Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method

This paper presents a gradient field representation using an analytical regularization of a hypersingular boundary integral equation for a two-dimensional time harmonic wave equation called the Helmholtz equation. The regularization is based on cancelation of the hypersingularity by considering properties of hypersingular elements that are adjacent to a singular node. Advantages to this regularization include applicability to evaluate corner nodes, no limitation for element size, and reduced computational cost compared to other methods. To demonstrate capability and accuracy, regularization is estimated for a problem about plane wave propagation. As a result, it is found that even at a corner node the most significant error in the proposed method is due to truncation error of non-singular elements in discretization, and error from hypersingular elements is negligibly small.