A simple and flexible model order reduction method for FFT-based homogenization problems using a sparse sampling technique

2019 ◽  
Vol 347 ◽  
pp. 622-638 ◽  
Author(s):  
Julian Kochmann ◽  
Kiran Manjunatha ◽  
Christian Gierden ◽  
Stephan Wulfinghoff ◽  
Bob Svendsen ◽  
...  
Keyword(s):  
Model Order Reduction ◽  
Reduction Method ◽  
Order Reduction ◽  
Sampling Technique ◽  
Sparse Sampling ◽  
Model Order ◽  
Order Reduction Method ◽  
Homogenization Problems ◽  
Flexible Model

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.

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