A general concurrent algorithm for plasma particle-in-cell simulation codes - Liewer, Paulett C; Decyk, Viktor K (Journal of computational physics, 1989)
We have developed a new algorithm for implementing plasma particle-in-cell (PIC) simulation codes on concurrent processors with distributed memory. This algorithm, named the general concurrent PIC algorithm (GCPIC), has been used to implement an electrostatic PIC code on the 32-node JPL Mark III Hypercube parallel computer. To decompose a PIC code using the GCPIC algorithm, the physical domain of the particle simulation is divided into sub-domains, equal in number to the number of processors, such that all sub-domains have roughly equal numbers of particles. For problems with non-uniform particle densities, these sub-domains will be of unequal physical size. Each processor is assigned a sub-domain and is responsible for updating the particles in its sub-domain. This algorithm has led to a very efficient parallel implementation of a well-benchmarked 1-dimensional PIC code. The dominant portion of the code, updating the particle positions and velocities, is nearly 100% efficient when the number of particles is increased linearly with the number of hypercube processors used so that the number of particles per processor is constant. For example, the increase in time spent updating particles in going from a problem with 11,264 particles run on 1 processor to 360,448 particles on 32 processors was only 3% (parallel efficiency of 97%). Although implemented on a hypercube concurrent computer, this algorithm should also be efficient for PIC codes on other parallel architectures and for large PIC codes on sequential computers where part of the data must reside on external disks.