Quadrature formulas based on spline Quasi-Interpolation for hypersingular integrals arising in IgA-SGBEM

In this paper, we study the construction of quadrature rules for the approximation of hypersingular integrals that occur when 2D Neumann or mixed Laplace problems are numerically solved using Boundary Element Methods. In particular the Galerkin discretization is considered within the Isogeometric Analysis setting and spline quasi-interpolation is applied to approximate integrand factors, then integrals are evaluated via recurrence relations. Convergence results of the proposed quadrature rules are given, with respect to both smooth and non smooth integrands. Numerical tests confirm the behavior predicted by the analysis. Finally, several numerical experiments related to the application of the quadrature rules to both exterior and interior differential problems are presented.