QTT-isogeometric solver in two dimensions

DOI10.1016/j.jcp.2020.109835OpenAlexW3086821890MaRDI QIDQ2123884

Yanyan Li

Publication date: 14 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.02839

zbMATH Keywords

finite element methodelliptic partial differential equationtensor trainquantized tensor train\(z\)-curve\(z\)-kron

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Related Items (1)

Low-rank tensor methods for partial differential equations

Uses Software

• FEniCS
• SyFi
• TT Toolbox
• TTPY

Cites Work

• Unnamed Item
• Tensor-Train Decomposition
• Low-rank tensor structure of linear diffusion operators in the TT and QTT formats
• \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
• Automated solution of differential equations by the finite element method. The FEniCS book
• The strong Kronecker product
• Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions
• Extrapolation algorithms and Padé approximations: A historical survey
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
• Simultaneous state-time approximation of the chemical master equation using tensor product formats
• Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• Paving: A new approach to automated quadrilateral mesh generation
• Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
• Solution of Linear Systems and Matrix Inversion in the TT-Format

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