The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains

j Araeo, B Bradshaw-Hajek, S Miklavcic, Dale Ward

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.

    Original languageEnglish
    Article number185202
    Pages (from-to)1-18
    Number of pages18
    JournalJournal of Physics A: Mathematical and General
    Volume43
    Issue number18
    DOIs
    Publication statusPublished - 2010

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