Virtual Element based Model Order Reduction

The goal of the project is the development of a new, powerful tool for the numerical approximations of problems that are interesting for the academic as well as for the industrial world. Among these we recall fracture propagation problems, contact problems and fluid-structure interaction problems. The mathematical models that describe these applications are parametric Partial Differential Equations (PDEs): the process to obtain the simulation of the behavior of the solution for these problems is very time consuming, and sometimes it requires powerful computational tools, such as supercomputers. To manage and reduce the cost of these simulations, we will blend the Model Order Reduction (MOR) technique with the Virtual Element (VEM) discretization. The VEM takes care of the spatial discretization of the original problem, and it builds a database, namely a set of solutions of the discretized problem, for chosen values of the parameters in the PDE. In a subsequent step the MOR is used to speed up the computations needed to find the solution of interest for new values of the parameters in the problem. We investigate the theoretical properties of the proposed methodology, as well as the computational advantages: we propose to do so by testing it with advanced applications, such as fluid-structure interaction problems.