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- titre
- Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries
- auteur
- Michel Duprez, Vanessa Lleras, Alexei Lozinski, Vincent Vigon, Killian Vuillemot
- article
- 2024
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- In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine .....
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- titre
- phi-FEM for the heat equation: optimal convergence on unfitted meshes in space
- auteur
- Michel Duprez, Vanessa Lleras, Alexei Lozinski, Killian Vuillemot
- article
- Comptes Rendus. Mathématique, 2023, 361 (G11), pp.1699-1710. ⟨10.5802/crmath.497⟩
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- Thanks to a finite element method, we solve numerically parabolic partial differential equations on .....
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- titre
- φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations
- auteur
- Michel Duprez, Vanessa Lleras, Alexei Lozinski
- article
- ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57, pp.1111-1142. ⟨10.1051/m2an/2023010⟩
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- We present an immersed boundary method to simulate the creeping motion of a rigid particle in a flui .....
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- titre
- A new $\phi$-FEM approach for problems with natural boundary conditions
- auteur
- Michel Duprez, Vanessa Lleras, Alexei Lozinski
- article
- Numerical Methods for Partial Differential Equations, 2023, 39 (1), pp.281-303. ⟨10.1002/num.22878⟩
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- We present a new finite element method, called φ-FEM, to solve numerically elliptic partial differ- .....
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- titre
- φ-FEM: an efficient simulation tool using simple meshes for problems in structure mechanics and heat transfer
- auteur
- Stéphane Cotin, Michel Duprez, Vanessa Lleras, Alexei Lozinski, Killian Vuillemot
- article
- Stéphane Bordas; Alexander Menk; Sundararajan Natarajan. Partition of Unity Methods, Wiley, pp.191-216, 2022, Wiley Series in Computational Mechanics, 978-0470667088. ⟨10.1002/9781118535875.ch7⟩
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- One of the major issues in the computational mechanics is to take into account the geometrical compl .....
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