First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

Felix Scholz*, Angelos Mantzaflaris, Bert Jüttler

*この研究の対応する著者

研究成果: Conference contribution

3 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルAdvanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017
編集者Thomas Apel, Ulrich Langer, Arnd Meyer, Olaf Steinbach
出版社Springer Verlag
ページ297-321
ページ数25
ISBN(印刷版)9783030142438
DOI
出版ステータスPublished - 2019
外部発表はい
イベント30th Chemnitz Finite Element Symposium, 2017 - St. Wolfgang, Austria
継続期間: 2017 9 252017 9 27

出版物シリーズ

名前Lecture Notes in Computational Science and Engineering
128
ISSN(印刷版)1439-7358
ISSN(電子版)2197-7100

Conference

Conference30th Chemnitz Finite Element Symposium, 2017
国/地域Austria
CitySt. Wolfgang
Period17/9/2517/9/27

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 工学(全般)
  • 離散数学と組合せ数学
  • 制御と最適化
  • 計算数学

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