90 citations · 116 across the 16 of their papers we have counts for
7 papers · 1 filter
Spectral Analysis of the Weighted Frobenius Objective
Vladislav Trifonov, Ivan Oseledets, Ekaterina Muravleva
We analyze a weighted Frobenius loss for approximating symmetric positive definite matrices in the context of preconditioning iterative solvers. Unlike the standard Frobenius norm,…
Locally Subspace-Informed Neural Operators for Efficient Multiscale PDE Solving
Alexander Rudikov, Vladimir Fanaskov, Sergei Stepanov +4
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use th…
Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving
Alexander Rudikov, Vladimir Fanaskov, Ekaterina Muravleva +2
Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, w…
On the structure of the Schur complement matrix for the Stokes equation
Vladislav Pimanov, Ekaterina Muravleva, Ivan Oseledets +1
In this paper, we investigate the structure of the Schur complement matrix for the fully-staggered finite-difference discretization of the stationary Stokes equation. Specifically,…
On the efficient preconditioning of the Stokes equations in tight geometries
Vladislav Pimanov, Oleg Iliev, Ivan Oseledets +1
If the Stokes equations are properly discretized, it is known that the Schur complement matrix is spectrally equivalent to the identity matrix. Moreover, in the case of simple geom…
Application of machine learning to viscoplastic flow modeling
E. Muravleva, I. Oseledets, D. Koroteev
We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approx…
Fast low-rank solution of the Poisson equation with application to the Stokes problem
E. A. Muravleva, I. V. Oseledets
We consider the problem of computing approximate solution of Poisson equation in the low-parametric tensor formats. We propose a new algorithm to compute the solution based on the…