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We propose a numerical algorithm for the reconstruction of a piecewiseconstant leading coefficient of an elliptic problem. The inverse problem isreduced to a shape reconstruction problem. The proposed algorithm is based onthe minimization of a cost functional where a control function is theright-hand side of an auxiliary elliptic equation for a level setrepresentation of unknown shape. The numerical implementation is based on thefinite element method and the open-source computing platform FEniCS. Theperformance of the algorithm is demonstrated on computationally simulated data.

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