Numerical integration schemes for evaluation of (hyper)singular integrals in 2D BEM

Abstract

We consider hypersingular integral equations associated with 2D boundary value problems and defined on domains given by piecewise smooth parametric representations. In particular, given any (polynomial) local basis, we consider all integrals whose evaluation is required when the equations are solved by Galerkin BEM. In order to compute these integrals we use very efficient numerical schemes, recently proposed, which require the user to define a mesh, not necessarily uniform, on the boundary and to specify the local degrees of the approximant. Therefore these rules are quite suitable for the construction of p- and h-p versions of Galerkin BEM.