationProgress in Electromagnetics Research Symposium 2006, PIERS 2006 Tokyo
    Place of PublicationCambridge, MA
    PublisherElectromagnetics Academy
    Pages68-72
    Number of pages5
    ISBN (Print)9781629939513
    Publication statusPublished - 2006
    EventProgress in Electromagnetics Research Symposium 2006, PIERS 2006 Tokyo - Tokyo, Japan
    Duration: 2 Aug 20065 Aug 2006

    Other

    OtherProgress in Electromagnetics Research Symposium 2006, PIERS 2006 Tokyo
    CountryJapan
    CityTokyo
    Period2/08/065/08/06

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