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Pseudospectral methods for density functional theory in bounded and unbounded domains

Nold, Andreas, Goddard, Benjamin D., Yatsyshin, Peter, Savva, Nikos and Kalliadasis, Serafim 2017. Pseudospectral methods for density functional theory in bounded and unbounded domains. Journal of Computational Physics 334 , pp. 639-664. 10.1016/j.jcp.2016.12.023

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Abstract

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze uids, which accounts for nanoscale uid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in uids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialized Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a signifcantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single- and multispecies hard-sphere and hard-disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Density functional theory; Pseudospectral methods
Publisher: Elsevier
ISSN: 0021-9991
Date of Acceptance: 13 December 2016
Last Modified: 06 Jun 2017 22:34
URI: http://orca.cf.ac.uk/id/eprint/98641

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