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MiS Preprint
4/2008
On Tensor Approximation of Green Iterations for Kohn-Sham Equations
Boris N. Khoromskij
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. %with linear scaling in the univariate problem size.
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 ${e^{-\lambda|x| }}/{|x|} $, respectively, with $x \in \mathbb{R}^{d} $. 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.
