A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM
For researchers in computational mechanics using isogeometric BEM, this work provides efficient quadrature rules, though it is an incremental improvement over existing methods.
The paper investigates two quadrature schemes for weakly singular integrals in isogeometric Galerkin BEM, finding that the second scheme achieves optimal convergence order with few quadrature nodes. Numerical tests on 2D Laplace problems validate the approach.
Two recently introduced quadrature schemes for weakly singular integrals [Calabrò et al. J. Comput. Appl. Math. 2018] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin Boundary Element Method (BEM). In the first scheme, the regular part of the integrand is approximated by a suitable quasi--interpolation spline. In the second scheme the regular part is approximated by a product of two spline functions. The two schemes are tested and compared against other standard and novel methods available in literature to evaluate different types of integrals arising in the Galerkin formulation. Numerical tests reveal that under reasonable assumptions the second scheme convergences with the optimal order in the Galerkin method, when performing $h$-refinement, even with a small amount of quadrature nodes. The quadrature schemes are validated also in numerical examples to solve 2D Laplace problems with Dirichlet boundary conditions.