An hp certified reduced basis method for parametrized parabolic partial differential equations

By Jens L. Eftang, David J. Knezevic, Anthony T. Patera. 2011

117 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0002c0f45b3ef0f1491f91cbfefe9543e9af6163

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

A localized reduced-order modeling approach for PDEs with bifurcating solutions (2018, methodology): “In [13] an hp-ROM approach is used to localize ROMs for improved accuracy.”
Parameter multi‐domain ‘hp’ empirical interpolation (2012, methodology): “Procedure In this section, we introduce the AP splitting procedure for the partition of the parameter domain; this procedure is an adaption of the approach introduced for the hp RB method in [7, 9].”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, methodology): “Eftang, Knezevic and Patera proposed an extension of POD to the RB approximation framework in [30] by combining POD with a greedy sampling procedure in parameter space for parametrized parabolic PDEs.”
Certified reduced basis approximation for parametrized partial differential equations and applications (2011, methodology): “Improvements in the efficiency of parameters space exploration are also crucial; see for example modified greedy algorithms and combined adaptive techniques [82], such as “hp” RB method [83, 84].”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “In [48] an improved h-p adaptive certified method is introduced to address the same natural convection problem, which has also been applied to a multiscale Stokes Fokker-Planck system modelling liquid crystals in [71].”
Convergence Rates of the POD–Greedy Method (2013, methodology): “The POD–Greedy method for reduced basis construction meanwhile has developed to the standard procedure for instationary problems [4, 6, 13].”
Reduced basis methods for partial differential equations with stochastic influences (2013, background): “In [30] and [29], the hp-Partitioning has been introduced for stationary and instationary problems, respectively, for already affine problems.”