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A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds
Author(s) -
Son Nguyen Thanh
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4408
Subject(s) - reduction (mathematics) , interpolation (computer graphics) , model order reduction , basis (linear algebra) , parametric statistics , mathematics , mathematical optimization , computational complexity theory , singular value decomposition , computer science , algorithm , order (exchange) , artificial intelligence , geometry , image (mathematics) , projection (relational algebra) , statistics , finance , economics
SUMMARY Model order reduction helps to reduce the computational time in dealing with large dynamical systems, for example, during simulation, control, optimization. In many cases, the considered model depends on parameters; Model order reduction techniques are, therefore, preferred to symbolically preserve this dependence or to be adaptive to the change of the model caused by the variation in the values of the parameters. In this paper, we first present the application of the interpolation technique on Grassmann manifolds to this problem. We then improve the method for the models whose system matrices depend affinely on parameters by considerably reducing the computational complexity on the basis of analyzing the structure of sums of singular value decompositions and decomposing the whole procedure into offline and online stages. A numerical example is shown to illustrate the method as well as to prove its effectiveness. Copyright © 2012 John Wiley & Sons, Ltd.