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, ) 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 Poisson's 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.
Keywords
spectral methods, localised basis set, infinite domains, domain transformation, UNBOUNDED-DOMAINS, SPECTRAL METHODS, PSEUDOSPECTRAL METHODS, MOLECULAR INTEGRALS, EQUATIONS, LINE
DOI
10.1080/00268976.2013.859311
Date of this Version
3-19-2014
Recommended Citation
Jovanovic, Raka; Kais, Sabre; and Alharbi, Fahhad H., "Efficient method for localised functions using domain transformation and Fourier sine series" (2014). Birck and NCN Publications. Paper 1579.
http://dx.doi.org/10.1080/00268976.2013.859311