Structure-Exploiting Symbolic-Numerical Model Reduction of Nonlinear Electrical Circuits

2012 ◽  
pp. 179-185 ◽  
Author(s):  
Oliver Schmidt
Keyword(s):  
Numerical Model ◽  
Model Reduction ◽  
Electrical Circuits

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 Stochastic and reliability analysis of a propeller with model reduction

2009 ◽  
pp. 195-215
Author(s):  
Othmane Bendaou ◽  
Jhojan Enrique Rojas ◽  
Abdelkhalak El Hami ◽  
Abdeslam Aannaque ◽  
Mohamed Agouzoul
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Model Reduction ◽  
Reliability Analysis ◽  
Synthesis Method ◽  
Point Of View ◽  
Finite Elements Method ◽  
Component Mode Synthesis ◽  
Design Parameters ◽  
Cpu Time

Nowadays, design based on purely deterministic analyses has been replaced by stochastic and reliability analyses which consider the uncertainties affecting the design parameters. But from a numerical point of view, these analyses become costly for industrial mechanical applications (modelled by finite elements method) because of their great number of freedom degrees. In this work, we take an interest in reducing the CPU time for stochastic and reliability analyses of an industrial mechanical application by the modal condensation of his numerical model with the component mode synthesis method. The example of a propeller is studied to validate the proposed methods. The results of this study tend to show the considerable gain in CPU which we save by the using of our methodology.

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.

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