Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation

Gosse L, Zuazua E (2017)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2017

Publisher: Springer International Publishing

Edited Volumes: Innovative Algorithms and Analysis

Series: Springer INdAM Series

Book Volume: 16

Pages Range: 197-227

ISBN: 978-3-319-49262-9

DOI: 10.1007/978-3-319-49262-9_7

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Consiglio Nazionale delle Ricerche (CNR) / National Research Council of Italy

Italy (IT) University of Deusto / Universidad de Deusto

Spain (ES)

How to cite

APA:

Gosse, L., & Zuazua, E. (2017). Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation. In Laurent Gosse, Roberto Natalini (Eds.), Innovative Algorithms and Analysis. (pp. 197-227). Springer International Publishing.

MLA:

Gosse, Laurent, and Enrique Zuazua. "Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation." Innovative Algorithms and Analysis. Ed. Laurent Gosse, Roberto Natalini, Springer International Publishing, 2017. 197-227.

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