In several problems of engineering interest in which parameterized Partial Differential Equations (PDE) solution require considerable computational effort, Reduced Order Models (ROMs) enable significant reduction in the the dimensionality of the discretized PDEs and consequently in the resources required for each calculation. In the seminar we will present different approaches to obtain efficient ROMs in several applications. Starting from classical approaches based on simplifying assumptions on the physical and mathematical models, we will move to more modern methodologies based on offline-online decomposition of the computational effort. In the latter group, we will discuss non intrusive methods such as Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition with Interpolation (PODI), and their application to problems arising from the naval industry. We will then present the application of intrusive POD-Galerkin ROMs to high Reynolds flows and, finally, discuss the effectiveness of Active Subspaces analysis in reducing the dimensionality of the parameter space.
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