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- Boris N. Khoromskij, Venera Khoromskaia
- SIAM J. Scientific Computing
- 2009

In this paper, we describe and analyze a novel tensor approximation method for discretized multidimensional functions and operators in Rd, based on the idea of multigrid acceleration. The approach stands on successive reiterations of the orthogonal Tucker tensor approximation on a sequence of nested refined grids. On the one hand, it provides a good initial… (More)

- Boris N. Khoromskij, Venera Khoromskaia, Heinz-Jürgen Flad
- SIAM J. Scientific Computing
- 2011

In this paper, we describe a novel method for robust and accurate iterative solution of the self-consistent Hartree-Fock equation in R3 based on the idea of tensorstructured computation of the electron density and the nonlinear Hartree and (nonlocal) Hartree-Fock exchange operators at all steps of the iterative process. We apply the self-consistent field… (More)

- Venera Khoromskaia, Boris N. Khoromskij
- Numerical Lin. Alg. with Applic.
- 2016

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 representations. This is a significant generalization of our recent technique for the grid-based summation of electrostatic potentials on the rectangular L L L lattices by… (More)

- Venera Khoromskaia, Boris N. Khoromskij, Reinhold Schneider
- SIAM J. Scientific Computing
- 2013

In this paper, the problem of efficient grid-based computation of the two-electron integrals (TEI) in a general basis is considered. We introduce the novel multiple tensor factorizations of the TEI unfolding matrix which decrease the computational demands for the evaluation of TEI in several aspects. Using the reduced higher-order SVD the redundancy-free… (More)

- Venera Khoromskaia, Boris N. Khoromskij
- Computer Physics Communications
- 2014

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation to operations involving only 1D vectors however retaining the linear complexity scaling in the number of potentials. Here, we introduce and study a novel tensor approach for… (More)

- Venera Khoromskaia
- Comput. Meth. in Appl. Math.
- 2014

The Hartree-Fock eigenvalue problem governed by the 3D integro-differential operator is the basic model in ab initio electronic structure calculations. Several years ago the idea to solve the Hartree-Fock equation by fully 3D grid based numerical approach seemed to be a fantasy, and the tensor-structured methods did not exist. In fact, these methods evolved… (More)

- Venera Khoromskaia, Boris N. Khoromskij
- Computer Physics Communications
- 2014

We present a tensor-structured method to calculate the Møller-Plesset (MP2) correction to the Hartree-Fock energy with reduced computational consumptions. The approach originates from the 3D grid-based low-rank factorization of the two-electron integrals performed by the purely algebraic optimization. The computational scheme benefits from fast multilinear… (More)

- Boris N. Khoromskij, Venera Khoromskaia, Sambasiva Rao Chinnamsetty, Heinz-Jürgen Flad
- J. Comput. Physics
- 2009

Modern problems of physical chemistry lead to computations of many-particle potentials and related integral transforms, involving quantities described by higher-order tensors. Conventional numerical treatment of these problems suffers from the so-called “curse of dimensionality”. Recently developed Tucker and canonical tensor approximation techniques… (More)

- Venera Khoromskaia, D. Andrae, Boris N. Khoromskij
- Computer Physics Communications
- 2012

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized… (More)