A New Transformed Distance for the Boundary Element Method to Solve Nearly Singular Integrals with Various Kernels

A novel distance transformation method is proposed to evaluate various nearly singular integrals accurately. Different from the traditional distance transformation method, the novel distance transformation method is based on a new distance function. This function can unify the normal and tangential distance functions used in the traditional distance transformation method. It can also accurately approximate the distance between a source point and a Gaussian integral point. By combining the novel distance transformation method with the conventional subdivision method, solutions for nearly weakly, strongly, and hyper singular integrals are obtained, respectively. The computational accuracy and efficiency of the proposed method are verified by solving potential and elastic problems for different geometric models with different boundary conditions.