An adaptive IGA-BEM with hierarchical B-splines based on quasi-interpolation quadrature schemes

Abstract

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.

References in corpus (3)

• Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
• Isogemetric Analysis and Symmetric Galerkin BEM: a 2D numerical study
• Adaptive isogeometric analysis with hierarchical box splines

Cited by in corpus (6)

• Mathematical foundations of adaptive isogeometric analysis
• A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM
• Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
• Adaptive isogeometric boundary element methods with local smoothness control
• Stable implementation of adaptive IGABEM in 2D in MATLAB
• Isoparametric singularity extraction technique for 3D potential problems in BEM