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

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.