Hypersingular integrals and the two dimensional Helmholtz equation.

摘要

Hypersingular integral equations have proven to be very effective tool in the boundary element analysis of regions containing cracks. In previous studies, the reduction of the singular terms to a computationally reasonable form has relied on the the ability to analytically integrate the Green's function over a flat element. The purpose of this paper is to investigate the integration of a more complicated fundamental solution, that of the two dimensional Helmholtz equation, over a curved element. The Hankel functions are treated by integrating the singular part analytically, and other Green's functions. However, the higher dimensional analogue of the procedure employed herein to treat the quadratic isoparametric element is not practical, and other techniques will be required. 19 refs., 2 figs.