A computational strategy for thermo‐poroelastic structures with a time–space interface coupling

Néron, David; Dureisseix, David

doi:10.1002/nme.2283

Cited by 38 publications

(37 citation statements)

References 43 publications

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“…The third term in (39) weakly inforced the continuity between the displacement and velocity fields over time. Remaining terms are similar to those of the one field case and have been previously described.…”

Section: Two-field Space-time Discontinuous Galerkin Methodsmentioning

confidence: 99%

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

Boucinha¹,

Gravouil²,

Ammar³

2013

Computer Methods in Applied Mechanics and Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. In this paper, we investigate ability of proper generalized decomposition (PGD) to solve transient elastodynamic models in space-time domain. Classical methods use time integration schemes and an incremental resolution process. We propose here to use standard time integration methods in a nonincremental strategy. As a result, PGD gives a separated representation of the space-time solution as a sum of tensorial products of space and time vectors, that we interpret as space-time modes. Recent time integration schemes are based on multi-field formulations. In this case, separated representation can be constructed using state vectors in space and same vectors in time. However, we have experienced bad convergence order using this decomposition. Furthermore, temporal approximation must be the same for all fields. Thus, we propose an extension of classical separated representation for multi-field problems. This multi-field PGD (MF-PGD) uses space and time vectors that are different for each field. Calculation of decomposition is done using a monolithic approach in space and time, potentially allowing the use of different approximations in space and time. Finally, several simulations are performed with the transient elastodynamic problem with one dimension in space. Different approximations in time are investigated: Newmark scheme, single field time discontinuous Galerkin method and two fields time continuous and discontinuous Galerkin methods.

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Section: Two-field Space-time Discontinuous Galerkin Methodsmentioning

confidence: 99%

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

Boucinha¹,

Gravouil²,

Ammar³

2013

Computer Methods in Applied Mechanics and Engineering

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“…; u F ðx; tÞ defined in a space-time domain X Â I. These fields can be related to different physics (various examples can be found in [19,32,33,6,10]) or as illustrated in [9,18], they can be different components of a vector field. Also, we allow different approximation spaces for each field, that is the discrete representation of a given field u i is stored in a second order tensor u i 2 R Nði;SÞ R Nði;TÞ (where Nði; dÞ gives the size of the approximation space related to the field i in the dimension d ¼ S or T).…”

Section: Extension To Multi-field Modelsmentioning

confidence: 99%

“…Following approaches used in [19,32,6,9,18,10], we introduce a rank-M approximation 3 of each second order tensor u i . We denote this multi-field decomposition fug M and define the corresponding subset S…”

Section: Optimal Approximation With Respect To the Target Normmentioning

confidence: 99%

“…Then, following [10], we introduce a monolithic definition of a priori decomposition of multi-field problems. This approach differs from [19,32,6] in the sense that we do not partition the multi-field problem, thus preserving the better convergence properties of monolithic approaches while allowing different approximation spaces for each field. The decomposition is searched as a minimizer of the residual of the monolithic problem, among all decompositions in S…”

Section: Classical Minimal Residual Pgdmentioning

confidence: 99%

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Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – Application to transient elastodynamics in space-time domain

Boucinha

Ammar

Gravouil

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. b s t r a c tIt is now well established that separated representations built with the help of proper generalized decomposition (PGD) can drastically reduce computational costs associated with solution of a wide variety of problems. However, it is still an open question to know if separated representations can be efficiently used to approximate solutions of hyperbolic evolution problems in space-time domain. In this paper, we numerically address this issue and concentrate on transient elastodynamic models. For such models, the operator associated with the space-time problem is non-symmetric and low-rank approximations are classically computed by minimizing the space-time residual in a natural L 2 sense, yet leading to non optimal approximations in usual solution norms. Therefore, a new algorithm has been recently introduced by one of the authors and allows to find a quasi-optimal low-rank approximation a priori with respect to a target norm. We presently extend this new algorithm to multi-field models. The proposed algorithm is applied to elastodynamics formulated over space-time domain with the Time Discontinuous Galerkin method in displacement and velocity. Numerical examples demonstrate convergence of the proposed algorithm and comparisons are made with classical a posteriori and a priori approaches.

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“…In section 4 we consider the coupling between global and many species kinetic local models and the issue related to the existence of different characteristic times of both the local and global model. This issue was addressed in the context of proper generalized decompositions in [17]. Finally, in section 5 we address a numerical example.…”

Section: Introductionmentioning

confidence: 99%

Proper generalized decomposition of multiscale models

Chinesta

Ammar

Cueto

2010

Numerical Meth Engineering

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In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space–time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non‐linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non‐incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations. Copyright © 2009 John Wiley & Sons, Ltd.

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A computational strategy for thermo‐poroelastic structures with a time–space interface coupling

Cited by 38 publications

References 43 publications

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – Application to transient elastodynamics in space-time domain

Proper generalized decomposition of multiscale models

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