Various near singularity regularization methods derived from distance transformations in 3D boundary element method

This paper focuses on applying non-linear transformations for near singularity regularization combined distance transformations. In the previous methods, near singularities are usually considered in only the polar direction, ignoring those in the circular direction, which leads to low accuracy when calculating nearly singular integrals of narrow element or when the projection point is located near the element end. In this paper, the near singularities are traced firstly based on the distance function, by which the distance function can be constructed in two ways. The general form of nearly singular integrals in the two directions is extracted. Then, several non-linear transformations are introduced about removal of the near singularities in one direction. In our method, the only one directional methods are combined to solve the nearly singular integrals. Finally, comparisons of the results by the combined distance transformations show that by employing the non-linear transformations in both directions, more stable and accurate results can be obtained especially for nearly singular integrals of the narrow elements.