A Multigrid Preconditioned Conjugate Gradient Method for Isogeometric Analysis

LIU Shi; CHEN De-xiang; FENG Yong-xin; XU Zi-li; ZHENG Li-kun

doi:10.3879/j.issn.1000-0887.2014.06.005

Volume 35 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(6): 630-639

LIU Shi, CHEN De-xiang, FENG Yong-xin, XU Zi-li, ZHENG Li-kun. A Multigrid Preconditioned Conjugate Gradient Method for Isogeometric Analysis[J]. Applied Mathematics and Mechanics, 2014, 35(6): 630-639. doi: 10.3879/j.issn.1000-0887.2014.06.005

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A Multigrid Preconditioned Conjugate Gradient Method for Isogeometric Analysis

doi: 10.3879/j.issn.1000-0887.2014.06.005

¹Electric Power Research Institute, Guangdong Power Grid Corporation, Guangzhou 510080, P.R.China;²State Key Laboratory for Strength and Vibration of Mechanical Structures;School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R.China

Funds: The National Basic Research Program of China (973 Program)(2011CB706505)；The National Natural Science Foundation of China(51275385)

Received Date: 2013-12-03
Rev Recd Date: 2014-05-04
Publish Date: 2014-06-11

Abstract

Abstract

Accuracy of the isogeometric analysis can be improved through increase of the order of the NURBS basis function, but convergence of the multigrid will be slowed down at the same time. A method which combined the multigrid technique and preconditioned conjugate gradient iteration was proposed to accelerate the multigrid convergence. In the proposed method, the conjugate gradient part serves as the primary iteration, while the multigrid part serves as the preconditioner. The Poisson’s equation was solved with the multigrid method and multigrid preconditioned conjugate gradient method repectively for comparison. The results show that the multigrid preconditioned conjugate gradient method converges faster than the multigrid method especially in the cases of high-order NURBS basis functions or 3-dimensional problems.
- isogeometric analysis,
- multigrid,
- conjugate gradient,
- Poisson’s equation,
- iterative algorithm,
- NURBS

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References(14)

References

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