[Dottorcomp] Seminari di Matematica Applicata. Martedì 6 febbraio. Zhaonan Dong e Matthias Möller.

[Stefano Lisini]

Martedì 6 febbraio 2024, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Zhaonan Dong (Inria Paris)terrà un seminario dal titolo:

A hypocoercivity-exploiting stabilised finite element method for Kolmogorov
equation,

e alle ore 16 precise,

Matthias Möller (TU Delft)
terrà un seminario dal titolo:

Bridging the gap between isogeometric analysis and deep operator learning.

I seminari verranno anche trasmessi in diretta su zoom.

Link Zoom:
https://us02web.zoom.us/j/8015593116


Abstract (Dong). We propose a new stabilised finite element method for the
classical Kolmogorov equation. The latter serves as a basic model problem
for large classes of kinetic-type equations and, crucially, is
characterised by degenerate diffusion. The stabilisation is constructed so
that the resulting method admits a numerical hypocoercivity property,
analogous to the corresponding property of the PDE problem. More
specifically, the stabilisation is constructed so that spectral gap is
possible in the resulting ”stronger-than-energy” stabilisation norm,
despite the degenerate nature of the diffusion in Kolmogorov, thereby the
method has a provably robust behaviour as the ”time” variable goes to
infinity. We consider both a spatially discrete version of the stabilised
finite element method and a fully discrete version, with the time
discretisation realised by discontinuous Galerkin time stepping. Both
stability and a priori error bounds are proven in all cases. Numerical
experiments verify the theoretical findings.

Abstract (Möller). Isogeometric Analysis (IgA) introduced by Hughes et al.
in 2005 has revived the vision of design-through-analysis (DTA) originally
proposed by Augustitus et al. in 1977. DTA means the fully virtual
creation, analysis and optimization of engineering designs, which requires
bidirectional exchange of data between computer-aided design (CAD) and
engineering analysis (CAE) tools.
While IgA targets at bridging the gap between CAD and CAE through the use
of spline basis functions throughout the entire process, the full potential
of DTA is hold back by high computational costs of simulation-based
analysis tools that hinder truly interactive DTA workflows.
In this presentation we will briefly review the mathematical basics of IgA
and present a novel approach – IgANets – that integrates the concept of
deep operator learning into the isogeometric framework. In particular, we
show that IgANets can be interpreted as a network-based variant of
least-squares collocation IgA (Lin et al. 2020), thereby inheriting its
consistency and convergence properties. We will moreover present a
prototype of an interactive VR workflow which allows the collaborative
creation and analysis of designs.

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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/
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