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PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and P. Iványi
A Time-Space-Parameters Proper Generalised Decomposition Approach for Nonlinear Computational Mechanics
M. Vitse, D. Néron and P.-A. Boucard
LMT-Cachan, ENS Cachan, CNRS, PRES UniverSud Paris, France
M. Vitse, D. Néron, P.-A. Boucard, "A Time-Space-Parameters Proper Generalised Decomposition Approach for Nonlinear Computational Mechanics", in B.H.V. Topping, P. Iványi, (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 171, 2014. doi:10.4203/ccp.106.171
Keywords: nonlinear problems, proper generalised decomposition, reduced order basis, parametric problems, LATIN method, reduced order modelling..
The cost associated with the resolution of parametric problems can be extremely prohibitive. Model reduction techniques are a good answer to circumvent this issue. This paper provides the first developments of an algorithm for solving nonlinear parametric problems, based on the LATIN method for the treatment of the nonlinear aspects and the proper generalised decomposition for the parameter dependency. A full time-space- parameter decomposition of the solution is introduced into the LATIN algorithm, and numerical examples of academic problems are given so as to point out the advantages and the limits of this extension. This paper concludes by giving directions for possible improvements to the strategy.
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