ΕΚΔΗΛΩΣΕΙΣ

ΣΕΜΙΝΑΡΙΟ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΚΑΙ ΕΦΑΡΜΟΣΜΕΝΗΣ ΑΝΑΛΥΣΗΣ - ΚΑΡΑΤΖΑΣ (ΣΕΜΦΕ, ΕΜΠ)

Παρασκευή 28 Φεβρουαρίου 2020 Α31

ΣΕΜΙΝΑΡΙΟ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΚΑΙ ΕΦΑΡΜΟΣΜΕΝΗΣ ΑΝΑΛΥΣΗΣ

Ημερομηνία: Παρασκευή 28 Φεβρουαρίου 2020

Ώρα: 15:15

Αίθουσα: Α31 (3ος όροφος, Κτήριο Τμήματος Μαθηματικών)

Ομιλητής: ΕΥΘΥΜΙΟΣ ΚΑΡΑΤΖΑΣ (ΣΕΜΦΕ, ΕΜΠ)

Θέμα: A Unified Reduced Order Basis for Parametrized PDEs based on Embedded Finite Element Methods and applications

Περίληψη:
We consider parametrized PDEs, geometrically deformed systems, and we present a new beneficial approach for reduced basis construction based on level set geometry descriptions and fixed background geometries. This unified Reduced Order Basis employs a background mesh, solves efficiently with less computational cost and it is independent of any random parameter which affects the physics of the PDE model. We will discuss results related to unfitted finite element methods for parameterized partial differential equations enhanced by a proper orthogonal decomposition method.
This approach achievements are twofold. Firstly, we reduce much the computational effort since the unfitted mesh method allows us to avoid remeshing when updating the parametric domain. Secondly, the proposed reduced order model technique gives an implementation advantage considering geometrical parametrization. Computational efforts are even exploited more efficiently since the mesh is computed once and the transformation of each geometry to a reference geometry is not required.
These combined advantages allow to solve many PDE problems faster and "cheaper" and to provide the capability to find solutions in cases that could not be resolved in the past.

Acknowledgments: Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under  grant agreement No[1115]. 


References

[–] K., G. Stabile, L. Nouveau, G. Scovazzi, and G. Rozza, “A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow”, Comput Methods Appl. Mech. Engrg. (2019).

[–] K., F. Ballarin, and G. Rozza, “Projection-based reduced order models for a cut finite element method in parametrized domains”, Computers & Mathematics with Applications (2020).

[–] K., G. Stabile, L. Nouveau, G. Scovazzi, G. Rozza, “A Reduced-Order Shifted Boundary Method for Parametrized Incompressible Navier-Stokes Equations”, submitted (2020).

[–] A. Aretaki, K., G. Katsouleas, “Random domains, preconditioned parameterized optimal control PDE problems discretized by a FEM with cut elements and Quasi Monte Carlo simulation”, submitted (2020).