Numerical simulation code for self-gravitating BoseEinstein condensates ?
We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a BoseEinstein Condensate (BEC). The BEC is described by the GrossPitaevskii equation, which can be solved numerically using the CrankNicholson method. The gravitational potential, in turn, is described by Poissons equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 10 9 years using a finer (100100100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Program title: bec3p Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating BoseEinstein condensate by simultaneous solution of the GrossPitaevskii and Poisson equations in three dimensions. Solution method: The GrossPitaevskii equation is solved numerically using the CrankNicholson method; Poissons equation is solved using the relaxation method. The time evolution of the system is governed by the GrossPitaevskii equation; the solution of Poissons equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method. Running time: Depends on the chosen size of the problem. On a typical personal computer, a 100100100 grid can be solved with a time span of 10Gyr in approx. a day of running time.
dark matter grosspitaevskii equation poissons equation gravity galaxy rotation