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Efficient numerical integration of arbitrarily broken cells using the moment fitting approach
Author(s) -
Hubrich Simeon,
Joulaian Meysam,
Di Stolfo Paolo,
Schröder Andreas,
Düster Alexander
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610089
Subject(s) - numerical integration , gaussian quadrature , quadrature (astronomy) , gauss , simple (philosophy) , mathematics , gauss–kronrod quadrature formula , moment (physics) , domain (mathematical analysis) , algorithm , computer science , tanh sinh quadrature , position (finance) , numerical analysis , mathematical optimization , nyström method , mathematical analysis , physics , classical mechanics , engineering , electronic engineering , boundary value problem , philosophy , epistemology , quantum mechanics , finance , economics
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)