

Preprint 79/2008
Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels
Cristobal Bertoglio and Boris N. Khoromskij
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Submission date: 11. Nov. 2008 (revised version: January 2010)
Pages: 19
published in: Computer physics communications, 183 (2012) 4, p. 904-912
DOI number (of the published article): 10.1016/j.cpc.2011.12.016
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35
Keywords and phrases: sinc-quadratures, tensor-product, Newton/Yukawa potentials
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Abstract:
Tensor-product approximation provides a convenient tool for efficient
numerical treatment of high dimensional problems that arise, in particular,
in electronic structure calculations in . In this work we apply tensor approximation to the Galerkin representation of the Newton and Yukawa potentials for a set of tensor-product, piecewise polynomial basis functions.
To construct tensor-structured representations, we make use of the well-known
Gaussian transform of the potentials, and then approximate the resulting
univariate integral in
by special sinc quadratures.
The novelty of
the approach lies on the heuristic optimization of the quadrature parameters
that allow
to reduce dramatically the initial tensor rank obtained by the
standard sinc-quadratures. The numerical
experiments show that this approach gives almost optimal tensor ranks
in 3D computations on large spatial grids and with linear complexity
in the univariate grid size.
This scheme becomes attractive for the multiple calculation of the Yukawa potential
when the exponents in gaussian functions vary during the computational process.