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

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 spl...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-07
Main Authors: Falini, Antonella, Giannelli, Carlotta, Kanduc, Tadej, Sampoli, Maria Lucia, Sestini, Alessandra
Format: Article
Language:English
Subjects:
Boundary element method
Galerkin method
Interpolation
Mathematical analysis
Mathematical models
Nonlinear programming
Splines
Two dimensional models
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1807.03563