TABLE OF CONTENTS Efficient processor-to-processor communication is vital. In order to calculate the neighbor sums in a SPAM algorithm, particles close to a subdomain ( processor ) boundary must have data available from all of their neighbors including neighbor particles in different subdomains ( processors ).
Most of the time spent communicating data during a parallel SPAM simulation occurs when sending and receiving data needed for particle sums. On parallel computers it is important to limit the search for neighbors within a local region of the domain so that the number of processors participating in the searches is small. A useful way to localize the search for interacting neighbors is to use a grid of cells with particles sorted into the cells. Using cell searches rather than searching the full domain for pairs reduces the computational time for the neighbor search from O( N 2), where N is the total number of particles, to O( nN), where n is the number of particles in the neighboring cells.
Although there are alternative methods for localizing the neighbor searches ( such as neighbor lists or a list of interacting pairs ), the cell model combines very well with partitioning techniques for parallel computers. The cell size is best chosen slightly larger than the interaction distance, h, so that a 3 3 grid of cells in two-dimensions will enclose all neighbors. Similarly, in three-dimensions nine cubes in each of three planes ( one plane of cubes...
