Multi-time-step and two-scale domain decomposition method for non-linear structural dynamics

In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocitie...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 58; no. 10; pp. 1545 - 1569
Main Authors: Gravouil, A., Combescure, A.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 14.11.2003
Wiley
Subjects:
Engineering Sciences
Mathematics
Mechanical engineering
Mechanics
multigrid
non-linear dynamics
Numerical Analysis
subcycling
subdomains
subdomains
subcycling
non-linear dynamics
multigrid
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two‐scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale. For non‐linear problems, we propose an algorithm with a single iteration level to deal with both the non‐linear equilibrium and the two space scales thanks to a two‐grid method in which the relaxation steps are performed using a non‐linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.
Bibliography:istex:8616871C33564482662625CBB3511481F63C1145
ArticleID:NME826
ark:/67375/WNG-Q7C9ZXF3-T
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.826