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
MSC-Numbers: 65F30, 65F50, 65N35
Keywords and phrases: Hartree-Fock method, tensor-product approximation, Density functional theory
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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 formula16, respectively, with formula18. 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.

03.07.2017, 01:41