Publisher DOI: 10.1007/s00466-017-1441-0
Title: Numerical integration of discontinuous functions: moment fitting and smart octree
Language: English
Authors: Hubrich, Simeon 
Di Stolfo, Paolo 
Kudela, Laszlo 
Kollmannsberger, Stefan 
Rank, Ernst 
Schröder, Andreas 
Düster, Alexander 
Keywords: numerical integration; quadrature; moment fitting; smart octree; finite cell method
Issue Date: 18-Jul-2017
Publisher: Springer
Source: Computational Mechanics 5 (60): 863-881 (2017)
Abstract (english): 
A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.
ISSN: 0178-7675
Journal: Computational Mechanics 
Institute: Konstruktion und Festigkeit von Schiffen M-10 
Document Type: Article
Project: High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen 
More Funding information: Deutsche Forschungsgemeinschaft (DFG)
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