Shape parametrization and computational reduction strategies for real-time flow simulations in varying geometries

• Relatore: Prof. Gianluigi Rozza

Abstract:  Many problems in scientific computing, such as shape optimization, shape registration/reconstruction, and more general inverse problems, are formulated on parametrized domains. We review some flexible and general methods used to represent shapes, either implicitly or explicitly, with a special emphasis on choosing methods that can be combined with existing model reduction approaches for PDEs. We present techniques developed recently for treating the complexities related to model reduction of PDEs on varying domains, focusing on viscous flows. Two different approaches may be considered: free-form deformations and radial basis functions. In both cases the problem is reduced to a fixed mesh with parameter-dependent coefficients, allowing us to apply the reduced basis method. Some remarks regarding the optimal choice of the shape parametrization will also presented in view of reducing the parametric dimension of the problem to a more tractable one. Numerical examples of the proposed techniques are presented for the rapid solution of shape-related inverse-like problems.

Referente:

Alberto Valli