

Preprint 4/2008
On Tensor Approximation of Green Iterations for Kohn-Sham Equations
Boris N. Khoromskij
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Submission date: 10. Jan. 2008
Pages: 25
published in: Computing and visualization in science, 11 (2008) 4/6, p. 259-271
DOI number (of the published article): 10.1007/s00791-008-0097-x
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35
Keywords and phrases: Hartree-Fock method, tensor-product approximation, Density functional theory
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Abstract:
In the present paper we discuss efficient rank-structured tensor
approximation methods for
3D integral transforms representing the Green iterations for
the Kohn-Sham equation. We analyse the local convergence of the
Newton iteration to solve the Green's function integral formulation of
the Kohn-Sham model in electronic structure calculations.
We prove the low-separation rank approximations for the arising
discrete convolving kernels given by
the Coulomb and Yukawa potentials 1/|x| , and
, respectively, with
.
Complexity analysis of the nonlinear iteration with truncation to the fixed
Kronecker tensor-product format is presented. Our method has
linear scaling in the univariate problem size.
Numerical illustrations demostrate uniform exponential convergence
of tensor approximations in the orthogonal Tucker and canonical formats.