Efficient numerical integration of arbitrarily broken cells using the moment fitting approach. Issue 1 (October 2016)

• Record Type: Journal Article
• Authors: Hubrich, Simeon; Joulaian, Meysam; Di Stolfo, Paolo; Schröder, Andreas; Düster, Alexander
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 201
• Page End: 202
• Publication Date: 2016-10
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610089
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The finite cell method is based on a fictitious domain approach, providing a simple and fast mesh generation of structures with complex geometries. However, this simplification leads to intersected cells where the standard Gauss quadrature does not perform well. To perform the numerical integration of these cells, we use the moment fitting approach that generates an individual quadrature rule for every broken cell. In this paper, we will perform a non‐linear optimization approach to find the optimal position and number of the integration points. The findings show that the proposed method leads to efficient quadrature rules that require less integration points than other existing integration methods. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)