Numerical dissipation for explicit, unconditionally stable time integration methods

2014 ◽  
Vol 7 (2) ◽  
pp. 159-178 ◽  
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Time Integration ◽  
Numerical Dissipation ◽  
Unconditionally Stable ◽  
Integration Methods ◽  
Time Integration Methods

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

2021 ◽  
Author(s):  
Yi Ji ◽  
Yufeng Xing
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Integration Methods ◽  
Stiffness Matrices ◽  
Difference Formula ◽  
Different Types ◽  
Time Integration Methods ◽  
Methods Numerical

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method

1993 ◽  
Vol 60 (2) ◽  
pp. 371-375 ◽  
Author(s):  
J. Chung ◽  
G. M. Hulbert
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Low Frequency ◽  
Numerical Dissipation ◽  
Integration Algorithm ◽  
Integration Methods ◽  
New Family ◽  
Time Integration Methods ◽  
Improved Performance ◽  
Dynamics Problems

A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

2014 ◽  
Vol 18 (5) ◽  
pp. 697-709 ◽  
Author(s):  
Sylvain Weill ◽  
Raphael di Chiara-Roupert ◽  
Philippe Ackerer
Keyword(s):  
Wave Equation ◽  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

scholarly journals Efficient time integration methods for Gross-Pitaevskii equations with rotation term

2019 ◽  
Vol 6 (2) ◽  
pp. 147-169 ◽  
Author(s):  
Philipp Bader ◽  
◽  
Sergio Blanes ◽  
Fernando Casas ◽  
Mechthild Thalhammer ◽  
...  
Keyword(s):  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Akbar Gholampour ◽  
Mehdi Ghassemieh ◽  
Mahdi Karimi-Rad
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Numerical Dispersion ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Similar Time ◽  
Unconditionally Stable ◽  
Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

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