A simple local smoothing scheme in strongly singular boundary integral representation of potential gradient

Abstract

A new approach for computation of potential gradient at and near boundary is introduced. A strongly singular boundary integral representation of potential gradient, whose integral density is the potential gradient, is derived and analysed. Applying the concept of the osculating circle, a local smoothing procedure which computes a continuous approximation of potential gradient from the results of a 2D Boundary Element Method (BEM) analysis using linear elements is proposed and evaluated. This approximation is used in the integral representation derived as an integral density which fulfills the continuity requirements. Numerical experiments demonstrate, for quasiuniform meshes, an O( h 2) accuracy of potential gradient computed by both the local smoothing procedure on smooth parts of the boundary and by the integral representation on smooth boundary parts and near smooth boundary parts for points inside the domain. A consequence of the latter result is that no significant increase in the error appears near the boundary, boundary layer effect thus being eliminated in this approach.