Non-singular boundary integral formulations for plane interior potential problems

In this article, a non-singular formulation of the boundary integral equation is developed to solve smooth and non-smooth interior potential problems in two dimensions. The subtracting and adding-back technique is used to regularize the singularity of Green’s function and to simplify the calculation of the normal derivative of Green’s function. After that, a global numerical integration is directly applied at theboundary, and thoseinte gration points arealso taken as collocation points to simplify thealgorithm of computation. The result indicates that this simple method gives the convergence speed of order N−3 in the smooth boundary cases for both Dirichlet and mix-type problems. For the non-smooth cases, the convergence speed drops at O(N−1=2) for the Dirichlet problems