An Efficient and Exponentially Accurate Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains - The Dirichlet Case

S.K. Tomar, P. Dutt, B.V. Ratish Kumar

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

    6 Citations (Scopus)
    60 Downloads (Pure)

    Abstract

    For smooth problems spectral element methods (SEM) exhibit exponential convergence and have been very successfully used in practical problems. However, in many engineering and scientific applications we frequently encounter the numerical solutions of elliptic boundary value problems in non-smooth domains which give rise to singularities in the solution. In such cases the accuracy of the solution obtained by SEM deteriorates and they offer no advantages over low order methods. A new Parallel h-p Spectral Element Method is presented which resolves this form of singularity by employing a geometric mesh in the neighborhood of the corners and gives exponential convergence with asymptotically faster results than conventional methods. The normal equations are solved by the Preconditioned Conjugate Gradient (PCG) method. Except for the assemblage of the resulting solution vector, all computations are done on the element level and we don't need to compute and store mass and stiffness like matrices. The technique to compute the preconditioner is quite simple and very easy to implement. The method is based on a parallel computer with distributed memory and the library used for message passing is MPI. Load balancing issues are discussed and the communication involved among the processors is shown to be quite small.
    Original languageEnglish
    Title of host publicationHigh Performance Computing — HiPC 2002
    Subtitle of host publication9th International Conference Bangalore, India, December 18–21, 2002 Proceedings
    EditorsSartaj Sahni, Viktor K. Prasanna, Uday Shukla
    Place of PublicationBerlin, Germany
    PublisherSpringer
    Pages534-544
    Number of pages11
    ISBN (Electronic)978-3-540-36265-4
    ISBN (Print)978-3-540-00303-8
    DOIs
    Publication statusPublished - 2002

    Publication series

    NameLecture Notes In Computer Science
    PublisherSpringer
    Volume2552
    ISSN (Print)0302-9743

    Keywords

    • METIS-207967
    • EWI-16263
    • IR-74817

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