Revisiting Calderon's Problem
Optimization and Control
2019-12-09 v1 Numerical Analysis
Numerical Analysis
Computational Physics
Abstract
A finite element code for heat conduction, together with an adjoint solver and a suite of optimization tools was applied for the solution of Calderon's problem. One of the questions whose answer was sought was whether the solution to these problems is unique and obtainable. The results to date show that while the optimization procedure is able to obtain spatial distributions of the conductivity that reduce the cost function significantly, the resulting conductivity is still significantly different from the target distribution sought. While the normal fluxes recovered are very close to the prescribed ones, the tangential fluxes can differ considerably.
Cite
@article{arxiv.1912.02970,
title = {Revisiting Calderon's Problem},
author = {Rainald Löhner and Harbir Antil},
journal= {arXiv preprint arXiv:1912.02970},
year = {2019}
}