On the verification of model reduction methods based on the proper generalized decomposition

2011 ◽  
Vol 200 (23-24) ◽  
pp. 2032-2047 ◽  
Author(s):  
Pierre Ladevèze ◽  
Ludovic Chamoin
Keyword(s):  
Model Reduction ◽  
Proper Generalized Decomposition ◽  
Reduction Methods

scholarly journals Implementing model reduction to the JuliaFEM platform

2018 ◽  
Vol 51 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Marja Liisa Rapo ◽  
Jukka Aho ◽  
Hannu Koivurova ◽  
Tero Frondelius
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Open Source ◽  
Degrees Of Freedom ◽  
Mass Matrices ◽  
Dynamic Condensation ◽  
Dynamic Analyses ◽  
Reduction Methods ◽  
Large Model

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

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