First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

Felix Scholz*, Angelos Mantzaflaris, Bert Jüttler

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

In this work, we develop a specialized quadrature rule for trimmed domains, where the trimming curve is given implicitly by a real-valued function on the whole domain. We follow an error correction approach: In a first step, we obtain an adaptive subdivision of the domain in such a way that each cell falls in a predefined base case. We then extend the classical approach of linear approximation of the trimming curve by adding an error correction term based on a Taylor expansion of the blending between the linearized implicit trimming curve and the original one. This approach leads to an accurate method which improves the convergence of the quadrature error by one order compared to piecewise linear approximation of the trimming curve. It is at the same time efficient, since essentially the computation of one extra one-dimensional integral on each trimmed cell is required. Finally, the method is easy to implement, since it only involves one additional line integral and refrains from any point inversion or optimization operations. The convergence is analyzed theoretically and numerical experiments confirm that the accuracy is improved without compromising the computational complexity.

Original languageEnglish
Title of host publicationAdvanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017
EditorsThomas Apel, Ulrich Langer, Arnd Meyer, Olaf Steinbach
PublisherSpringer Verlag
Pages297-321
Number of pages25
ISBN (Print)9783030142438
DOIs
Publication statusPublished - 2019
Externally publishedYes
Event30th Chemnitz Finite Element Symposium, 2017 - St. Wolfgang, Austria
Duration: 2017 Sep 252017 Sep 27

Publication series

NameLecture Notes in Computational Science and Engineering
Volume128
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference30th Chemnitz Finite Element Symposium, 2017
Country/TerritoryAustria
CitySt. Wolfgang
Period17/9/2517/9/27

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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