TY - JOUR
T1 - An isogeometric collocation method using superconvergent points
AU - Anitescu, Cosmin
AU - Jia, Yue
AU - Zhang, Yongjie Jessica
AU - Rabczuk, Timon
N1 - Funding Information:
The authors would like to thank the support by the European Union through the FP7-grant ITN (Marie Curie Initial Training Networks) INSIST (Integrating Numerical Simulation and Geometric Design Technology) PITN-GA-2011-289361 . Y. Zhang was supported in part by the PECASE Award N00014-14-1-0234 and NSF CAREER Award OCI-1149591 .
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - We develop an IGA collocation method modified by collocating at points other than the standard Greville abscissae. The method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory, therefore we refer to this method as "super-collocation" (IGA-SC). By carefully choosing the collocation points, it can be seen that the IGA-SC converges in the first derivative (energy) norms at rates similar to that of the Galerkin solution. This is different from the collocation at Greville abscissae (IGA-C), where the convergence in energy norm for odd polynomial degrees is typically suboptimal. The method is tested on 1D, 2D and 3D numerical examples, in which it is compared to IGA-C and Galerkin's method (IGA-G). The comparison includes a detailed cost vs. accuracy analysis, which shows an improved efficiency of the proposed method in particular for odd polynomial degrees.
AB - We develop an IGA collocation method modified by collocating at points other than the standard Greville abscissae. The method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory, therefore we refer to this method as "super-collocation" (IGA-SC). By carefully choosing the collocation points, it can be seen that the IGA-SC converges in the first derivative (energy) norms at rates similar to that of the Galerkin solution. This is different from the collocation at Greville abscissae (IGA-C), where the convergence in energy norm for odd polynomial degrees is typically suboptimal. The method is tested on 1D, 2D and 3D numerical examples, in which it is compared to IGA-C and Galerkin's method (IGA-G). The comparison includes a detailed cost vs. accuracy analysis, which shows an improved efficiency of the proposed method in particular for odd polynomial degrees.
KW - Galerkin method
KW - Greville abscissae
KW - IGA collocation
KW - Least-squares
KW - Orthogonal collocation
KW - Superconvergence
UR - http://www.scopus.com/inward/record.url?scp=84920068525&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2014.11.038
DO - 10.1016/j.cma.2014.11.038
M3 - Article
AN - SCOPUS:84920068525
SN - 0045-7825
VL - 284
SP - 1073
EP - 1097
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -