A LATIN computational strategy for multiphysics problems: application to poroelasticity

Dureisseix, David; Ladevèze, Pierre; Schrefler, B. A.

doi:10.1002/nme.622

Cited by 37 publications

(63 citation statements)

References 22 publications

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“…Indeed, for such a condition to be taken into account, the descent search direction can no longer be written as (36), but must be expressed in the weak form (37), with a test function F ⋆ which no longer belongs to F, but to F ad instead. The substructure part of (37) remains unchanged:…”

Section: Relation With Newton-schur Domain Decomposition Methodsmentioning

confidence: 99%

“…This technique, which is commonly used in the LATIN method [19], consists in defining an approximation based on generalized radial functions. It has been shown in previous works [19,37,29] that under small-displacement assumptions this approach reduces the computational cost drastically. All the details can be found in [16].…”

Section: Radial Loading Approximationmentioning

confidence: 99%

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On a mixed and multiscale domain decomposition method

Ladevèze

Néron

Gosselet

2007

Computer Methods in Applied Mechanics and Engineering

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This paper presents a reexamination of a multiscale computational strategy with homogenization in space and time for the resolution of highly heterogeneous structural problems, focusing on its suitability for parallel computing. Spatially, this strategy can be viewed as a mixed, multilevel domain decomposition method (or, more accurately, as a "structure decomposition" method). Regarding time, a "parallel" property is also described. We also draw bridges between this and other current approaches.Key words: domain decomposition, multiscale, computational mechanics IntroductionIn the structural mechanics field, one can observe a surge of interest in the multiscale analysis of structures with complex microstructural geometry and/or complex behavior. When accurate solutions are required, calculations must be performed on a finely discretized model of the structure (defined on what is called the "micro" level) consistent with short lengths of variation, both in space and in time. A major application is the analysis of composite structures described on the microscale or on the mesoscale [1]; there are also other applications, such as in [2,3]. These types of situations lead to problems with very large numbers of degrees of freedom and computation costs which are prohibitive if one uses classical finite element codes. One of the main objectives * Corresponding author. E-mail: pierre.ladeveze@lmt.ens-cachan.fr Preprint of the last few decades has been to develop efficient and robust computational strategies suitable for these types of problems. One of these strategies uses the theory of the homogenization of periodic media [4][5][6]. Other developments and the associated computational approaches can be found in [7][8][9][10][11][12][13][14]. Besides periodicity, these strategies rely on the fundamental assumption that the ratio between the two scales is small. Thus, the boundary zones require specific treatment because in these zones the microstructure cannot be homogenized. Here, we follow a recently introduced multiscale computational strategy for nonlinear evolution problems. This strategy involves an automatic homogenization technique in space as well as in time [15,16] which is an extension of previous works limited to space alone [17,18]. This strategy, developed in a general framework, makes no a priori assumption regarding the form of the solution and, therefore, does not suffer from the limitations of standard homogenization techniques; moreover, it relies on an iterative algorithm. Until now, this strategy has been developed in the framework of small displacements of (visco)plastic structures under possible contact with or without friction. This paper is a reconsideration of this computational strategy in order to assess its adaptability to parallel computing. Therefore, we examine its three main characteristics. The first characteristic is that it can be viewed as a mixed, multilevel domain decomposition method or, more precisely as will explained further on, as a "structure decomposition" method. Ind...

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Section: Relation With Newton-schur Domain Decomposition Methodsmentioning

confidence: 99%

Section: Radial Loading Approximationmentioning

confidence: 99%

On a mixed and multiscale domain decomposition method

Ladevèze

Néron

Gosselet

2007

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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Multifield Problems

Schrefler¹

2004

Encyclopedia of Computational Mechanics

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This chapter deals with multifield problems with overlapping domains. A review of a series of typical problems belonging to this filed is first presented where examples of up to six overlapping fields are shown. Then the most popular solution procedures are discussed. They are either the monolithic method or methods involving some matrix partitioning. These methods are illustrated on selected model problems. The respective numerical properties and connected problems are discussed and examples are shown.

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A LATIN computational strategy for multiphysics problems: application to poroelasticity

Cited by 37 publications

References 22 publications

On a mixed and multiscale domain decomposition method

On a mixed and multiscale domain decomposition method

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

Multifield Problems

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