Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

QIN Yu-yue; DENG Zi-chen; HU Wei-peng

doi:10.3879/j.issn.1000-0887.2014.01.003

Volume 35 Issue 1

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QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System[J]. Applied Mathematics and Mechanics, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003

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Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

doi: 10.3879/j.issn.1000-0887.2014.01.003

¹Department of Engineering Mechanics, Northwestern Polythechnical University, Xi’an 710072, P.R.China;²State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China(11172239；11372252；11372253)

Received Date: 2013-10-15
Rev Recd Date: 2013-10-22
Publish Date: 2014-01-15

Abstract

Abstract

Based on Hamilton variational principle and Bridges’ multi-symplectic integration theory, a new structure-preserving algorithm was proposed to simulate the steady-state solution to the complex infinite dimensional Hamilton system. With Zufiria’s Boussinesq-type equations as an example, the high-order partial differential equation describing the steady-state solution to the Zufiria model was rewritten into a symmetric form under the energy flux conservation law and momentum flux conservation law firstly; then the box scheme for the symmetric form was constructed to simulate the steady-state solution to the Zufiria model. The numerical results show that the box scheme can well simulate the steady-state solution to the Zufiria model while properly preserving the momentum flux conservation law.
- infinite dimensional Hamilton system,
- structure-preserving,
- steady-state solution,
- momentum flux

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References(10)

References

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