Numerical studies of the lagrangian approach for reconstruction of the conductivity in a waveguide
Paper i proceeding, 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

Författare

Larisa Beilina

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

K. Niinimäki

Université 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,

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

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

Mer information

Senast uppdaterat

2019-01-10