Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions

DOI10.1137/20M1341659zbMath1496.65220arXiv2006.01455OpenAlexW3033183059WikidataQ114074195 ScholiaQ114074195MaRDI QIDQ5099860

Christoph Schwab, M. V. Rakhuba, Ivan V. Oseledets, Vladimir A. Kazeev

Publication date: 26 August 2022

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.01455

zbMATH Keywords

low-rank approximationmultiscale problemsmatrix product statestensor trainmultilevel structurelow-rank tensorsdata-driven discretization

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Multilinear algebra, tensor calculus (15A69) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (2)

Low-rank tensor methods for partial differential equations ⋮ Limitations of neural network training due to numerical instability of backpropagation

Uses Software

• TensorRefinement.jl

Cites Work

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