Parameter multi‐domain ‘hp’ empirical interpolation

By Jens L. Eftang, Benjamin Stamm. 2012

101 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/97fda4f50890149c2a973da836f56a59bf14bb25

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In Mechanics of Materials

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “Recent work has proposed approaches to split Ω into multiple subdomains and construct reduced models in each subdomain [10, 76, 82, 121, 190, 221].”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “…been successfully pursued to mitigate the modal deformation of the POD basis by partitioning the state space, 164–167 time domain, 157,168–175 physical domain, 176–179 or parameter space 180–182 using multiple local, piecewise afﬁne subspace approximations instead of a single global approximation.”
The Empirical Interpolation Method (2013, methodology): “The previous work [1, 10, 2] suggest that the basis functions can be integrated with existing quadrature rules.”
The Generalized Empirical Interpolation Method: Stability theory on Hilbert spaces with an application to the Stokes equation (2015, methodology): “In case it cannot be implemented directly, we can follow two strategies that have been introduced on greedy approaches for reduced basis approximations either based on (parameter) domain decomposition like in [15] or [16] based on an adaptive construction of the sample subset, starting from a very c”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “We first consider the example adopted from [31] and already provided in (4.”
CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS (2012, background): “Recently, hp techniques have been proposed for reduced basis approximations12,13 and also for the EIM.14 These ideas help limit the online cost by reducing the size of N and M required to achieve a desired accuracy at the expense of a higher offline cost.”