A numerical quadrature for nearly singular boundary element integrals

Abstract Nearly singular integrals arise in the boundary element method when analyzing thin structures and gaps and when calculating the field very near the boundary. Hayami proposed the PART method for the accurate and efficient calculation of such nearly singular integrals over general curved surface elements. In this paper, a new radial variable transformation for the method, which reduces the number of integration points for flux integrals, is proposed with theoretical error analysis using complex function theory. Also, an implementation technique of the method is proposed, which considerably reduces the number of integration points.