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Applications of singular value decomposition in structural optimisation
Author(s) -
Gerzen Nikolai,
Barthold FranzJoseph
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910261
Subject(s) - singular value decomposition , singular value , context (archaeology) , decomposition , scope (computer science) , matrix (chemical analysis) , sensitivity (control systems) , computer science , matrix decomposition , mathematical optimization , value (mathematics) , focus (optics) , algorithm , mathematics , engineering , machine learning , chemistry , physics , eigenvalues and eigenvectors , quantum mechanics , chromatography , electronic engineering , biology , programming language , paleontology , organic chemistry , optics
The usage of the singular value decomposition (SVD) in scope of structural optimisation is motivated. We briefly outline several applications of SVD from different scientific fields to point out their similarities with structural optimisation. Here, our focus is on model reduction, on numerical defects and on their quantitative description using SVD. In this context we address the singular value decomposition of matrices which appear in an optimisation algorithm, i.e. the pseudo load matrix and the sensitivity matrix. In this contribution on the example of topology optimisation we would like to clarify all the properties of SVD. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)