Nuevos métodos numéricos y software para la simulación de propagación de ondas electromagnéticas en medios heterogéneos

Objective:

Numerical simulation of wave propagation is at the core of many applications. For example, radar or sonar detection, medical imaging, seismology and oil field exploitation. It is a phenomenon that unfolds in an infinite (or very large) computational domain relative to the simulated wavelengths. However, the propagation phenomenon is visible in the immediate vicinity of the source (e.g. from the epicentre in the context of earthquake simulation). Therefore, it is sufficient to perform the calculations in a box or computational domain that contains the source and in which we can apply a finite element approximation method. These discretisation methods are very efficient, but still need to be improved in order to obtain accurate simulations when the medium is very heterogeneous. Computational accuracy is not the only objective to be guaranteed; it is also necessary to reduce computational costs. In fact, the simulation of wave propagation in heterogeneous media generates a very significant computational cost, especially when finite element techniques are applied. These computational costs can become prohibitive if one considers solving an inverse problem based on solving successive wave equations, as in the case of medical or seismic imaging. We need to find a good method that guarantees high accuracy while minimising the computational burden. The aim of this research project is to combine the expertise of the two research teams to develop a common solution program for electromagnetic wave propagation in complex media. We wish to develop original approximation techniques that should guarantee the accuracy of the computations and also reduce the computational burden by constructing optimised boundary conditions that minimise the size of the computational domain and also the computational burden. The fruit of this collaboration has several applications in imaging, with special emphasis on proposing an efficient methodology to solve inverse problems based on the developed direct methods.