An adaptive IGA-BEM with hierarchical B-splines based on quasi-interpolation quadrature schemes
For researchers in computational mechanics, it offers an efficient adaptive BEM method, though it is an incremental improvement over existing isogeometric BEM approaches.
This paper introduces an adaptive isogeometric BEM using hierarchical B-splines and quasi-interpolation quadrature schemes for 2D Laplace problems, achieving optimal convergence rates in numerical examples.
The isogeometric formulation of Boundary Element Method (BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems are introduced. The new quadrature schemes are based on a spline quasi-interpolant (QI) operator and properly framed in the hierarchical setting. The local nature of the QI perfectly fits with hierarchical spline constructions and leads to an efficient and accurate numerical scheme. An automatic adaptive refinement strategy is driven by a residual based error estimator. Numerical examples show that the optimal convergence rate of the BEM solution is recovered by the proposed adaptive method.