Azahar Monge holds a Postdoctoral position at the ERC Advanced Grant project DyCon under the supervision of Prof. Enrique Zuazua (UAM and DeustoTech). Before that, she earned her PhD in Numerical Analysis at the Centre for Mathematical Sciences, Lund University (Sweden) under the supervision of Prof. Philipp Birken. Her thesis was focused on the numerical aspects around the partitioned approach for the simulation of time-dependent thermal fluid-structure interaction. Earlier, she was awarded an Erasmus Mundus scholarship to participate in the MSc programme MATHMODS (Mathematical Modelling in Engineering - Theory, Numerics, Applications). Her main research interests are domain decomposition methods, coupled problems, PDEs and time adaptive multirate time integration methods.
The aim of this work is to recover the initial sparse sources that lead to a given final measurements using the diffusion equation. It is assumed that the initial condition can be written down as a linear combination of unitary deltas and their weights. In that context, an algorithm that combines the adjoint methodology with least squares is presented. In particular, the adjoint methodology is used to find the localization of the sparse sources and least squares to find the corresponding intensities.
This tutorial explains how to use the Dirichlet-Neumann method to coordinate the numerical solutions of two linear heat equations with strong jumps in the material coefficients accross a common interface.