Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation

By Boris N. Khoromskij. 2007

17 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics

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In Atomic and Molecular Physics, and Optics

In Computational Mathematics

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…• approximation of Green’s functions of high-dimensional PDEs [30,113]; • the solution of the Boltzmann equation [129, 149], and the chemical master / Fokker-Planck equations [4,6,61,64,86,122,133,135,196] • the solution of high-dimensional Schr¨odinger equations…”
Mathematik in den Naturwissenschaften Leipzig Tensor-Product Approximation to Operators and Functions in High Dimensions (2007, methodology): “Applications to nonlocal operators associated with the density matrix ansatz for solving the Hartree-Fock equation [7, 2], computation of molecular density functions by the Ornstein-Zernicke equation [6], as well as collision integrals of the deterministic Boltzmann equation [18] have demonstrated t”
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions (2005, background): “Note that the quadrature error analysis in the more general case f (ρ) = 1/ρ, μ > 0, can be found in [17].”
On tensor approximation of Green iterations for Kohn-Sham equations (2008, methodology): “In particular, we mention results for many-particle models based on the electronic Schrodinger [3,13,31] and Hartree-Fock [4,5,22] equations in electronic structure calculations, for the Ornstein-Zernicke equation in molecular density simulations [8], and for the deterministic Boltzmann equation [ 2”
Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods (2011, unknown): “6.1 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.2 Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140”
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions (2008, methodology): “Low separation rank decomposition to the multivariate functions 1/ρ, 1/ √ ρ and to the related Galerkin approximations were discussed in [2, 17, 18, 19, 24], while the kernel function ρ, μ ∈ R, was considered in [23].”
Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling (2008, background): “In particular, some functions of the Euclidean distance in R, say, 1/|x− y|, |x− y|, e−|x−y|, e−λ|x−y|/|x− y|, x, y ∈ R, can be approximated by Sinc-quadratures of the corresponding Gaussian integral on the semiaxis [41, 53, 54, 64].”