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.