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A reduced‐order representation of the Poincaré–Steklov operator: an application to coupled multi‐physics problems
Author(s) -
Aletti Matteo,
Lombardi Damiano
Publication year - 2017
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.5490
Subject(s) - eigenfunction , operator (biology) , representation (politics) , computation , mathematics , order (exchange) , basis (linear algebra) , reduction (mathematics) , laplace operator , computer science , algebra over a field , physics , mathematical analysis , pure mathematics , algorithm , eigenvalues and eigenvectors , quantum mechanics , geometry , repressor , law , chemistry , biochemistry , political science , transcription factor , finance , politics , economics , gene
Summary This work investigates a model reduction method applied to coupled multi‐physics systems. The case in which a system of interest interacts with an external system is considered. An approximation of the Poincaré–Steklov operator is computed by simulating, in an offline phase, the external problem when the inputs are the Laplace–Beltrami eigenfunctions defined at the interface. In the online phase, only the reduced representation of the operator is needed to account for the influence of the external problem on the main system. An online basis enrichment is proposed in order to guarantee a precise reduced‐order computation. Several test cases are proposed on different fluid–structure couplings. Copyright © 2016 John Wiley & Sons, Ltd.