Inverse conductivity equation with internal data

03/30/2020
by   Faouzi Triki, et al.
0

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from a single solution of that equation. This theory finds applications in several multi-wave imaging modalities including photo-acoustic tomography, and greedy methods to approximate parameter-dependent elliptic problems. We first show that the inverse problem for smooth coefficients can be rewritten as a linear transport equation. Assuming that the coefficient is known near the boundary, we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin method. We propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization parameter. We finally provide numerical examples for the inversion assuming a lower regularity of the coefficient, and using synthetic data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/08/2023

Hybridizable discontinuous Galerkin methods for the Monge-Ampere equation

We introduce two hybridizable discontinuous Galerkin (HDG) methods for n...
research
12/22/2020

Quantitative PAT with simplified P_N approximation

The photoacoustic tomography (PAT) is a hybrid modality that combines th...
research
03/17/2023

Nonlinearity parameter imaging in the frequency domain

Nonlinearity parameter tomography leads to the problem of identifying a ...
research
07/05/2020

Boundary stabilization of a one-dimensional wave equation by a switching time-delay: a theoretical and numerical study

This paper deals with the boundary stabilization problem of a one-dimens...
research
10/14/2022

On the simultanenous identification of two space dependent coefficients in a quasilinear wave equation

This paper considers the Westervelt equation, one of the most widely use...

Please sign up or login with your details

Forgot password? Click here to reset