Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency

By Charbel Farhat, Philip Avery, Todd Chapman, Julien Cortial. 2014

372 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b97900b33f30c8ca3313786807a39e3350824992

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In Civil and Structural Engineering

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Structure‐preserving, stability, and accuracy properties of the energy‐conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models (2015, methodology): “Most recently, an energy-based method was developed in [29, 30] for the hyper reduction of nonlinear FE dynamic models.”
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem (2015, positive): “…methods were developed using the Petrov–Galerkin projection for reducing the dimension of a discrete nonlinear dynamic computational model, see e.g. Hyper-reduction method [13,14], Gauss–Newton with Approximation Tensor (GNAT) method [14–16] or Discrete Empirical Interpolation (DEIM) method [9,17].”
On the use of simulation in robotics: Opportunities, challenges, and suggestions for moving forward (2020, methodology): “The approach could be used to methodically reduce model (and therefore computational) complexity through systematic dimensional reduction and/or model compression (45, 46).”
A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models (2017, methodology): “caveat is remedied by equipping an MOR method with a rigorous procedure for approximating the resulting reduced operators whose computational complexity scales only with the small size n of the ROM [2, 4, 13, 14].”
A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics (2017, methodology): “Furthermore, the ECSW method distinguishes itself from alternative hyper reduction methods through its preservation of the Lagrangian structure associated with Hamilton’s principle.”