The Natural Boundary Integral Equation in Two-dimensional Potential Problems

摘要

This paper focuses on the BIE in the potential problems. A series of transformations are manipulated on the conventional potential derivative BIE in order to eliminate the hyper-singularity. It leads to a new natural BIE in the two-dimensional potential problems. The natural BIE also belongs to the derivative BIE, but only contains the strongly singular integral. As a result, another boundary element analysis based on the natural BIE can obtain more accurate potential derivatives on the boundary and at the interior points close to the boundary in comparison with the conventional BEM.