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The Convergence Properties of a Series of R-Functions for Simple Polygonal Shapes

In: Numerical Techniques for Engineering Analysis and Design

Author

Listed:
  • D. V. Altiparmakov

    (The Boris Kidrič Institute of Nuclear Sciences)

  • M. S. Milgram

    (Atomic Energy of Canada Ltd., Chalk River Nuclear Laboratories)

Abstract

Summary A numerical study of the convergence of the R-function solution to the Helmholtz equation is presented in this paper. Several two-dimensional domains of simple polygonal shape have been considered. Calculations have been carried out by four types of trial functions derived from two different solution structures. In addition, a singular function series is applied for the purpose of comparison. In the case of convex domains, one of the presented approximations yields an accurate solution with a very low number of degrees of freedom. However, the accuracy is very poor for the reentrant region and a separate treatment of singularity seems to be necessary.

Suggested Citation

  • D. V. Altiparmakov & M. S. Milgram, 1987. "The Convergence Properties of a Series of R-Functions for Simple Polygonal Shapes," Springer Books, in: G. N. Pande & J. Middleton (ed.), Numerical Techniques for Engineering Analysis and Design, chapter 0, pages 255-262, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3653-9_29
    DOI: 10.1007/978-94-009-3653-9_29
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