One of the last "KAUST Opportunity Found Program" grants has been assigned to NumPDE.
The research will be focused on "Model reduction methods for modal analysis in computational mechanics" and the NumPDE team, lead by Prof. Daniele Boffi, will collaborate with Prof. Fleurianne Bertrand (Chemnitz, Germany) and Prof. Luca Heltai (SISSA, Italy).
Short abstract
In this project we will work on the modeling and the simulation of large, complex systems described in terms of eigenvalue problems associated with partial differential equations. We aim at reducing the complexity of the problem in the spirit of Reduced Order Methods (ROMs).
The analysis of ROMs for eigenvalue problems is still at a preliminary stage and the available results show the potential and the difficulties of different approaches. We will then develop new techniques and apply them to solid mechanics. We start from linear elasticity and the challenges associated with problems in mixed form and with the imposition of the symmetry of the stress at discrete level. We then move to nonlinear solid mechanics where we consider the vibration of hyperelastic structures.