102 citations · 329 across the 25 of their papers we have counts for
29 papers
Reduced Higher Order SVD: ubiquitous rank-reduction method in tensor-based scientific computing
Venera Khoromskaia, Boris N. Khoromskij
Tensor numerical methods, based on the rank-structured tensor representation of -variate functions and operators, are designed to provide complexity of numerical calcula…
Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format
Cleophas Kweyu, Venera Khoromskaia, Boris Khoromskij +2
The Poisson-Boltzmann equation (PBE) is an implicit solvent continuum model for calculating the electrostatic potential and energies of ionic solvated biomolecules. However, its nu…
Tensor numerical method for optimal control problems constrained by an elliptic operator with general rank-structured coefficients
Boris N. Khoromskij, Britta Schmitt, Volker Schulz
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in , , with variable coefficients, which can be…
Tensor-based techniques for fast discretization and solution of 3D elliptic equations with random coefficients
Venera Khoromskaia, Boris N. Khoromskij
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in , . We consider the stochasti…
Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients
Britta Schmitt, Boris N. Khoromskij, Venera Khoromskaia +1
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve t…
Prospects of tensor-based numerical modeling of the collective electrostatic potential in many-particle systems
Venera Khoromskaia, Boris N. Khoromskij
Recently the rank-structured tensor approach suggested a progress in the numerical treatment of the long-range electrostatic potentials in many-particle systems and the respective…
Numerical study in stochastic homogenization for elliptic PDEs: convergence rate in the size of representative volume elements
Venera Khoromskaia, Boris N. Khoromskij, Felix Otto
We describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homoge…
Computing electrostatic potentials using regularization based on the range-separated tensor format
Peter Benner, Venera Khoromskaia, Boris Khoromskij +2
In this paper, we apply the range-separated (RS) tensor format [6] for the construction of new regularization scheme for the Poisson-Boltzmann equation (PBE) describing the electro…
Range-separated tensor representation of the discretized multidimensional Dirac delta and elliptic operator inverse
Boris N. Khoromskij
In this paper, we introduce the operator dependent range-separated tensor approximation of the discretized Dirac delta in . It is constructed by application of the di…
Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints
Gennadij Heidel, Venera Khoromskaia, Boris N. Khoromskij +1
We introduce the tensor numerical method for solution of the -dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $…
Computing the density of states for optical spectra by low-rank and QTT tensor approximation
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij +1
In this paper, we introduce a new interpolation scheme to approximate the density of states (DOS) for a class of rank-structured matrices with application to the Tamm-Dancoff appro…
Tucker Tensor analysis of Matern functions in spatial statistics
Alexander Litvinenko, David Keyes, Venera Khoromskaia +2
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required…
Quantized-CP Approximation and Sparse Tensor Interpolation of Function Generated Data
Boris N. Khoromskij, Kishore K. Naraparaju, Jan Schneider
In this article we consider the iterative schemes to compute the canonical (CP) approximation of quantized data generated by a function discretized on a large uniform grid in an in…
Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach
V. Khoromskaia, B. N. Khoromskij
This paper introduces and analyses the new grid-based tensor approach to approximate solution of the elliptic eigenvalue problem for the 3D lattice-structured systems. We consider…
Rank structured approximation method for quasi--periodic elliptic problems
B. Khoromskij, S. Repin
We consider an iteration method for solving an elliptic type boundary value problem , where a positive definite operator is generated by a quasi--per…
Range-separated tensor formats for numerical modeling of many-particle interaction potentials
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij
We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format which aims for numerical modeling of the 3D long-range interaction potentials in multi-particle…
Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation
Peter Benner, Sergey Dolgov, Venera Khoromskaia +1
In this paper, we study and implement the structural iterative eigensolvers for the large-scale eigenvalue problem in the Bethe-Salpeter equation (BSE) based on the reduced basis a…
A fast iteration method for solving elliptic problems with quasiperiodic coefficients
Boris N. Khoromskij, Sergey I. Repin
The paper suggests a preconditioning type method for fast solving of elliptic equations with oscillating quasiperiodic coefficients specified by the small parameter . We…
A reduced basis approach for calculation of the Bethe-Salpeter excitation energies using low-rank tensor factorizations
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij
The Bethe-Salpeter equation (BSE) is a reliable model for estimating the absorption spectra in molecules and solids on the basis of accurate calculation of the excited states from…
Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States
Venera Khoromskaia, Boris N. Khoromskij
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the l…
Polynomial Chaos Expansion of random coefficients and the solution of stochastic partial differential equations in the Tensor Train format
Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko +1
We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with…
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…