On the treatment of corners in the boundary element method

摘要

A new technique for treating surface discontinuities within boundary element calculations is proposed. Multiple nodes are used to represent the geometry, and the necessary additional equations are obtained by differentiating the usual boundary element integral equation. In deriving expressions for the resulting singular integrals, it is found that constraints must be placed on the functional approximation at the discontinuity. An algorithm for incorporating these constraints is developed and numerical tests for an exactly solvable three-dimensional Laplace equation problem are presented.