Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation

From MaRDI portal
Publication:4908651

DOI10.1137/120864210zbMath1259.82075OpenAlexW1963973528MaRDI QIDQ4908651

Boris N. Khoromskij, Ivan V. Oseledets, Sergey V. Dolgov

Publication date: 6 March 2013

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/120864210



Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).


Related Items (48)

Randomized Algorithms for Rounding in the Tensor-Train FormatUncertainty propagation in orbital mechanics via tensor decompositionTensor rank bounds for point singularities in \(\mathbb{R}^3\)A low-rank approach to the computation of path integralsRank Bounds for Approximating Gaussian Densities in the Tensor-Train FormatComputation of extreme eigenvalues in higher dimensions using block tensor train formatWavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution EquationsAdaptive integration of nonlinear evolution equations on tensor manifoldsQTT-finite-element approximation for multiscale problems. I: Model problems in one dimensionA block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equationsLow-rank tensor structure of linear diffusion operators in the TT and QTT formatsTensor Approximation of Stationary Distributions of Chemical Reaction NetworksSimultaneous state-time approximation of the chemical master equation using tensor product formatsFast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximationLow-rank tensor methods for partial differential equationsImplicit integration of nonlinear evolution equations on tensor manifoldsState estimation in nonlinear parametric time dependent systems using tensor trainNumerical solutions for solving model time‐fractional<scp>Fokker–Planck</scp>equationParallel Algorithms for Computing the Tensor-Train DecompositionThe tensor-train mimetic finite difference method for three-dimensional Maxwell's wave propagation equationsQuantized tensor-structured finite elements for second-order elliptic PDEs in two dimensionsNumerical solution of a class of third order tensor linear equationsA two-step accelerated Levenberg-Marquardt method for solving multilinear systems in tensor-train formatA space-time adaptive low-rank method for high-dimensional parabolic partial differential equationsParallel cross interpolation for high-precision calculation of high-dimensional integralsAn optimization approach for dynamical Tucker tensor approximationApproximation rates for the hierarchical tensor format in periodic Sobolev spacesComputing the density of states for optical spectra of molecules by low-rank and QTT tensor approximationTensor Train Construction From Tensor Actions, With Application to Compression of Large High Order Derivative TensorsAlternating iterative methods for solving tensor equations with applicationsRange-Separated Tensor Format for Many-Particle ModelingTensor networks and hierarchical tensors for the solution of high-dimensional partial differential equationsFractional Fokker-Planck equationA note on tensor chain approximationGrid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximationA Fokker-Planck control framework for stochastic systemsBlock tensor train decomposition for missing data estimationSuperfast Fourier transform using QTT approximationFast low-rank solution of the multidimensional hyperbolic problemsA numerical solver for high dimensional transient Fokker-Planck equation in modeling polymeric fluidsProspects of tensor-based numerical modeling of the collective electrostatics in many-particle systemsA tensor decomposition algorithm for large ODEs with conservation lawsQuasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolationLow-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficientsTensor Spaces and Hierarchical Tensor RepresentationsA literature survey of low-rank tensor approximation techniquesEstimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train FormatNumerical solution for the time-fractional Fokker-Planck equation via shifted Chebyshev polynomials of the fourth kind




This page was built for publication: Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation