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

Raka Jovanovic; Sabre Kais; Fahhad H. Alharbi

doi:10.1080/00268976.2013.859311

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

Raka Jovanovic
, Sabre Kais
, Fahhad H. Alharbi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English
Pages (from-to)	762-769
Number of pages	8
Journal	Molecular Physics
Volume	112
Issue number	5-6
DOIs	https://doi.org/10.1080/00268976.2013.859311
State	Published - 19 Mar 2014
Externally published	Yes

Bibliographical note

Funding Information:
aQatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar; bInstitute of Physics, University of Belgrade, Pregrevica 118, Zemun, Serbia; cDepartment of Chemistry, Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA; dKing Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia

Keywords

Domain transformation
Infinite domains
Localised basis set
Spectral methods

ASJC Scopus subject areas

Biophysics
Molecular Biology
Condensed Matter Physics
Physical and Theoretical Chemistry

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Cite this

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title = "Efficient method for localised functions using domain transformation and Fourier sine series",

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.",

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author = "Raka Jovanovic and Sabre Kais and Alharbi, \{Fahhad H.\}",

note = "Funding Information: aQatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar; bInstitute of Physics, University of Belgrade, Pregrevica 118, Zemun, Serbia; cDepartment of Chemistry, Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA; dKing Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia",

year = "2014",

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doi = "10.1080/00268976.2013.859311",

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AU - Jovanovic, Raka

AU - Kais, Sabre

AU - Alharbi, Fahhad H.

N1 - Funding Information: aQatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar; bInstitute of Physics, University of Belgrade, Pregrevica 118, Zemun, Serbia; cDepartment of Chemistry, Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA; dKing Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia

PY - 2014/3/19

Y1 - 2014/3/19

N2 - 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.

AB - 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.

KW - Domain transformation

KW - Infinite domains

KW - Localised basis set

KW - Spectral methods

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JO - Molecular Physics

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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