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arXiv · 2009.00370

Numerical recovery of the piecewise constant leading coefficient of an elliptic equation

Aleksandr E. Kolesov·Petr N. Vabishchevich
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Abstract

We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the minimization of a cost functional where a control function is the right-hand side of an auxiliary elliptic equation for a level set representation of unknown shape. The numerical implementation is based on the finite element method and the open-source computing platform FEniCS. The performance of the algorithm is demonstrated on computationally simulated data.

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Aleksandr E. Kolesov, Petr N. Vabishchevich. 2020-09-01. Numerical recovery of the piecewise constant leading coefficient of an elliptic equation. https://arxiv.org/abs/2009.00370

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