Title
Reduction Of The Dimensionality Of Transient Fem Solutions Using Proper Orthogonal Decomposition
Abstract
A method of reducing the number of degrees of freedom in FEM analysis has been devised. As in the case of FEM, Galerkin weighted residuals is based on weak formulation. The distinct feature of the method is the usage of a set of globally defined trial (and weighting) functions defined as a linear combination of the shape functions. The coefficients of this combination are evaluated employing the Proper Orthogonal Decomposition method ensuring optimal approximation properties of the trial functions. The resulting set of ODEs of much lower dimensionality than the standard FEM is then solved analytically using the modal analysis technique. In the included numerical examples, the number of unknowns is reduced by several orders of magnitude while the maximum error is of the order of 1%. The technique leads also to a significant reduction of the execution times. A method of controlling the error introduced by the POD is proposed. © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Publication Date
12-1-2003
Publication Title
36th AIAA Thermophysics Conference
Document Type
Article; Proceedings Paper
Personal Identifier
scopus
Copyright Status
Unknown
Socpus ID
84896746698 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84896746698
STARS Citation
Białecki, R. A.; Kassab, A. J.; and Fic, A., "Reduction Of The Dimensionality Of Transient Fem Solutions Using Proper Orthogonal Decomposition" (2003). Scopus Export 2000s. 1350.
https://stars.library.ucf.edu/scopus2000/1350