102 citations · 329 across the 25 of their papers we have counts for
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Tucker tensor method for fast grid-based summation of long-range potentials on 3D lattices with defects
Venera Khoromskaia, Boris N. Khoromskij
In this paper, we present a method for fast summation of long-range potentials on 3D lattices with multiple defects and having non-rectangular geometries, based on rank-structured…
Tensor Numerical Methods for High-dimensional PDEs: Basic Theory and Initial Applications
Boris N. Khoromskij
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of…
Tensor Numerical Approach to Linearized Hartree-Fock Equation for Lattice-type and Periodic Systems
Venera Khoromskaia, Boris N. Khoromskij
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D latt…
Efficient computation of highly oscillatory integrals by using QTT tensor approximation
Boris Khoromskij, Alexander Veit
We propose a new method for the efficient approximation of a class of highly oscillatory weighted integrals where the oscillatory function depends on the frequency parameter $ω\geq…
Computation of the Response Surface in the Tensor Train data format
Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko +1
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochasti…
Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation
Venera Khoromskaia, Boris N. Khoromskij
We introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D gr…