Open AccessNumerical method for solving the piecewise constant source inverse problem of an elliptic equation from a partial boundary observation data
Author(s) -
D Kh Ivanov,
Aleksandr E. Kolesov,
П. Н. Вабищевич
Publication year - 2021
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 - 10.1088/1742-6596/2092/1/012006
Subject(s) - inverse problem , piecewise , mathematics , boundary value problem , finite element method , mathematical analysis , boundary (topology) , method of mean weighted residuals , constant (computer programming) , computer science , physics , programming language , galerkin method , thermodynamics
We present results of numerical investigation of the source term recovery in a boundary value problem for an elliptic equation. An additional information about the solution is considered as its normal derivative taken on a part of the boundary. Such source inverse problem is related with inverse gravimetry problem of determining an inhomogeneity from gravitational potential anomalies on the Earth’s surface. We propose an iterative method for numerical recovery of the source term on the base of minimization of the observation residual by a gradient type method. The numerical implementation is based on finite element approximation using the FEniCS scientific computing platform and the dolfin-adjoint package. The capabilities of the developed computational algorithm are illustrated by results of numerical solutions of two dimensional test problems.