Fundamental Areas / Numerical Analysis of Partial Differential Equations
The inverse problem in electroencephalography consists in the localization of brain activity from measurements of the electric potential on the surface of the head. An adaptive finite element method has been used to solve the corresponding state equation, which involves derivatives of a Dirac measure on the right-hand side. The figure on the left shows that the objective function presents local minima, which makes the problem hard to solve. The figure on the right shows a zoom of the end of the minimizer trajectory produced by the proposed adaptive method. Further details are available in:
Alonso-Rodríguez, A., Camaño, J., Rodríguez, R. and Valli, A.: Assessment of two approximation methods for the inverse problem of electroencephalography. Preprint 2014-05, Centro de Investigacion en Ingenieria Matematica (CI²MA), Universidad de Concepcion, (2014).