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A shape domain estimation for the heat equation

Kebir Chaji, Mohammed El Bagdouri


In this paper an internal shape of a domain is identified by exploiting the temperature and flux measurements performed on the external boundary of this domain. The temperature in the material is governed by the non homogeneous linear heat equation. A parametric representation of the unknown boundary is adopted and the radial function is approximated using trigonometric polynomials. The estimation problem is then posed as an optimization problem of an output least-squares criterion. The effective optimization is performed by the Newton method while the gradient of the objective function is established using the domain derivative techniques. The identification algorithm is numerically implemented with the help of the finite element software FreeFem. Numerical tests are carried out to demonstrate the validity and efficiency of the proposed method.


Heat equation, Inverse problem, Output least-squares, Domain derivation, Implicit scheme, Finite elements

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