We propose a new algorithm for the recovery of a piecewise constant lower 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. Numerical implementation is based on the finite element method and the open-source computing platform FEniCS and dolfin-adjoint. The performance of the algorithm is demonstrated on computationally simulated data.
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