Efficient method for localised functions using domain transformation and Fourier sine series

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

An efficient approach to handle localised states by using spectral methods (SM) in one and three dimensions is presented. The method consists of transformation of the infinite domain to the bounded domain in (0, π) and using the Fourier sine series as a set of basis functions for the SM. It is shown that with an appropriate choice of transformation functions, this method manages to preserve the good properties of original SMs; more precisely, superb computational efficiency when high level of accuracy is necessary. This is made possible by analytically exploiting the properties of the transformation function and the Fourier sine series. An especially important property of this approach is the possibility of calculating the Hartree energy very efficiently. This is done by exploiting the positive properties of the sine series as a basis set and conducting an extinctive part of the calculations analytically. We illustrate the efficiency of this method and implement it to solve the Poissons and Helmholtz equations in both one and three dimensions. The efficiency of the method is verified through a comparison to recently published results for both one-and three-dimensional problems.

Original languageEnglish
Pages (from-to)762-769
Number of pages8
JournalMolecular Physics
Volume112
Issue number5-6
DOIs
Publication statusPublished - 19 Mar 2014

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sine series
Fourier Analysis
spectral methods
Helmholtz equation
Poisson equation
Computational efficiency
Helmholtz equations
conduction

Keywords

  • Domain transformation
  • Infinite domains
  • Localised basis set
  • Spectral methods

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Condensed Matter Physics
  • Biophysics
  • Molecular Biology

Cite this

Efficient method for localised functions using domain transformation and Fourier sine series. / Jovanovic, Raka; Kais, Sabre; Alharbi, Fahhad.

In: Molecular Physics, Vol. 112, No. 5-6, 19.03.2014, p. 762-769.

Research output: Contribution to journalArticle

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