Digital Library

of the European Council for Modelling and Simulation



Reduced Order Computational Continua


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


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



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.

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