A low‐cost, goal‐oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems

By Kevin T. Carlberg, Charbel Farhat. 2011

127 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/84fda1c120c39044e8c27e91f2e9d86a7e09564f

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In Biomedical Engineering

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics (2017, background): “Furthermore, while this work considers only state snapshots for the construction of Vk, other types of snapshots such as Krylov vectors [34] and state sensitivities [35, 36] can be appended to Nk in order to improve the computational efficiency of the training procedure chosen for constructing the R”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “In the optimization application of static systems, Carlberg and Farhat [18] proposed a goal-oriented framework, so-called compact POD, using snapshots from state vectors and their sensitivity derivatives with respect to system input parameters.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “A “compact POD” approach based on goal-oriented Petrov-Galerkin projection was proposed in [28], in order to minimize the approximation error subject to a chosen output criteria, also including sensitivity information (with proper weighting coming from the Taylor-expansion) and including “mollificat”
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, unknown): “For a given application, the construction of V is typically based on the pre-computation of solution ‘snapshots’ and their sensitivities with respect to the parameters %k [3], for various problems related to the application.”