Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation
Entity
UAM. Departamento de MatemáticasPublisher
Springer, ChamDate
2017-03-09Citation
10.1007/978-3-319-49262-9_7
Innovative Algorithms and Analysis. Eds. Laurent Gosse, Roberto Natalini. Springer INdAM Series (SINDAMS), 16 (2017): 197-227
ISBN
978-3-319-49261-2 (print); 978-3-319-49262-9 (online)DOI
10.1007/978-3-319-49262-9_7Funded by
Acknowledgements This work was partially supported by the Advanced Grant 694126-DYCON (Dynamic Control) of the European Research Council Executive Agency, ICON of the French ANR (2016-ACHN-0014-01), FA9550-15-1-0027 of AFOSR, A9550-14-1-0214 of the EOARD-AFOSR, and the MTM2014-52347 Grant of the MINECO (Spain)Project
info:eu-repo/grantAgreement/EC/H2020/694126/EU//DYCON; Gobierno de España. MTM2014-52347Editor's Version
https://doi.org/10.1007/978-3-319-49262-9_7Subjects
MatemáticasNote
The final publication is available at Springer via https://doi.org/10.1007/978-3-319-49262-9_7Rights
© Springer International Publishing AG 2017Abstract
Inverse design for hyperbolic conservation laws is exemplified through the 1D Burgers equation which is motivated by aircraft’s sonic-boom minimization issues. In particular, we prove that, as soon as the target function (usually a Nwave) isn’t continuous, there is a whole convex set of possible initial data, the backward entropy solution being possibly its centroid. Further, an iterative strategy based on a gradient algorithm involving “reversible solutions” solving the linear adjoint problem is set up. In order to be able to recover initial profiles different from the backward entropy solution, a filtering step of the backward adjoint solution is inserted, mostly relying on scale-limited (wavelet) subspaces. Numerical illustrations, along with profiles similar to F-functions, are presented
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Zuazua Iriondo, Enrique
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