The ERC NEMESIS project has been funded in the 2023 Synergy call for a duration of six years.
Its goal is to lay the groundwork for a novel generation of numerical simulators by tackling some key difficulties of PDE problems of the 21st century:
Incomplete differential operators in Hilbert complexes;
The efficient solution of the discrete problems relating to the latter;
Robustness to physical parameters;
The presence of nonlinear and hybrid-dimensional multi-physics, encountered in applications such as geological flows or magneto-hydrodynamics.
The NEMESIS project aims at overcoming the above difficulties, therefore boosting the prediction capabilities of numerical simulators in engineering and applied sciences. A key point will be the use of polytopal meshes and the higher-level point of view provided by polytopal constructions.