72 citations · 536 across the 51 of their papers we have counts for
6 papers · 1 filter
Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods
Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern +1
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discr…
Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media
Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy
This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic dif…
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations
Loic Giraldi, Anthony Nouy
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy…
Principal bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falco, Anthony Nouy
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb…
Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats
Anthony Nouy
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert…
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
Anthony Nouy, Florent Pled
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the u…