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

D. V. Altiparmakov and M. S. Milgram
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D. V. Altiparmakov: The Boris Kidrič Institute of Nuclear Sciences
M. S. Milgram: Atomic Energy of Canada Ltd., Chalk River Nuclear Laboratories

Chapter D29 in Numerical Techniques for Engineering Analysis and Design, 1987, pp 255-262 from Springer

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.

Keywords: Convex Domain; Trial Function; Regular Polygon; Rayleigh Quotient; Geometric Symmetry (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-94-009-3653-9_29

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