A ‘best points’ interpolation method for efficient approximation of parametrized functions

By Ngoc Cuong Nguyen, Anthony T. Patera, Jaime Peraire. 2008

204 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8d20fc0a02309b460842780b6970bd5a2903270c

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Citations in the corpus

Efficient non‐linear proper orthogonal decomposition/Galerkin reduced order models with stable penalty enforcement of boundary conditions (2012, methodology): “Given the ‘best points’ for N , that is, the solutions to (17) (or any set of interpolation points), denoted by 1xN m omD1, it is straightforward to apply the interpolation procedure outlined in [21, 22] to the non-linear function N .”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “There are a variety of methods to select these interpolation indices [26, 67, 180].”
Efficient sensor placement for ocean measurements using low-dimensional concepts (2009, methodology): “These are not the only possible optimization approaches, and one can use the reconstruction error directly as alternative cost function or set up different minimization procedures using other sets of sampling points, e.g., see Nguyen et al. (2008).”
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows (2012, unknown): “For example, for the various forms of empirical interpolation outlined in Section 1, several algorithms for selecting sample indices have been developed around the objective of minimizing the error in the interpolated snapshots [22, 31, 25], the difference between the interpolated snapshots and thei”
High-performance model reduction techniques in computational multiscale homogenization (2014, methodology): “For this reason, we shall refer to the set of points arising from solving this minimization problem as the standard or basic sampling points — these are, for instance, the Best Interpolation Points of Nguyen et al. [53].”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “This nonlinear function is from an example in [27].”
POD‐based model reduction with empirical interpolation applied to nonlinear elasticity (2016, methodology): “A very similar approach to the DEIM is the best point interpolation method based on [31].”
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, methodology): “Another similar technique for non-linear treatments is the best points interpolation method (BPIM) [29].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “There are some techniques, which provide efficient estimates of f(V z(t)) as the (discrete) empirical interpolation methods (DEIM or EIM) [21, 56], the missing point estimation method [8], or a best points interpolation method [146].”
An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations (2008, methodology): “See [ 34 ] for application of the BPIM to face recognition and optimal sensor placement for field reconstruction and [35] for application of the EIM to polynomial interpolation and numerical integration.”
The Empirical Interpolation Method (2013, unknown): “In addition to the GLL points mentioned earlier, alternatives to EIM include “best points” [16] and Fekete points [18].”