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Identifier

000375657

Title

Optimal control adjoint method for inversion in wave propagation

Alternative Title

Μέθοδος βελτιστοποίησης με τη χρήση του συζυγούς τελεστή για τη λύση αντίστροφων προβλημάτων κυματικής διάδοσης

Author

Karasmani, Eftychia V

Author

Καρασμάρη, Ευτυχία Β

Thesis advisor

Παπαδάκης, Ιωάννης

Reviewer

Ταρουδάκης, Μιχαήλ
Μακράκης, Γεώργιος

Abstract

We suppose that the wave propagation inside a medium is modelled by a well posed mathematical problem. Speci¯cally, the adopted model consists of: 1. the properties of the medium (e.g., density, wave speed, attenuation, etc.) 2. the properties and the location of the source 3. the boundary conditions 4. the propagated ¯eld. We choose to write the above problem in terms of a system of partial di®erential equations with initial and boundary conditions. The task of specifying the propagated ¯eld when the properties of the medium, the properties and the location of the source as well as the boundary conditions are assumed to be known, is called the Direct Problem. We suppose that we can obtain a numerical solution for this problem, using an appropriate model. On the other hand, an Inverse Problem arise when the propagated ¯eld is assumed to be known by experimental measurements and the objective is to recover the properties of the medium, or ¯nd the location and the properties of the source, or even determine the boundary conditions. A solution for the Inverse problem can be derived by minimizing the mis¯t between the measured ¯eld and the ¯eld predicted by the model using as control parameters the unknown model parameters. In this work, the wave propagation in a waveguide is modelled via the parabolic approximation and a non-local boundary condition in the form of a Neumann to Dirichlet map is used. An Optimal Control Method using the Adjoint Operator of the problem is exhibited for recovering the properties of the medium.

Language

Greek

Subject

Adjoint operator

Direct problem

Inverse problem

Optics

Parabolic operator

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