The particle positions are stepped according to the particle velocities x = x + v * dt. The velocities are unaffected at this point. Boundary conditions in x and z are always periodic, whereas in the y direction boundary conditions can be either periodic or non-periodic; in the non-periodic case the particle's position is reflected at the boundary and the velocity components are inverted according to the routine bound_particle (source file boundary.F90). Finally the subroutine redistribute (see below) is called to identify and transfer particles that have moved into the spatial domain treated by another processor.
The subroutine redistribute rearranges the particles such that each particle is stored in the particle buffer of that processor that treats the spatial subdomain in which the particle is presently located. It needs to be called whenever the position of the particles may have changed and when the particle buffers are loaded at start-up.
The subroutine stepv steps the particle velocities from t to t + dt and leaves the particle positions unaffected.
- smooth the electric field E (call to subroutine smooth_e, source file boundary.F90), interpolate the electric and the magnetic field at the exact location of the particle between grid points (volume weighting rule).
- in relativistic case: convert velocity into momentum, v = gamma * v
- apply first half of electric momentum change: v = v + dt/2 * E.
- apply magnetic momentum change (rotation), reduce rotation angle (magnetic field) by factor gamma in relativistic case
- apply second half of electric momentum change
- in relativistic case convert momentum back into velocity by dividing by gamma.
The subroutine calc_rho calculates the mean charge from the particle position by distributing the charge to the neighboring grid points:
- on request the array rho is deleted first, otherwise only the ghost cells are cleared
- the particles' charge is distributed to the eight grid points that are clostest to the particle's position (volume weighting rule).
- if non-periodic boundary conditions in y a virtual charge is added if the particle is sufficiently close to the wall. The sign of the virtual charge is determined by the subroutine virtual_charge (source file boundary.F90).
- Finally the charge that was collected in the ghost cell layer is transfered to the neighboring processing element (see subroutine bound_rho_j below).
The subroutine calc_j calculates the current density from the particle positions and velocities in full analogy to calc_rho. The virtual currents associated to non-periodic (conducting) walls in y are determined by the subroutine virtual_current (source file boundary.F90)
The subroutine bound_rho_j is only called by the calc_rho and calc_j. It transfers the charge and current that was accumulated in the ghost cell layer to the remote processor that is responsible for the adjacent subdomain. For non-periodic boundary conditions in y the ghost cells
at the boundary of the whole computational domain are not transfered.
The algorithms used throughout the code do not require any specific order of the particles within the particle buffer of one processor. As a consequence the memory accesses may be randomly scattered over the full subdomain treated by the processor, for example when the forces on the particle due to the electric and the magnetic fields are calculated. This leads to a large number of cache misses in the hardware memory cache and therefore may result in poor performance. To speed up execution the subroutine partsort rearranges the particles in the buffer such, that memory accesses become grouped together and allow to make use of the cache.