The large number of degrees-of-freedom of finite difference, finite element, or molecular dynamics models for complex systems is often a significant barrier to both efficient computation and increased understanding of the relevant phenomena. Thus there is a benefit to constructing reduced-order models with many fewer degrees-of-freedom that retain the same accuracy as the original model. Constructing reduced-order models for linear dynamical systems relies substantially on the existence of global modes such as eigenmodes where a relatively small number of these modes may be sufficient to describe the response of the total system. For systems with very many degrees-of-freedom that arise from spatial discretization of partial differential equation models, computing the eigenmodes themselves may be the major challenge. In such cases the use of alternative modal models based upon proper orthogonal decomposition or singular value decomposition have proven very useful. In the present paper another facet of reduced-order modeling is examined, i.e., the effects of “local” nonlinearity at the nanoscale. The focus is on nanoscale devices where it will be shown that a combination of global modal and local discrete coordinates may be most effective in constructing reduced-order models from both a conceptual and computational perspective. Such reduced-order models offer the possibility of reducing computational model size and cost by several orders of magnitude.
Multiscale, Multiphenomena Modeling and Simulation at the Nanoscale: On Constructing Reduced-Order Models for Nonlinear Dynamical Systems With Many Degrees-of-Freedom
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Dec. 9, 2001; final revision, Sept. 25, 2002. Associate Editor: A. K. Ferri. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Dowell, E. H., and Tang, D. (June 11, 2003). "Multiscale, Multiphenomena Modeling and Simulation at the Nanoscale: On Constructing Reduced-Order Models for Nonlinear Dynamical Systems With Many Degrees-of-Freedom ." ASME. J. Appl. Mech. May 2003; 70(3): 328–338. https://doi.org/10.1115/1.1558079
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