An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations

By Ngoc Cuong Nguyen, Jaime Peraire. 2008

125 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a0de450af7d7367e84db4bbd5de8e0e32983204f

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In Mechanical Engineering

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency (2014, methodology): “A variant of this method [20] uses ‘best [interpolation] points’ and a proper orthogonal decomposition (POD) basis.”
Efficient non‐linear proper orthogonal decomposition/Galerkin reduced order models with stable penalty enforcement of boundary conditions (2012, methodology): “From these snapshots, the interpolation points 1xN m omD1 are computed following the approach outlined previously (and discussed in detail in Section 2 of [22]).”
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): “A variant of EIM, which uses ‘best [interpolation] points’ and a POD basis, was also introduced in [21].”
POD‐based model reduction with empirical interpolation applied to nonlinear elasticity (2016, methodology): “In [32], the best point interpolation method was applied to nonlinear and non-affine parameterized PDEs.”
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows (2012, methodology): “[24] relies for the same purpose on ‘best [interpolation] points’ and a POD basis.”
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, background): “This is because the evaluation of the integrals involving the non-affine and non-linear terms is computationally expensive and cannot be pre-computed [30].”
Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation (2015, methodology): “However, the POD/Galerkin method is not able to reduce the computation cost of nonlinearities of the 3-dimensional Bubnov–Galerkin Navier–Stokes equation [20].”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, background): “In particular, in [28], Nguyen and Peraire discuss the limitations of such approaches and give a number of examples of equations involving nonpolynomial nonlinearities.”
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations (2011, methodology): “This strategy differs from those advocated in [30, 24, 25, 27, 28].”