Master Thesis

A posteriori error estimation for reduced basis approximations built over a boundary element method

In order to set reliable reduced-order models (ROMs) for the rapid solution of parametrized partial differential equations we need to rely on suitable a posteriori error estimates. This is mandatory both at the evaluation stage of a ROM, in order to ensure the precision of the reduced-order solution with respect to a corresponding high-fidelity, full-order approximation, and during the construction of a ROM, in order to set efficient strategies to sample the parameter space and retain few snapshots of the original problem, which yield the reduced-order subspace characterizing a ROM.

Shape optimization and Fluid-Structure Interaction problems based on Isogeometric Analysis and Reduced Basis Methods in naval hydrodynamic applications

In this Master Thesis we foresee to develop an efficient numerical framework exploiting Isogeometric Analysis and Reduced Basis Methods for the efficient solution of shape optimization problems arising in naval hydrodynamics, such as the ones involving propeller blades or ship hulls. We take advantage of Isogeometric Analysis to frame the geometrical description of admissible shapes and, possibly, to implement a high-fidelity solver for the problem at hand (e.g. by using an Isogeometric Boundary Element Method).

Reduced basis methods and Isogeometric Analysis for the efficient solution of hydrodynamic problems

In this Master Thesis we foresee to develop an efficient numerical framework exploiting Isogeometric Analysis and Reduced Basis Methods for the efficient solution of parametrized problems arising in naval hydrodynamics. Real-time flow simulation past bodies/profiles of variable shape (airfoils, hydrofoils, propeller blades, ship hulls), flow control and sensitivity analysis are just some examples of applications in this very broad field.

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