7 papers · 1 filter
A High-Order Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems
Moritz Hauck, Alexei Lozinski
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes…
Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry
Maxime Dalery, Genevieve Dusson, Virginie Ehrlacher +1
The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop non…
Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski +1
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the - and…
A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
Moritz Hauck, Alexei Lozinski, Roland Maier
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we a…
Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries
Michel Duprez, Vanessa Lleras, Alexei Lozinski +2
In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we u…
MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite E…