A Multi-Time-Scale Strategy for Multiphysics Problems: Application to Poroelasticity

Dureisseix, David; Ladevèze, Pierre; Néron, David; Schrefler, Bernhard A.

doi:10.1615/intjmultcompeng.v1.i4.50

Cited by 22 publications

(35 citation statements)

References 16 publications

(30 reference statements)

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“…In that case, following the proof given in [19] which uses anti-monotony and monotony properties (15), one can prove that the quantity 1 2 (s n+1 + s n ) converges towards s ref , the solution of Problem (29).…”

Section: Single-scale Structure Decomposition Methodsmentioning

confidence: 81%

“…This method is a general, mechanics-based computational strategy for the resolution of time-dependent nonlinear problems, which operates over the entire time-space domain. It has been successfully applied to a variety of problems: quasi-static and dynamic analysis, post-buckling analysis, analysis of highly heterogeneous systems [23,22,17,15,18] and multiphysics problems [29].…”

Section: Single-scale Structure 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%

See 2 more Smart Citations

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: Single-scale Structure Decomposition Methodsmentioning

confidence: 81%

Section: Single-scale Structure Decomposition Methodsmentioning

confidence: 99%

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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“…The feasibility of this approach was presented in [2][3][4] in the case of a strongly coupled problem: the consolidation of a saturated poroelastic structure in which the two physics involved were the fluid phase in the connected porosity and the solid phase as the skeleton of the porous medium.…”

Section: Simulation Of Coupled Multiphysics Problemsmentioning

confidence: 99%

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

Néron

Dureisseix

2008

Numerical Meth Engineering

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International audienceThis paper deals with a computational strategy suitable for the simulation of multiphysics problems, based on the Large Time INcrement (LATIN) method. The simulation of such problems must encounter the possible different time and space scales which usually arise with the different physics. Herein, we focus on using different time and space discretizations for each physics by introducing an interface with its own discretization. The feasibility of both a time and space couplings is exemplified on a nonlinear 3-physics strongly coupled problem: the thermal / fluid / structure interaction in a thermo-poroelastic structure

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“…In multiphysics problems, coupling between time grids may be envisaged. This type of problem was solved in [5] by introducing "micro-macro projectors" between grids. None of these strategies involves a true time-homogenization technique.…”

Section: Preprintmentioning

confidence: 99%

On a multiscale computational strategy with time and space homogenization for structural mechanics

Ladevèze

Nouy

2003

Computer Methods in Applied Mechanics and Engineering

136

126

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A new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale. This strategy, which involves homogenization in space as well as in time, could replace in several domains of application the standard homogenization techniques, which are generally limited to the space domain. It is an iterative strategy which calls for the resolution of problems on both a micro (fine) scale and a macro (homogenized) scale. In this paper, we review the bases of this approach and present improved approximation techniques to solve the micro and macro problems.

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A Multi-Time-Scale Strategy for Multiphysics Problems: Application to Poroelasticity

Cited by 22 publications

References 16 publications

On a mixed and multiscale domain decomposition method

On a mixed and multiscale domain decomposition method

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

On a multiscale computational strategy with time and space homogenization for structural mechanics

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