The vmf90 program for the numerical resolution of the Vlasov equation for mean-field systems

Abstract

The numerical resolution of the Vlasov equation provides complementary information with respect to analytical studies and forms an important research tool in domains such as plasma physics. The study of mean-field models for systems with long-range interactions is another field in which the Vlasov equation plays an important role. We present the vmf90 program that performs numerical simulations of the Vlasov equation for this class of mean-field models with the semi-Lagrangian method. Program summaryProgram title: vmf90Catalogue identifier: AESO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 7794No. of bytes in distributed program, including test data, etc.: 58851Distribution format: tar.gzProgramming language: Fortran 95.Computer: Single CPU computer.Operating system: No specific operating system, the program is tested under Linux and OS X.RAM: About 5 M bytesClassification: 1.5, 19.8, 19.13, 23.External routines: HDF5 for the code (tested with HDF5 v1.8.8 and above). Python, NumPy, h5py and Matplotlib for analysis.Nature of problem:Numerical resolution of the Vlasov equation for mean-field models (Hamiltonian Mean-Field model and Single Wave model).Solution method:The equation is solved with the semi-Lagrangian method and cubic spline interpolation.Running time:The examples provided with the program take 1 m 30 for the Hamiltonian-Mean Field model and 10 m for the Single Wave model, on an Intel Core i7 CPU @ 3.33 GHz. Increasing the number of grid points or the number of time steps increases the running time.