This project is based on a collaboration between researchers in geophysics, applied mathematics and numerical sciences. It proposes to develop a new generation of methods to jointly analyze satellite deformation data (InSAR) and gravity variation data in order to better discriminate the nature, location and geometry of the sources of volcanic activity, and to better anticipate magmatic refills and eruptions. The project will make it possible to exploit the increasing volumes of satellite data, It is also located upstream of new instrumental developments for the measurement of gravity on volcanoes. In order to take into account 3D heterogeneous elastic media, simulations will be carried out by fictitious domain methods, faster than classical finite elements. As an example, this method will be applied to 3 recent eruptions of the Piton de la Fournaise, which is one of the most active and best monitored volcanoes in the world. The codes will be shared with all geodesy researchers and volcanological observatories and the methods will be ported to an on-demand computing platform.