Numerical integration of discontinuous functions: moment fitting and smart octree

Journal
Computational Mechanics  
Volume
60
Issue
5
Start Page
863
End Page
881
Citation
Computational Mechanics 5 (60): 863-881 (2017)
Publisher DOI
10.1007/s00466-017-1441-0
Scopus ID
2-s2.0-85024482684
Publisher
Springer
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.
Subjects
numerical integration
quadrature
moment fitting
smart octree
finite cell method
DDC Class
500: Naturwissenschaften
Funding(s)
High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen  
More Funding Information
Deutsche Forschungsgemeinschaft (DFG)