Two examples of partitioning approaches for multiscale and multiphysics coupled problems

Authors

  • David Dureisseix Laboratoire de Mécanique et Génie Civil (LMGC) CNRS UMR 5508/Université Montpellier 2 CC048 Place Eugène Bataillon F-34095 Montpellier cedex 5

DOI:

https://doi.org/10.13052/REMN.17.807-818

Keywords:

partitioning, interface, multiphysics, multiscale, transfer, non matching discretizations, finite elements

Abstract

Partitioning strategies usually focus on interaction between subsystems. They are good candidates to model couplings at different spatial or time scales. A mechanism for the information transfer between subsystems and / or between scales is therefore required. Herein, we propose examples of a subdomain gluing with different spatial scales, and of a poroelastic coupling featuring different time scales.

Downloads

Download data is not yet available.

References

Amini A. M., Dureisseix D., Cartraud P., Buannic N., “ A micro-macro strategy for ship structural

analysis with FETI-DP method”, Third European Conference on Computational Mechanics

— ECCM 2006 — Solids, Structures and Coupled Problems in Engineering, 2006.

Ben Dhia H., “ Multiscale mechanical problems: the Arlequin method”, Comptes Rendus à

l’Académie des Sciences, vol. 326, n° 326, p. 899-904, 1998. Série IIb.

Ben Dhia H., Rateau G., “ The Arlequin method as a flexible engineering design tool”, International

Journal for Numerical Methods in Engineering, vol. 62, p. 1442-1462, 2005.

Bernardi C., Maday Y., Patera A. T., “ A new nonconforming approach to domain decomposition:

the mortar element method”, in H. Brezzi (ed.), Nonlinear partial differential

equations and their applications, Paris, p. 13-51, 1994.

Borri M., Bottaso C., “ A general framework for interpreting time finite element formulations”,

Computational Mechanics, vol. 13, p. 133-142, 1993.

Bramble J. H., Pasciak J. E., Schatz A. H., “ The construction of preconditioners for elliptic

problems by substructuring, I”, Mathematics of Computation, vol. 47, n° 175, p. 103-134,

Combescure A., Gravouil A., Herry B., “ An algorithm to solve transient structural nonlinear

problems for non-matching time-space domains”, Computers and Structures, vol.

, p. 1211 -1222, 2003.

Coussy O., Poromechanics, John Wiley & Sons, 2004.

Dureisseix D., Bavestrello H., “ Information transfer between incompatible finite element

meshes: application to coupled thermo-viscoelasticity”, Computer Methods in Applied Mechanics

and Engineering, vol. 195, n° 44-47, p. 6523-6541, 2006.

Dureisseix D., Ladevèze P., Néron D., Schrefler B. A., “ A multi-time-scale strategy for multiphysics

problems: application to poroelasticity”, International Journal for Multiscale Computational

Engineering, vol. 1, n° 4, p. 387-400, 2003a.

Dureisseix D., Ladevèze P., Schrefler B. A., “ A LATIN computational strategy for multiphysics

problems: application to poroelasticity”, International Journal for Numerical Methods in

Engineering, vol. 56, n° 10, p. 1489-1510, 2003b.

Eriksson K., Johnson C., Thomée V., “ Time discretization of parabolic problems by the discontinuous

Galerkin formulation”, RAIRO Modélisation Mathématique et Analyse Numérique,

vol. 19, p. 611-643, 1985.

Farhat C., Géradin M., “ Using a reduced number of Lagrange multipliers for assembling parallel

incomplete field finite element approximations”, Computer Methods in Applied Mechanics

and Engineering, vol. 97, p. 333-354, 1992.

Farhat C., Lesoinne M., “ Two efficient staggered algorithms for the serial and parallel solution

of three-dimensional nonlinear transient aeroelastic problems”, Computer Methods in

Applied Mechanics and Engineering, vol. 182, p. 499-515, 2000a.

Farhat C., Lesoinne M., Le Tallec P., Pierson K., Rixen D., “ FETI-DP: a dual-primal unified

FETI method - part I: a faster alternative to the two-level FETI method”, International

Journal for Numerical Methods in Engineering, vol. 50, n° 7, p. 1523-1544, 2001.

Farhat C., Lesoinne M., Pierson K., “ A scalable dual-primal domain decomposition method”,

Numerical Linear Algebra with Applications, vol. 7, p. 687-714, 2000b.

Farhat C., Roux F.-X., “ Implicit parallel processing in structural mechanics”, in J. T. Oden

(ed.), Computational Mechanics Advances, vol. 2, North-Holland, 1994.

