The natural boundary integral equation of the orthotropic potential problem

The governing equation of two-dimensional orthotropic potential problem is transformed into standard Laplace equation by the coordinate transformation method. Then a novel potential derivative boundary integral equation termed natural boundary integral equation (NBIE) is established for the two-dimensional orthotropic potential problem. The NBIE reduces the singularity by one order when compared with the conventional potential derivative boundary integral equation (CDBIE). Thus the potential derivative of the two-dimensional orthotropic potential problem can be computed more accurately by using the NBIE at the same boundary mesh. Furthermore, after using the analytical integral regularization algorithm of nearly singular integrals, the NBIE can obtain more accurate potential derivatives of interior points which are very close to the boundary than the CDBIE. Numerical examples verify the accuracy and efficiency of the present method.