A matrix rational Lanczos method for model reduction in large-scale first- and second-order dynamical systems

2016 ◽  
Vol 24 (1) ◽  
pp. e2077 ◽  
Author(s):  
H. Barkouki ◽  
A.H. Bentbib ◽  
K. Jbilou
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Large Scale ◽  
Lanczos Method ◽  
Second Order

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Masih Mahmoodi ◽  
Kamran Behdinan
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Second Order ◽  
Computational Time ◽  
Original Structure ◽  
Fe Model ◽  
Krylov Methods ◽  
Convergence Criteria ◽  
Large Scale Systems ◽  
Reduction Techniques

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

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