We propose to incorporate a Response Surface (RS) approximation of variables over a parametric domain into a weak form of parametric Partial Differential Equations (PDEs). Hence a multidimensional model-reduction can be achieved. We propose a multidimensional a priori model reduction method to generate or to enrich RSs. It is coined multidimensional because the fields to forecast are defined over an augmented domain in term of dimension. They are functions of both space variables and parameters that simultaneously evolve in time. This changes the functional space related to the weak form of the PDEs and the definition of the reduced bases. It has a significant impact on the proposed model reduction method. In particular, a new point of view on interpolation of variables has to be addressed. A Multidimensional Reduced Integration Domain (MRID) is proposed to reduce the complexity of the reduced formulation. A multidimensional Hyper-Reduction method extract from the MRID truncated equilibrium equations, truncated residuals and a truncated error indicator.
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ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
July 2–4, 2012
Nantes, France
Conference Sponsors:
- International
ISBN:
978-0-7918-4484-7
PROCEEDINGS PAPER
Multidimensional Hyper-Reduction of Large Mechanical Models Involving Internal Variables
David Ryckelynck
David Ryckelynck
Mines ParisTech University, Evry, France
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David Ryckelynck
Mines ParisTech University, Evry, France
Paper No:
ESDA2012-82971, pp. 99-106; 8 pages
Published Online:
August 12, 2013
Citation
Ryckelynck, D. "Multidimensional Hyper-Reduction of Large Mechanical Models Involving Internal Variables." Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control. Nantes, France. July 2–4, 2012. pp. 99-106. ASME. https://doi.org/10.1115/ESDA2012-82971
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