Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations

Faucher, Vincent; Combescure, Alain

doi:10.1002/nme.1058

Cited by 12 publications

(7 citation statements)

References 12 publications

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“…Note that in the time integration process the new configuration x n+1 , induced by the displacements d n+1 , is obtained first (except at the initial time, when the configuration x 0 is known by definition); then, equilibrium (in a dynamic sense) is solved on the current configuration, resulting in the current accelerations a n+1 ; finally, the current velocities v n+1 are obtained as the last result of the time stepping procedure. The CD time integration scheme (7), (4), (6) is explicit in that all quantities in the right-hand-side terms are known when the equations are applied, thus no system solver is needed. This greatly simplifies the implementation and the treatment of non-linearities arising from geometric effects (large displacements, large strains) or from material effects (e.g.…”

Section: Methodsmentioning

confidence: 99%

“…in taking the global minimum value among those of all elements i in the computational mesh. Then, Equations (7), (4), (6) are repeatedly applied until the final time is reached, by using for prudence a somewhat reduced time increment where C s is the stability safety factor (0 < C s 1). Typically one assumes C s in the range between 0.5 and 0.8 to account for the fact that, for all but the simplest FE types and material models, relations of the type (10) are just an estimation of the real stability limit.…”

Section: Constant Time Increment Schemementioning

confidence: 99%

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Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics

Casadei

Halleux

2008

Numerical Meth Engineering

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SUMMARYThis paper proposes a generalization of the explicit central-difference time integration scheme, using a time step variable not only in time but also in space. The solution at each element/node is advanced in time following local rather than global stability limitations. This allows substantial saving of computer time in realistic applications with non-uniform meshes, especially in multi-field problems like fluid-structure interactions. A binary scheme in space is used: time steps are not completely arbitrary, but stay in a constant ratio of two when passing from one partition level to the next one. This choice greatly facilitates implementation (via an integer-based logic), ensures inherent synchronization and avoids any interpolations, necessary in other partitioning schemes in the literature, but which may reduce numerical stability. The mesh partition is automatically built up and continuously updated by simple spatial adjacency considerations. The resulting algorithm deals automatically with large variations in time of stability limits. The paper introduces the core spatial partitioning technique in the Lagrangian formulation. Some academic numerical examples allow a detailed comparison with the standard, spatially uniform algorithm. A final more realistic example shows the application of partitioning in simulations with arbitrary Lagrangian Eulerian formulation and fully-coupled boundary conditions (fluid-structure interaction).

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Section: Methodsmentioning

confidence: 99%

Section: Constant Time Increment Schemementioning

confidence: 99%

Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics

Casadei

Halleux

2008

Numerical Meth Engineering

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“…In order to define the discretized energy balance using the previous notations (16), one can consider the variation of the kinetic and internal energies between t n and t n+1 :…”

Section: Energy Balancementioning

confidence: 99%

“…However for large ratio of time scales, numerical dissipation can occur at the interface. Furthermore, this method was extended to the cases of incompatible meshes, contact problems and modal methods (see [7,8,16,21,22]). In the works of Combescure et al previously mentioned, the calculation may be performed with arbitrary and different pairs of parameters (γ , β) of the Newmark scheme [28] for each subdomain.…”

Section: Introductionmentioning

confidence: 99%

Coupling subdomains with heterogeneous time integrators and incompatible time steps

2009

Self Cite

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The work presented in this publication can be categorized among domain decomposition methods of the dual Schur type applied to structural dynamics. This approach leads to lower CPU times and better control of the accuracy of the time discretization and allows to take into account multi-time-scale effects which arise in transient structural dynamics. In order to consider incompatible time scales, one has to enforce continuity at the interfaces between the subdomains. Here, we propose a general formalism which enables the coupling of subdomains with their own numerical time integration scheme. The proposed method enables one to take into account possible nonlinearities which may present different time scale between the subdomains in a general manner for a wide range of time numerical scheme. This method also offers an important improvement for industrial software with easy implementation. Linear and nonlinear numerical examples are proposed in order to show the efficiency and the robustness of the method.

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“…Gravouil and Combescure [25,26] extended the dynamic FETI algorithm to include multiple time steps based on the equality of velocities across the interface and proved the stability of their method using the energy method (GC method). This method has been generalized for the Newmark time integration family in linear dynamics as well as many other situations [27,28]. Stability analysis using the energy method shows that the coupling algorithm is unconditionally stable for continuity of velocities and the critical time step for each explicit subdomain is governed by the Courant limit.…”

Section: Introductionmentioning

confidence: 99%

Multi‐time‐step domain coupling method with energy control

Mahjoubi

Krenk

2010

Numerical Meth Engineering

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SUMMARYA multi-time-step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state-space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time-integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state-space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces.

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Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations

Cited by 12 publications

References 12 publications

Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics

Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics

Coupling subdomains with heterogeneous time integrators and incompatible time steps

Multi‐time‐step domain coupling method with energy control

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