The parallel implementation of the one-dimensional Fourier transformed Vlasov–Poisson system

Abstract

A parallel implementation of an algorithm for solving the one-dimensional, Fourier transformed Vlasov–Poisson system of equations is documented, together with the code structure, file formats and settings to run the code. The properties of the Fourier transformed Vlasov–Poisson system is discussed in connection with the numerical solution of the system. The Fourier method in velocity space is used to treat numerical problems arising due the filamentation of the solution in velocity space. Outflow boundary conditions in the Fourier transformed velocity space removes the highest oscillations in velocity space. A fourth-order compact Padé scheme is used to calculate derivatives in the Fourier transformed velocity space, and spatial derivatives are calculated with a pseudo-spectral method. The parallel algorithms used are described in more detail, in particular the parallel solver of the tri-diagonal systems occurring in the Padé scheme. Program summary Title of program:vlasov Catalogue identifier:ADVQ Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: Sun Solaris; HP-UX; Read Hat Linux Programming language used: FORTRAN 90 with Message Passing Interface (MPI) Computers: Sun Ultra Sparc; HP 9000/785; HP IPF (Itanium Processor Family) ia64 Cluster; PCs cluster Number of lines in distributed program, including test data, etc.:3737 Number of bytes in distributed program, including test data, etc.:18 772 Distribution format: tar.gz Nature of physical problem: Kinetic simulations of collisionless electron–ion plasmas. Method of solution: A Fourier method in velocity space, a pseudo-spectral method in space and a fourth-order Runge–Kutta scheme in time. Memory required to execute with typical data: Uses typically of the order 10 5–10 6 double precision numbers. Restriction on the complexity of the problem: The program uses periodic boundary conditions in space. Typical running time: Depends strongly on the problem size, typically few hours if only electron dynamics is considered and longer if both ion and electron dynamics is important. Unusual features of the program: No