Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics

LUO Han-zhong; LIU Xue-wen; HUANG Xing-chun

doi:10.3879/j.issn.1000-0887.2011.06.010

Volume 32 Issue 6

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LUO Han-zhong, LIU Xue-wen, HUANG Xing-chun. Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics[J]. Applied Mathematics and Mechanics, 2011, 32(6): 730-740. doi: 10.3879/j.issn.1000-0887.2011.06.010

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Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics

doi: 10.3879/j.issn.1000-0887.2011.06.010

School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, P. R. China;
Siemens Industry Software(China) Co., Ltd., Shanghai 200042, P. R. China

Received Date: 2010-07-21
Rev Recd Date: 2011-04-13
Publish Date: 2011-06-15

Abstract

Abstract

Reproducing kernel collocation method based on strong formulation was introduced for transient dynamics.von Neumann stability and dispersion analysis of reproducing kernel collocation method with central difference temporal discretization was derived to evaluate the stability condition for second order wave problem.The stability analysis algorithm proposed firstly given an approach to predict critical time step for second order wave problem which can greatly save computational time in application.A numerical test was conducted to validate this algorithm.The comparison of numerical critical time step and predicted results shows good agreement.The guidance to choose a proper support size of reproducing kernel shape function is also given.The results by radial basis collocation method are also listed for comparison.
- reproducing kernel collocation method(RKCM),
- stability analysis,
- dispersion analysis,
- transient dynamics

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References(31)

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