TY - JOUR
T1 - Numerical integration on trimmed three-dimensional domains with implicitly defined trimming surfaces
AU - Scholz, Felix
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 ERC Advanced Grant “CHANGE” , GA no. 694515 .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We present a novel technique for the numerical integration of trivariate functions on trimmed domains. In our setting, we assume that the trimming surface is defined implicitly. Our approach combines a linear approximation of the trimming surface with a correction term. The latter term makes it possible to achieve a cubic convergence rate, which is one order higher than the rate obtained by using the linear approximation only. We also present numerical experiments that demonstrate the method's potential for applications in isogeometric analysis.
AB - We present a novel technique for the numerical integration of trivariate functions on trimmed domains. In our setting, we assume that the trimming surface is defined implicitly. Our approach combines a linear approximation of the trimming surface with a correction term. The latter term makes it possible to achieve a cubic convergence rate, which is one order higher than the rate obtained by using the linear approximation only. We also present numerical experiments that demonstrate the method's potential for applications in isogeometric analysis.
KW - Isogeometric analysis
KW - Numerical integration
KW - Quadrature
KW - Trimming
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U2 - 10.1016/j.cma.2019.112577
DO - 10.1016/j.cma.2019.112577
M3 - Article
AN - SCOPUS:85070805419
SN - 0045-7825
VL - 357
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 112577
ER -