Séminaire Doctorants
organisé par l'équipe DOCT
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Killian Vuillemot
A new unfitted finite element method: $\phi$-FEM
4 avril 2024 - 16:30Salle de conférences IRMA
$\phi$-FEM is a new finite element method, proposed to solve partial differential equations on complex domains, using simple non conform meshes. The method relies on the use of a level-set function $\phi$, which defines the domain and its boundary. In this presentation, I will introduce the method in the simple case of the resolution of the Poisson equation with Dirichlet boundary conditions. Then I will present the extension of the method to the case of time-dependent PDE's, and more precisely the case of the Heat equation with Dirichlet boundary conditions. Then, I will present a way to combine $\phi$-FEM and neural networks. This method, called $\phi$-FEM-FNO, has been introduced to achieve the resolution of multiple physics problems with good accuracy in real time. I will illustrate the interest of this approach with numerical results on two test cases solving the Poisson-Dirichlet equation on different types of shapes. -
Paul Laubie
TBA
11 avril 2024 - 16:30Salle de conférences IRMA
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Jules Bangard
TBA
18 avril 2024 - 16:30Salle de conférences IRMA