Faucher V., Combescure A., “ A time and space mortar method for coupling linear modal subdomains

and non-linear subdomains in explicit structural dynamics”, Computer Methods in

Applied Mechanics and Engineering, vol. 192, n° 5-6, p. 509-533, 2003.

Faucher V., Combescure A., “ Local modal reduction in explicit dynamics with domain decomposition.

Part 2: specific interface treatment when modal subdomains are involved”,

International Journal for Numerical Methods in Engineering, vol. 61, n° 1, p. 69-95, 2004.

Felippa C. A., Park K. C., Farhat C., “ Partitioned analysis of coupled mechanical systems”,

Computer Methods in Applied Mechanics and Engineering, vol. 190, p. 3247-3270, 2001.

Gravouil A., Combescure A., “ Multi-time-step explicit-implicit method for non-linear structural

dynamics”, International Journal for Numerical Methods in Engineering, vol. 50,

p. 199 -225, 2001.

Guidault P.-A., Allix O., Champaney L., Cornuault C., “ Une approche micro-macro pour le

suivi de fissure avec enrichissement local”, Revue Européenne de Mécanique Numérique,

vol. 15, p. 187-198, 2006.

Guidault P.-A., Allix O., Navarro J.-P., “ A two-scale approach with homogenization for the

computation of cracked structures”, Computers and Structures, vol. 85, n° 17-18, p. 1360-

, 2007.

Jean M., “ The non-smooth contact dynamics method”, Computer Methods in Applied Mechanics

and Engineering, vol. 177, p. 235-257, 1999.

Ladevèze P., Nonlinear computational structural mechanics — New approaches and nonincremental

methods of calculation, Springer Verlag, 1999.

Ladevèze P., Dureisseix D., “ A new micro-macro computational strategy for structural analysis”,

Comptes-Rendus de l’Académie des Sciences, vol. 327, p. 1237-1244, 1999.

Ladevèze P., Loiseau O., Dureisseix D., “ A micro-macro and parallel computational strategy

for highly heterogeneous structures”, International Journal for Numerical Methods in Engineering,

vol. 52, n° 1-2, p. 121-138, 2001.

Ladevèze P., Nouy A., “ On a multiscale computational strategy with time and space homogenization

for structural mechanics”, Computer Methods in Applied Mechanics and Engineering,

vol. 192, p. 3061-3087, 2003.

Le Tallec P., “ Domain decomposition methods in computational mechanics”, Computational

Mechanics Advances, vol. 1, North-Holland, 1994.

Lewis R. W., Schrefler B. A., The finite element method in the static and dynamic deformation

and consolidation of porous media, 2nd edn, John Wiley & Sons, 1998.

Lubineau G., Ladevèze P., Violeau D., “ Durability of CFRP laminates under thermomechanical

loading: A micro-meso damage model”, Composites Science and Technology, vol. 66,

p. 983-992, 2006.

Magoulès F. (ed.), Mesh partitioning techniques and domain decomposition methods, Civil-

Comp Press / Saxe-Coburg, 2007.

Moreau J. J., “ Numerical aspects of sweeping process”, Computer Methods in Applied Mechanics

and Engineering, vol. 177, p. 329-349, 1999.

Néron D., Dureisseix D., “ A computational strategy for poroelastic problems with a time interface

between coupled physics”, International Journal for Numerical Methods in Engineering,

To appear.

Nineb S., Alart P., Dureisseix D., “ Domain decomposition approach for nonsmooth discrete

problems, example of a tensegrity structure”, Computers and Structures, vol. 85, n° 9,

p. 499-511, 2007.

Nouy A., Ladevèze P., Loiseau O., “ A multiscale computational approach for contact problems”,

Computer Methods in Applied Mechanics and Engineering, vol. 191, p. 4869-4891,

Rey C., Chiaruttini V., “ An efficient multiscale parallel-in-time strategy for nonlinear poroplastic

problems”, 8th ESAFORM Conference on Material Forming, p. 137-140, 2005.

Rixen D., Farhat C., Géradin M., “ A two-step, two-field hybrid method for the static and dynamic

analysis of substructure problems with conforming and non-conforming interfaces”,

Computer Methods in Applied Mechanics and Engineering, vol. 154, n° 154, p. 229-264,

Violeau D., Ladevèze P., Lubineau G., “ Micromodel based computations for laminated composites”,

th International Conference on Computational Structures Technology, 2006.

Downloads

Published

2008-05-17

How to Cite

Dureisseix, D. (2008). Two examples of partitioning approaches for multiscale and multiphysics coupled problems. European Journal of Computational Mechanics, 17(5-7), 807–818. https://doi.org/10.13052/REMN.17.807-818

Issue

Section

Original Article