Recovery of a piecewise constant lower coefficient of an elliptic equation

Аннотация. 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-ha...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-11, Vol.1392 (1), p.12084
Main Authors: Kolesov, A E, Kh Ivanov, D, Vabishchevich, P N
Format: Article
Language:English
Subjects:
Algorithms
coefficient inverse problem
elliptic equation
Finite element method
Inverse problems
Mathematical analysis
Physics
Recovery
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Summary:Аннотация. 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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1392/1/012084