Multi‐time‐step domain coupling method with energy control

Mahjoubi, Najib; Krenk, Steen

doi:10.1002/nme.2878

Cited by 7 publications

(9 citation statements)

References 29 publications

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“…Figure 19 provides a pictorial description of the problem. A similar problem is also considered in Reference [22], which also addressed multi-time-step coupling method for structural dynamics.…”

Section: Representative Numerical Resultsmentioning

confidence: 99%

“…Real time partitioned time-integration using the LSRT methods has been of interest recently in [21]. Mahjoubi and Krenk proposed a multi-time-step coupling method using state-pace time integration in [22], a more general presentation of which appears in [23]. Another work that is relevant to the current paper is by Prakash and Hjelmstad [24], which we shall refer to as the PH method.…”

Section: Introductionmentioning

confidence: 99%

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On multi-time-step monolithic coupling algorithms for elastodynamics

Karimi

Nakshatrala

2014

Journal of Computational Physics

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We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and enforce the continuity of velocities at system time levels. The resulting equations will be in the form of differential-algebraic equations. To crystallize the ideas we shall employ Newmark family of time-stepping schemes. The proposed method can handle multiple subdomains, and allows different time-steps as well as different time stepping schemes from the Newmark family in different subdomains. We shall use the energy method to assess the numerical stability, and quantify the influence of perturbations under the proposed coupling method. We also discuss the conditions under which the proposed method will be energy preserving, and the conditions under which the method will be energy conserving. Several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method. We shall also compare the proposed multi-time-step coupling method with some other similar methods available in the literature

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Section: Representative Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On multi-time-step monolithic coupling algorithms for elastodynamics

Karimi

Nakshatrala

2014

Journal of Computational Physics

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“…They concluded that the PH method is energy conserving when coupling non‐dissipative Newmark schemes such as the implicit constant average acceleration (CAA) scheme and the explicit central difference (CD) scheme. Recently, the Mahjoubi Gravouil Combescure (MGC) method (based on a similar macro timescale velocity continuity assumption) has been built in order to be able to couple the Newmark schemes, HHT‐ α scheme , Simo scheme , and Krenk scheme (balance dissipation scheme, ) in linear dynamics . In other words, the MGC method can be seen as an extension of the PH method to the HHT‐ α scheme.…”

Section: Heterogeneous Asynchronous Time Integratorsmentioning

confidence: 99%

Heterogeneous asynchronous time integrators for computational structural dynamics

Gravouil

Combescure

Brun

2014

Numerical Meth Engineering

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SUMMARYComputational structural dynamics plays an essential role in the simulation of linear and nonlinear systems. Indeed, the characteristics of the time integration procedure have a critical impact on the feasibility of the calculation. In order to go beyond the classical approach (a unique time integrator and a unique timescale), the pioneer approach of Belytschko and co-workers consisted in developing mixed implicit-explicit time integrators for structural dynamics. In a first step, the implementation and stability analyses of partitioned integrators with one time step have been achieved for a large class of time integrators. In a second step, the implementation and stability analyses of partitioned integrators with different time steps were studied in detail for particular cases. However, stability results involving different time steps and different time integrators in different parts of the mesh is still an open question in the general case for structural dynamics. The aim of this paper is to propose a state-of-the art of heterogeneous (different time schemes) asynchronous (different time steps) time integrators (HATI) for computational structural dynamics. Finally, an alternative approach based on energy considerations (with velocity continuity at the interface) is proposed in order to develop a general class of HATI for structural dynamics.

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“…As shown in [12], the normal contact conditions (37) in combination with the trapezoidal rule yield an unstable algorithm if inertia terms are present. In this case, it is advisable to change the time discretization of (37) like, e.g., described in [27,55].…”

Section: Frictional Contactmentioning

confidence: 99%

“…In [34,35], a time sub stepping scheme with linear interpolation of the velocity and the Lagrange multipliers has been proposed which is stable but dissi pative at the interface. An improved energy conserving scheme with linear interpolation of the multipliers has been analyzed in [36,37]. However, both methods rely on the expensive exact solu tion of the resulting coupled system.…”

Section: Introductionmentioning

confidence: 99%

Solving dynamic contact problems with local refinement in space and time

Hager

Hauret

Tallec

et al. 2012

Computer Methods in Applied Mechanics and Engineering

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International audienceFrictional dynamic contact problems with complex geometries are a challenging task from the compu tational as well as from the analytical point of view since they generally involve space and time multi scale aspects. To be able to reduce the complexity of this kind of contact problem, we employ a non conforming domain decomposition method in space, consisting of a coarse global mesh not resolving the local struc ture and an overlapping fine patch for the contact computation. This leads to several benefits: First, we resolve the details of the surface only where it is needed, i.e., in the vicinity of the actual contact zone. Second, the subproblems can be discretized independently of each other which enables us to choose a much finer time scale on the contact zone than on the coarse domain. Here, we propose a set of interface conditions that yield optimal a priori error estimates on the fine meshed subdomain without any artificial dissipation. Further, we develop an efficient iterative solution scheme for the coupled problem that is robust with respect to jumps in the material parameters. Several complex numerical examples illustrate the performance of the new scheme

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Multi‐time‐step domain coupling method with energy control

Cited by 7 publications

References 29 publications

On multi-time-step monolithic coupling algorithms for elastodynamics

On multi-time-step monolithic coupling algorithms for elastodynamics

Heterogeneous asynchronous time integrators for computational structural dynamics

Solving dynamic contact problems with local refinement in space and time

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