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

TL;DR

This paper introduces an adaptive isogeometric BEM using hierarchical B-splines and quasi-interpolation quadrature schemes, enhancing efficiency and accuracy for 2D Laplace problems.

Contribution

It develops a novel adaptive BEM framework with hierarchical B-splines and spline quasi-interpolant quadrature, improving convergence and computational efficiency.

Findings

Achieves optimal convergence rates with the proposed adaptive method.

Demonstrates efficiency of hierarchical B-splines in BEM.

Validates accuracy through numerical examples.

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.