Title : Two approaches for the numerical identification of cardiac potentials: parameter identification and Cauchy problem
Abstract : In this talk, I will present two inverse problems related to the modeling of the cardiac potential but which can appear in many other contexts. In the first problem, we consider a reaction-diffusion equation and try to identify numerically a source term. For this nonlinear problem, I will present an algorithm which globally converges. In the second problem, we consider the electrical potential in the extra-cardiac domain and are interested by the numerical resolution of the classical Cauchy problem: we want to identify the potential on the heart from measurement of the extra-cardiac potentials. This ill-posed problem is regularized thanks to stabilized finite element methods. Both methods strongly relies on central tools in the analysis of inverse problems: Carleman estimates and stability inequalities. The first work is in common with Maya de Buhan and Erica Schwindt and the second work is in common with Erik Burman, Justine Dorsz and Miguel Fernandez.
