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Digital Library of the
European Council for Modelling and Simulation |
Title: |
Reduced
Order Computational Continua |
Authors: |
Jacob Fish, Vasilina Filonova, Zheng Yuan |
Published in: |
(2011).ECMS
2011 Proceedings edited by: T. Burczynski, J. Kolodziej, A. Byrski, M. Carvalho. European Council for Modeling and Simulation. doi:10.7148/2011 ISBN:
978-0-9564944-2-9 25th
European Conference on Modelling and Simulation, Jubilee Conference Krakow,
June 7-10, 2011
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Citation
format: |
Fish, J., Filonova,
V., & Yuan, Z. (2011). Reduced Order Computational Continua. ECMS 2011
Proceedings edited by: T. Burczynski, J. Kolodziej, A. Byrski, M. Carvalho (pp. 7-10). European
Council for Modeling and Simulation. doi:10.7148/2011-0007-0010 |
DOI: |
http://dx.doi.org/10.7148/2011-0007-0010 |
Abstract: |
The
paper presents a new multiscale framework that is
both mathematically rigorous and practical in the sense that it has been
successfully applied in aerospace, automotive and civil engineering
industries. The “rigor” aspect of the method is provided by recently
developed 2ζ
computational continua (C) formulation (Fish
and Kuznetsov, 2009),
which is endowed with fine-scale details, introduces no scale separation,
makes no assumption about infinitesimality of the
fine-scale structure, does not require higher order continuity, introduces no
new degrees-of-freedom and is free of higher order boundary conditions. The
“practicality” aspect of the proposed method is inherited from the reduced
order homogenization (Yuan and Fish, 2009, Fish and Yuan, 2008) approach,
which constructs residual free-fields that eliminate the bottleneck of
satisfying fine-scale equilibrium equations and is endowed with a
hierarchical model improvement capability where the cost of the most inexpensive
member of the sequence is comparable to that of semi- analytical or
phenomenological methods. Blending of the two methods into a
single cohesive computational framework, hereafter to be referred to as the Reduced order Computational Continua or simply RC2, that inherits the underlying
characteristics of its two ingredients, is the main objective of the present
manuscript. We conclude the manuscript with a brief summary and discussion of
future research directions. |
Full
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