A novel three sub‐step explicit time integration method for wave propagation and dynamic problems

A novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A de...

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Published in:International journal for numerical methods in engineering Vol. 124; no. 15; pp. 3299 - 3328
Main Authors: Wen, Weibin, Wu, Lang, Liu, Tianhao, Deng, Shanyao, Duan, Shengyu
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 15.08.2023
Wiley Subscription Services, Inc
Subjects:
Algorithms
B‐spline
explicit
Finite element method
Interpolation
momentum corrector
Numerical analysis
Numerical dissipation
Stability analysis
structural dynamics
Time integration
Wave dispersion
Wave propagation
ISSN:0029-5981, 1097-0207
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Abstract A novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A demonstrative dispersion analysis for wave propagation is presented to acquire optimal algorithm parameter value for finite element analysis of wave propagation problems. Numerical tests demonstrate that new method show desirable algorithm accuracy and convergence for dynamic problems. Especially, for highly nonlinear problems, the new method can provide very accurate and stable solutions.
AbstractList A novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A demonstrative dispersion analysis for wave propagation is presented to acquire optimal algorithm parameter value for finite element analysis of wave propagation problems. Numerical tests demonstrate that new method show desirable algorithm accuracy and convergence for dynamic problems. Especially, for highly nonlinear problems, the new method can provide very accurate and stable solutions.
Author Deng, Shanyao
Wen, Weibin
Wu, Lang
Liu, Tianhao
Duan, Shengyu
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  organization: Beijing Institute of Technology
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SubjectTerms Algorithms
B‐spline
explicit
Finite element method
Interpolation
momentum corrector
Numerical analysis
Numerical dissipation
Stability analysis
structural dynamics
Time integration
Wave dispersion
Wave propagation
Title A novel three sub‐step explicit time integration method for wave propagation and dynamic problems
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