NumSBT: A subroutine for calculating spherical Bessel transforms numerically

A previous subroutine, LSFBTR, for computing numerical spherical Bessel (Hankel) transforms is updated with several improvements and modifications. The procedure is applicable if the input radial function and the output transform are defined on logarithmic meshes and if the input function satisfies reasonable smoothness conditions. Important aspects of the procedure are that it is simply implemented with two successive applications of the fast Fourier transform, and it yields accurate results at very large values of the transform variable. Applications to the evaluation of overlap integrals and the Coulomb potential of multipolar charge distributions are described.

Program summary

Program title: NumSBTCatalogue identifier: AANZ_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AANZ_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 476No. of bytes in distributed program, including test data, etc.: 4451Distribution format: tar.gzProgramming language: Fortran 90Computer: GenericOperating system: LinuxClassification: 4.6Catalogue identifier of previous version: AANZ_v1_0Journal reference of previous version: Comput. Phys. Comm. 30 (1983) 93Does the new version supersede the previous version?: NoNature of problem: This program is a subroutine which, for a function defined numerically on a logarithmic mesh in the radial coordinate, generates the spherical Bessel, or Hankel, transform on a logarithmic mesh in the transform variable. Accurate results for large values of the transform variable are obtained, that would not be otherwise obtainable.Solution method: The program applies a procedure proposed by the author 1] that treats the problem as a convolution. The calculation then requires two applications of the fast Fourier transform method.Reasons for new version: The method of computing the transform at small values of the transform variable has been substantially changed and the whole procedure simplified. In addition, the possibility of computing the transform for a single transform variable value has been incorporated. The code has also been converted to Fortran 90 from Fortran 77.Restrictions: The procedure is most applicable to smooth functions defined on (0,∞) with a limited number of nodes.Running time: The example provided with the distribution takes a few seconds to execute.References:1] J.D. Talman, J. Comp. Phys. 29 (1978) 35.