A Boundary Integral Equation Formulation in Derivative Unknowns for Two-Dimensional Potential Problems

Abstract

A boundary integral equation called Derivative BIE is developed for two-dimensional potential problems in terms of tangential and normal derivatives of the potential on the boundary, by integrating by parts the Cauchy formula. The potential values on the boundary can be calculated by integration after the solution is obtained. The primary unknowns in this formulation can be of direct interest in a shape design sensitivity analysis where the tangential derivatives of the potential are also required. The method is applied to several test problems, and the results show better accuracy than those by the conventional boundary element method, not only for the derivatives of the potential but also for the potential itself.