Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems

2012 ◽  
Vol 45 (2) ◽  
pp. 112-117 ◽  
Author(s):  
Markus Dihlmann ◽  
Sven Kaulmann ◽  
Bernard Haasdonk
Keyword(s):  
Model Reduction ◽  
Reduced Basis ◽  
Construction Procedure ◽  
Basis Construction ◽  
Evolution Systems

scholarly journals Combining spectral and POD modes to improve error estimation of numerical model reduction for porous media

2021 ◽  
Author(s):  
Fredrik Ekre ◽  
Fredrik Larsson ◽  
Kenneth Runesson ◽  
Ralf Jänicke
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Model Reduction ◽  
Error Control ◽  
Mode Selection ◽  
Selection Strategy ◽  
Error Estimator ◽  
Reduced Basis ◽  
The One ◽  
Estimated Error

AbstractNumerical model reduction (NMR) is used to solve the microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. The reduction technique and an associated error estimator for the NMR error have been presented in prior work, where both spectral decomposition (SD) and proper orthogonal decomposition (POD) were used to construct the reduced basis. It was shown that the POD basis performs better w.r.t. minimizing the residual, but the SD basis has some advantageous properties for the estimator. Since it is the estimated error that will govern the error control, the most efficient procedure is the one that results in the lowest error bound. The main contribution of this paper is further development of the previous work with a proposed combined basis constructed using both SD and POD modes together with an adaptive mode selection strategy. The performance of the combined basis is compared to (i) the pure SD basis and (ii) the pure POD basis via numerical examples. The examples show that it is possible to find a combination of SD/POD modes which is improved, i.e. it yields a smaller estimate, compared to the cases of pure SD or pure POD.

scholarly journals Reduced-Order Quasilinear Model of Ocean Boundary-Layer Turbulence

2020 ◽  
Vol 50 (3) ◽  
pp. 537-558 ◽  
Author(s):  
Joseph Skitka ◽  
J. B. Marston ◽  
Baylor Fox-Kemper
Keyword(s):  
Boundary Layer ◽  
Model Reduction ◽  
Turbulent Transport ◽  
Galerkin Projection ◽  
Surface Boundary ◽  
Reduced Basis ◽  
Surface Boundary Layer ◽  
Boundary Layer Turbulence ◽  
Basis Size ◽  
Quasilinear Approximation

AbstractThe combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary layer turbulence is investigated. Idealized horizontally homogeneous problems of surface-forced thermal convection and Langmuir turbulence are studied in detail. Model reduction is achieved with a Galerkin projection of the governing equations onto a subset of modes determined by proper orthogonal decomposition (POD). When applied to boundary layers that are horizontally homogeneous, POD and a horizontally averaged quasilinear approximation both assume flow features that are horizontally wavelike, making the pairing very efficient. For less than 0.2% of the modes retained, the reduced quasilinear model is able to reproduce vertical profiles of horizontal mean fields as well as certain energetically important second-order turbulent transport statistics and energies to within 30% error. Reduced-basis quasilinear statistics must approach the full-basis statistics as the basis size approaches completion; however, some quasilinear statistics resemble those found in the fully nonlinear simulations at smaller basis truncations. Thus, model reduction could possibly improve upon the accuracy of quasilinear dynamics.

Reduced Basis Model Reduction of Parametrized Two—Phase Flow in Porous Media

2012 ◽  
Vol 45 (2) ◽  
pp. 722-727 ◽  
Author(s):  
Martin Drohmann ◽  
Bernard Haasdonk ◽  
Mario Ohlberger
Keyword(s):  
Porous Media ◽  
Model Reduction ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Reduced Basis ◽  
Two Phase

scholarly journals A poro-viscoelastic substitute model of fine-scale poroelasticity obtained from homogenization and numerical model reduction

2020 ◽  
Vol 65 (4) ◽  
pp. 1063-1083 ◽  
Author(s):  
Ralf Jänicke ◽  
Fredrik Larsson ◽  
Kenneth Runesson
Keyword(s):  
Numerical Model ◽  
Model Reduction ◽  
Evolution Equations ◽  
Present Model ◽  
Scale Model ◽  
Reduced Basis ◽  
Pressure Fields ◽  
Linearly Independent ◽  
Macro Scale ◽  
Scale Fluctuation

AbstractNumerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested $$\hbox {FE}^2$$FE2 setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged $$\hbox {FE}^2$$FE2 computations.

scholarly journals Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media

2015 ◽  
Author(s):  
Martin E Hess ◽  
Jan Hesthaven ◽  
Peter Benner
Keyword(s):  
Wave Propagation ◽  
Model Reduction ◽  
Approximation Error ◽  
Dispersive Media ◽  
Dielectric Waveguides ◽  
Reduced Basis ◽  
Model Order ◽  
Optical Wave ◽  
Error Indicator ◽  
Optical Wave Propagation

Simulation of electromagnetic and optical wave propagation in, e.g. water, fog or dielectric waveguides requires modeling of linear, temporally dispersive media. Using a POD-greedy sampling driven by an error indicator, we seek to generate a reduced model which accurately captures the dynamics. Typically, the reduced basis model reduction reduces the model order by a factor of more than 100, while maintaining an approximation error of less than 1%.

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