Energy-conserving interface dynamics with asynchronous direct time integration employing arbitrary time steps

Dvořák, R.; Kolman, Radek; Mračko, M.; Kopačka, Ján; Fíla, Tomáš; Jiroušek, Ondřej; Falta, Jan; Neühauserová, Michaela; Rada, Václav; Adámek, Vítězslav; González, José Luís Galán

doi:10.1016/j.cma.2023.116110

Computer Methods in Applied Mechanics and Engineering

2023

DOI: 10.1016/j.cma.2023.116110

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Energy-conserving interface dynamics with asynchronous direct time integration employing arbitrary time steps

R. Dvořák

Radek Kolman

M. Mračko

et al.

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2024

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Cited by 3 publications

References 26 publications

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A Multi‐Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration

Chan,

Bombace,

Sap

et al. 2024

Numerical Meth Engineering

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Heterogeneous solids often exhibit complex dynamic behavior, requiring simulations to use varying time steps. However, the conventional use of a single‐time step for the entire domain can be inefficient. This article proposes a multi‐time stepping algorithm that addresses this challenge by relaxing the constraint for an integer or constant time step ratio between subdomains and eliminating the need for kinematic interpolation. The algorithm ensures the satisfaction of the Courant‐Friedrichs‐Lewy condition, deviating only to allow subdomains to remain in synchronization. Consequently, less integration steps are performed in comparison to state‐of‐the‐art asynchronous integrators. We extend to the coupling of multiple subdomains, where each subdomain has its time step. Simulating stress wave propagation in metamaterials demonstrates that the proposed algorithm significantly accelerates simulation time, without sacrificing accuracy.

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A Multi‐Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration

Chan,

Bombace,

Sap

et al. 2024

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

Improving the accuracy of the Newmark method through backward error analysis

Takács,

Fülöp

2024

Comput Mech

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We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted equations, we give expressions for the numerically or algorithmically distorted stiffness and damping matrices of a system simulated using the Newmark scheme. Using these results, we show how to construct compensation terms from the original parameters of the system, which improve the performance of Newmark simulations. The required compensation terms turn out to be slight modifications to the original system parameters (e.g. the damping or stiffness matrices), and can be applied without changing the time step or modifying the scheme itself. Two such compensations are given: one eliminates numerical damping, while the other achieves fourth-order accurate calculations using the traditionally second-order Newmark method. The performance of both compensation methods is evaluated numerically to demonstrate their validity, and they are compared to the uncompensated Newmark method, the generalized-$$\alpha $$ α method and the 4th-order Runge–Kutta scheme.

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Numerically Stable Integrated Simulation Method for Coupled Dynamic Systems

Wang,

Huang,

Kwon

et al. 2024

J. Struct. Eng.

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Energy-conserving interface dynamics with asynchronous direct time integration employing arbitrary time steps

Cited by 3 publications

References 26 publications

A Multi‐Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration

A Multi‐Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration

Improving the accuracy of the Newmark method through backward error analysis

Numerically Stable Integrated Simulation Method for Coupled Dynamic Systems

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