TY - GEN

T1 - First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

AU - Scholz, Felix

AU - Mantzaflaris, Angelos

AU - Jüttler, Bert

N1 - Funding Information:
The authors gratefully acknowledge the support provided by the Austrian Science Fund (FWF) through project NFN S11708 and by the European Research Council (ERC), project GA 694515.
Funding Information:
Acknowledgements The authors gratefully acknowledge the support provided by the Austrian Science Fund (FWF) through project NFN S11708 and by the European Research Council (ERC), project GA 694515.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85069228452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069228452&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-14244-5_15

DO - 10.1007/978-3-030-14244-5_15

M3 - Conference contribution

AN - SCOPUS:85069228452

SN - 9783030142438

T3 - Lecture Notes in Computational Science and Engineering

SP - 297

EP - 321

BT - Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017

A2 - Apel, Thomas

A2 - Langer, Ulrich

A2 - Meyer, Arnd

A2 - Steinbach, Olaf

PB - Springer Verlag

T2 - 30th Chemnitz Finite Element Symposium, 2017

Y2 - 25 September 2017 through 27 September 2017

ER -