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Two recently introduced quadrature schemes for weakly singular integrals[Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the contextof boundary integral equations arising in the isogeometric formulation ofGalerkin Boundary Element Method (BEM). In the first scheme, the regular partof the integrand is approximated by a suitable quasi--interpolation spline. Inthe second scheme the regular part is approximated by a product of two splinefunctions. The two schemes are tested and compared against other standard andnovel methods available in literature to evaluate different types of integralsarising in the Galerkin formulation. Numerical tests reveal that underreasonable assumptions the second scheme convergences with the optimal order inthe Galerkin method, when performing $h$-refinement, even with a small amountof quadrature nodes. The quadrature schemes are validated also in numericalexamples to solve 2D Laplace problems with Dirichlet boundary conditions.

A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM