An adaptive IgA‐BEM with hierarchical B‐splines based on quasi‐interpolation quadrature schemes. (5th December 2018)

• Record Type: Journal Article
• Authors: Falini, Antonella; Giannelli, Carlotta; Kanduč, Tadej; Sampoli, Maria Lucia; Sestini, Alessandra
• Is Part Of: International journal for numerical methods in engineering. Volume 117:Number 10(2019)
• Page Start: 1038
• Page End: 1058
• Publication Date: 2018-12-05
• Subjects: boundary element method -- hierarchical B‐splines -- isogeometric analysis -- local refinement -- quadrature formulas -- quasi‐interpolation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5990
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: The isogeometric formulation of the boundary element method (IgA‐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 proposed quadrature schemes are based on a spline quasi‐interpolation (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 Galerkin solution is recovered by the proposed adaptive method.