A pure boundary element method approach for solving hypersingular boundary integral equations

This paper is concerned with discretization and numerical solution of a regularized version of the hypersingular boundary integral equation (HBIE) for the two-dimensional Laplace equation. This HBIE contains the primary unknown, as well as its gradient, on the boundary of a body. Traditionally, this equation has been solved by combining the boundary element method (BEM) together with tangential differentiation of the interpolated primary variable on the boundary. The present paper avoids this tangential differentiation. Instead, a “pure” BEM method is proposed for solving this class of problems. Dirichlet, Neumann and mixed problems are addressed in this paper, and some numerical examples are included in it.