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POD–ISAT: An efficient POD‐based surrogate approach with adaptive tabulation and fidelity regions for parametrized steady‐state PDE discrete solutions
Author(s) -
Bui D.,
Hamdaoui M.,
De Vuyst F.
Publication year - 2013
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.4468
Subject(s) - point of delivery , representation (politics) , robustness (evolution) , partial differential equation , computer science , surrogate model , mathematical optimization , proper orthogonal decomposition , algorithm , mathematics , control theory (sociology) , mathematical analysis , artificial intelligence , biochemistry , chemistry , control (management) , politics , political science , law , gene , agronomy , biology
SUMMARY A combination of proper orthogonal decomposition (POD) analysis and in situ adaptive tabulation (ISAT) is proposed for the representation of parameter‐dependent solutions of coupled partial differential equation problems. POD is used for the low‐order representation of the spatial fields and ISAT for the local representation of the solution in the design parameter space. The accuracy of the method is easily controlled by free threshold parameters that can be adjusted according to user needs. The method is tested on a coupled fluid‐thermal problem: the design of a simplified aircraft air control system. It is successfully compared with the standard POD; although the POD is inaccurate in certain areas of the design parameters space, the POD–ISAT method achieves accuracy thanks to trust regions based on residuals of the fluid‐thermal problem. The presented POD–ISAT approach provides flexibility, robustness and tunable accuracy to represent solutions of parametrized partial differential equations.Copyright © 2013 John Wiley & Sons, Ltd.