Structure-preserving model reduction for mechanical systems

By Sanjay Lall, Petr Krysl, Jerrold E. Marsden. Physica A: Statistical Mechanics and its Applications, 2003

208 citations recorded by the source corpus.

This paper focuses on methods of constructing of reduced-order models of mechanical systems which preserve the Lagrangian structure of the original system. These methods may be used in combination with standard spatial decomposition methods, such as the Karhunen–Loeve expansion, balancing, and wavelet decompositions. The model reduction procedure is implemented for three-dimensional finite-element models of elasticity, and we show that using the standard Newmark implicit integrator, significant savings are obtained in the computational costs of simulation. In particular simulation of the reduced model scales linearly in the number of degrees of freedom, and parallelizes well.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/beed5991557b3732e2e03938b2131aae7d70c43b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Dimensional model reduction in non‐linear finite element dynamics of solids and structures (2001, methodology): “( 47 ) The non - zero spectra of Cs and C d are the same , and the eigenvectors of C d corresponding to the non - zero eigenvalues are recovered by the procedure described in Reference [ 12 ] .”
Model Reduction by Moment Matching for Linear and Nonlinear Systems (2010, methodology): “Energy-based methods have been discussed, for example, in [21], [23], [32], [33]; model reduction of systems in special forms, such as differential-algebraic systems, bilinear systems or mechanical/Hamiltonian systems, have been discussed in [34], [35], [36], [37], [38], and reduction around a limit”
A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations (2016, background): “It is shown in section 4 that this variational principle is preserved when the NTFA decomposition is assumed so that the NTFA model can be said to be "structure-preserving" in the sense of Lall et al. (2003).”
A New Look at Proper Orthogonal Decomposition (2003, methodology): “Structure preserving model reduction based on POD for mechanical systems with Lagrangian structure has been developed in [15].”
The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains (2007, unknown): “[30].”
Model Reduction via Proper Orthogonal Decomposition (2008, background): “More precisely, we have the following result [20]: Theorem 1.”
A subspace approach to balanced truncation for model reduction of nonlinear control systems (2002, methodology): “Methods for model reduction, which take account of this underlying geometry and preserve it, are developed in References [7, 40 ].”