Numerical integration schemes for the BEM solution of hypersingular integral equations

Abstract

In this paper we consider singular and hypersingular integral equations associated with 2D boundary value problems defined on domains whose boundaries have piecewise smooth parametric representations. In particular, given any (polynomial) local basis, we show how to compute efficiently all integrals required by the Galerkin method. The proposed numerical schemes require the user to specify only the local polynomial degrees; therefore they are quite suitable for the construction of p- and h-p versions of Galerkin BEM. Copyright © 1999 John Wiley & Sons, Ltd.