Implementing methods of PIC simulation by a special purpose computer system for gravitational N-body problems

Particle In Cell (PIC) simulation using GRAPE-6 (G6), a special-purpose computer for gravitational N-body problems, is demonstrated. The calculation time is decreased by approximately 20 times, as compared to the usual method. There are two problems associated with simulation of plasma by the G6. First, G6 calculates only Coulomb force and three-dimensional (3D) calculations, which means that one-dimensional (1D) and two-dimensional (2D) simulations cannot be performed. Calculation of the electric field is achieved by arranging virtual particles. Virtual particles are arranged on a plane in 1D and along a line in 2D. As a result, in addition to 3D simulations, 1D and 2D simulations can be performed using the G6, and the PIC method can be applied. In addition, the G6 can only be used in free space. The FFT method assumes a cyclic boundary condition. This problem is solved by calculating the electric field outside the simulation space. The obtained external electric field is added to the electric field in the simulation space. By this operation, the error can be suppressed to approximately 1/80, as compared to the case in which this operation is not performed.