Almost complete analytical integration in Galerkin BEM (2112.05028v1)

Abstract: In this work, semi-analytical formulae for the numerical evaluation of surface integrals occurring in Galerkin boundary element methods (BEM) in 3D are derived. The integrals appear as the entries of BEM matrices and are formed over pairs of surface triangles. Since the integrands become singular if the triangles have non-empty intersection, the transformation presented by Sauter and Schwab is used to remove the singularities. It is shown that the resulting integrals admit analytical formulae if the triangles are identical or share a common edge. Moreover, the four-dimensional integrals are reduced to one- or two-dimensional integrals for triangle pairs with common vertices or disjoint triangles respectively. The efficiency and accuracy of the formulae is demonstrated in numerical experiments.