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Numerical approximation of some inverse problems arising in Elastography

Banff International Research Station for Mathematical Innovation and Discovery

We will deal with the numerical approximation of some geometric inverse problems for the wave and the Lam\'e equations motivated by Elastography. We present several recent results and open questions concerning the numerical reconstruction of the unknown domain where the equations evolve. In the numerical experiments, we solve appropriate optimization problems. Two different numerical techniques will be proposed. Firstly, the finite element method for the numerical solution of the PDE's, that will be performed with \texttt{FreeFem++}. The routines on the \texttt{ff-NLopt} package, that provide an interface to a free/open-source library for nonlinear optimization, are also required. On the other hand, we will consider the numerical approximation based on the method of fundamental solutions. We present some numerical results in the 2D and 3D cases. The first part is joint work with E. Fern\'andez-Cara (Dpto.\ E.D.A.N., Universidad de Sevilla, cara@us.es) and the second part is joint work with E. Fern\'andez-Cara, Jairo Rocha de Faria (Universidade Federal da Paraiba, jairo@ci.ufpb.br) y Pitágoras P. de Carvalho (Universidad Federal Fluminense (Niteroi), pitagorascarvalho@gmail.com).

Mathematics; Partial differential equations; Systems theory; control; Control/optimization/operation research

video/mp4

Author affiliation: Universidad de Sevilla Spain

2018-01-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64378

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/