Applied and Computational Mathematics Seminar

Speaker: Dmitry Glotov

Title: A Boundary Value Transformation for an Inverse Source Problem

Abstract: We consider a non-linear problem of determining the harmonic function given the magnitude of its gradient on the boundary of a domain. This problem originated in magnetometry as an inverse source problem. The type of non-linearity considered here also arises in the inverse conductivity problem with the interior data obtained from MRI measurements. We present analysis for the two-dimensional case as well as a reconstruction algorithm and some results of numerical experiments both in 2d and 3d.