Numerical studies of the lagrangian approach for reconstruction of the conductivity in a waveguide
Paper in proceedings, 2018

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions.

Hyperbolic equation

Lagrangian approach

Coefficient inverse problem

Tikhonov functional

Domain decomposition

Author

Larisa Beilina

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

K. Niinimäki

University Paris-Saclay

Springer Proceedings in Mathematics and Statistics

2194-1009 (ISSN) 2194-1017 (eISSN)

Vol. 243 93-117

38th Progress in Electromagnetics Research Symposium, PIERS 2017
St. Petersburg, Russia,

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1007/978-3-319-94060-1_8

More information

Latest update

1/10/2019