FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

Abstract

A Fortran program package is introduced for the rapid evaluation of the screened Coulomb interactions of N particles in three dimensions. The method utilizes an adaptive oct-tree structure, and is based on the new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related packages are also available at http://www.fastmultipole.org/. This paper is a brief review of the program and its performance. Program summaryProgram title: FMM-YukawaCatalogue identifier: AEEQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPL 2.0No. of lines in distributed program, including test data, etc.: 12 385No. of bytes in distributed program, including test data, etc.: 79 222Distribution format: tar.gzProgramming language: Fortran77 and Fortran90Computer: AnyOperating system: AnyRAM: Depends on the number of particles, their distribution, and the adaptive tree structureClassification: 4.8, 4.12Nature of problem: To evaluate the screened Coulomb potential and force field of N charged particles, and to evaluate a convolution type integral where the Green's function is the fundamental solution of the modified Helmholtz equation.Solution method: An adaptive oct-tree is generated, and a new version of fast multipole method is applied in which the “multipole-to-local” translation operator is diagonalized.Restrictions: Only three and six significant digits accuracy options are provided in this version.Unusual features: Most of the codes are written in Fortran77. Functions for memory allocation from Fortran90 and above are used in one subroutine.Additional comments: For supplementary information see http://www.fastmultipole.org/Running time: The running time varies depending on the number of particles (denoted by N) in the system and their distribution. The running time scales linearly as a function of N for nearly uniform particle distributions. For three digits accuracy, the solver breaks even with direct summation method at about N=750.