On numerical cubatures of nearly singular surface integrals arising in BEM collocation (Q1319045)

The discretization of the boundary element method (BEM) in \(\mathbb{R}^ 3\) using collocation requires the numerical estimation of numerous nearly singular surface integrals. Efficient computational methods tailored to this application are developed. Local polar coordinates with a corner of the triangular surface elements as origin are used, and the radial inner integral is evaluated analytically. The second integration is performed using Gauss-Legendre quadrature of an adaptively chosen order. Numerical results illustrate the efficiency of the procedures.