Innovative Algorithms and Analysis pp 197-227

Part of the Springer INdAM Series book series (SINDAMS, volume 16) | Cite as

Filtered Gradient Algorithms for Inverse Design Problems of One-Dimensional Burgers Equation

Chapter

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 N-wave) 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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IACCNRRomaItaly
  2. 2.DeustoTech, Fundación DeustoAvda UniversidadesBilbao, Basque CountrySpain
  3. 3.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  4. 4.Facultad IngenieríaUniversidad de Deusto, Avda. UniversidadesBasque CountrySpain

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