**EXIFSI** is a 4-years research project funded by the French National Research Agency (ANR) through the JCJC program.

Incompressible fluid-structure interaction problems, i.e., mathematical models that describe the interaction of a deformable structure with an internal or surrounding incompressible fluid flow, are among the most widespread multi-physics problems. Their numerical simulation is of major interest in practically all the engineering fields, from the aeroelasticity of bridge decks and parachutes, to naval hydrodynamics and the biomechanics of blood and airflow.

The separate simulation of either an elastic structure in large displacements or incompressible flow in fixed domains is rather well established. Yet, making both models interact via efficient numerical methods is a permanent challenge in scientific computing and numerical analysis. In fact, besides the increasing complexity of the models (contacting structures, active mechanics, porous media, etc.), there is also an emerging interest in addressing inverse problems (e.g., to improve clinical diagnosis via personalized fluid-structure models) which definitely calls for efficient numerical methods.

Nowadays, numerical simulations of these multi-physics systems are generally obtained at the expense of efficiency. They are much more computationally onerous than solving two independent fluid and structure problems. This indicates that, in terms of efficiency, the coupling scheme does not fully exploits the maturity of the numerical methods for each of the sub-systems, which is a major obstacle. The basic principle of this project is that, to guarantee efficiency, the coupling scheme must allow a decoupled time-marching of the fluid and the structure. This is a particularly challenging problem in numerical analysis since fluid incompressibility generally makes the coupling extremely stiff. *The scientific objective is thus to marry decoupling with stability and accuracy.*