KRYLOV SUBSPACE MODEL ORDER REDUCTION OF LARGE SCALE FINITE ELEMENT DYNAMICAL SYSTEMS

2013 ◽  
Vol 2013 (03) ◽  
pp. 428-433
Author(s):  
Jaroslav Sindler ◽  
Matej Sulitka
Keyword(s):  
Finite Element ◽  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Model Order

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

scholarly journals A New MEMS Stochastic Model Order Reduction Method: Research and Application

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Bian Xiangjuan ◽  
Youping Gong ◽  
Chen Guojin ◽  
Lv Yunpeng
Keyword(s):  
Finite Element ◽  
Stochastic Model ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Order Reduction ◽  
Fast Time ◽  
Random Input ◽  
Model Order ◽  
Order Reduction Method

Modeling and simulation of MEMS devices is a very complex tasks which involve the electrical, mechanical, fluidic, and thermal domains, and there are still some uncertainties that need to be accounted for during the robust design of MEMS actuators caused by uncertain material and/or geometric parameters. According to these problems, we put forward stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses; the method makes use of polynomial chaos expansions in terms of the random input variables for the matrices of a finite element model of the system and then uses its transformation matrix to reduce the model; the method is independent of the MOR algorithm, so it is seamlessly compatible with MOR method used in popular finite element solvers. The simulation results verify the method is effective in large scale MEMS design process.

Deterministic and Stochastic Model Order Reduction for Vibration Analyses of Structures With Uncertainties

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Ji Yang ◽  
Béatrice Faverjon ◽  
Herwig Peters ◽  
Steffen Marburg ◽  
Nicole Kessissoglou
Keyword(s):  
Finite Element ◽  
Stochastic Model ◽  
Dynamic Characteristics ◽  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Element Model ◽  
Uncertain Parameters ◽  
Model Order ◽  
Frequency Responses

To reduce the computational effort using polynomial chaos expansion to predict the dynamic characteristics of structures with several uncertain parameters, hybrid techniques combining stochastic finite element analysis with either deterministic or stochastic model order reduction (MOR) are developed. For the deterministic MOR, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. For the stochastic MOR, a stochastic reduced basis method is implemented in which the structural modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. To demonstrate the computational efficiency of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate randomized by uncertain geometrical and material parameters is examined. Results are compared with both Monte Carlo (MC) simulations and nonreduced stochastic models. Using the reduced models, the effects of the individual uncertain parameters as well as the combined uncertainties on the dynamic characteristics of the plate are examined.

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