Abstract
We propose and study a method for imaging an approximate electrical conductivity from the magnitude of one interior current density field without any knowledge of the boundary voltage potential. Solely from this interior data, the exact conductivity is impossible to recover as non-unique solutions exist. We propose a method to recover a minimum residual type solution. The method is based on a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. We prove existence and uniqueness for a nearby problem, and study the continuous dependence data for a regularized problem. The computational effectiveness and numerical convergence of this method is demonstrated in numerical experiments.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
