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Computational Mechanics
Erschienen in: Computational Mechanics 2/2013

01.08.2013 | Original Paper

Optimal spatiotemporal reduced order modeling, Part I: proposed framework

verfasst von: Allen LaBryer, Peter J. Attar, Prakash Vedula

Erschienen in: Computational Mechanics | Ausgabe 2/2013

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Abstract

An optimal spatiotemporal reduced order modeling framework is proposed for nonlinear dynamical systems in continuum mechanics. In this paper, Part I, the governing equations for a general system are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which subgrid-scale dynamics arise with a coarse computational grid. Models are then developed to account for the underlying spatiotemporal structure via inclusion of statistical information into the governing equations on a multi-point stencil. These subgrid-scale models are designed to provide closure by accounting for the interactions between spatiotemporal microscales and macroscales as the system evolves. Predictions for the modified system are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation, thus rendering the optimal solution with respect to the chosen resolution. Practical methods are suggested for model construction, appraisal, error measure and implementation. The companion paper, Part II, is devoted to demonstrating the methodology through a computational study of a nonlinear beam.
Vorheriger Artikel Quasi-explicit time-integration schemes for dynamic fracture with set-valued cohesive zone models
Nächster Artikel Optimal spatiotemporal reduced order modeling, Part II: application to a nonlinear beam

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Metadaten
Titel
Optimal spatiotemporal reduced order modeling, Part I: proposed framework
verfasst von
Allen LaBryer
Peter J. Attar
Prakash Vedula
Publikationsdatum
01.08.2013
Verlag
Springer-Verlag
Erschienen in
Computational Mechanics / Ausgabe 2/2013
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-012-0820-9

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