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28 Settembre, 2023 14:30
MOX Seminar

Numerical approximation of time-harmonic and time-dependent wave propagation problems

Francesca Bonizzoni, Dipartimento di Matematica, Laboratorio MOX, Politecnico di Milano
Aula Saleri
Abstract

The present talk deals with numerical techniques to discretize wave propagation problems. In the first part of the talk I will focus on the interior Helmholtz equation as well as on scattering problems. Due to oscillations in the analytical solutions, accurate finite element approximations are computationally expensive and time-consuming, already for moderate frequencies. Therefore, when responses at many frequencies are of interest, their direct computation is unaffordable. I will discuss a model order reduction method aimed at reducing the computational costs by producing an approximation of (some functional of) the frequency response map.
In the second part of the talk, I will present a space-time discretization for the scalar-valued dissipative wave equation in two- and three-dimensions. It is a structured approach based on the Virtual Element Method for space discretization coupled with the Discontinuous Galerkin finite element method for time integration. I will discuss the theoretical analysis of the scheme and present some numerical examples to demonstrate its practical capabilities. Finally, I will conclude with some perspectives and future developments.

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Seminari Matematici
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