Open AccessRecovery of a piecewise constant lower coefficient of an elliptic equation
Author(s) -
Aleksandr E. Kolesov,
D Kh Ivanov,
Petr N. Vabishchevich
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1392/1/012084
Subject(s) - piecewise , constant (computer programming) , mathematics , finite element method , constant coefficients , inverse problem , minification , inverse , constant function , elliptic curve , function (biology) , representation (politics) , mathematical analysis , algorithm , mathematical optimization , computer science , geometry , physics , evolutionary biology , biology , thermodynamics , programming language , politics , political science , law
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.