Venera Khoromskaia

Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays

In this paper, we describe and analyze a novel tensor approximation method for discretized multidimensional functions and operators in

Numerical Solution of the Hartree-Fock Equation in Multilevel Tensor-Structured Format

\mathbb{R}^d

Low rank Tucker-type tensor approximation to classical potentials

, 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 guess for the nonlinear iterations to find the approximating subspaces on finer grids; on the other hand, it allows us to transfer from the coarse-to-fine grids the important data structure information on the location of the so-called most important fibers in directional unfolding matrices. The method indicates linear complexity with respect to the size of data representing the input tensor. In particular, if the target tensor is given by using the rank-

Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation

R

Fast and accurate 3D tensor calculation of the Fock operator in a general basis

canonical model, then our approximation method is proved to have linear scaling in the univariate grid size

Tensor-structured factorized calculation of two-electron integrals in a general basis

n

Black-Box Hartree–Fock Solver by Tensor Numerical Methods

and in the input rank

Møller–Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals

R

A Reduced Basis Approach for Calculation of the Bethe-Salpeter Excitation Energies by using Low-Rank Tensor Factorisations

. The method is tested by three-dimensional (3D) electronic structure calculations. For the multigrid accelerated low Tucker-rank approximation of the all electron densities having strong nuclear cusps, we obtain high resolution of their 3D convolution product with the Newton potential. The accuracy of order

QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations

10^{-6}