Geometrically Parallel Algorithms

Abstract

A natural way to implement the simulation on a parallel computer of any system that involves a regular geometry and spatially limited interactions is to divide the volume into equally sized portions, each of which are then assigned to one of the parallel processing elements. This geometric parallelism, sometimes referred to as domain decomposition, can be implemented in a variety of ways, of which we present here some of the principle ones. The expression data parallelism is sometimes used in the literature to describe these types of algorithms, but we feel that the expression geometric parallelization describes more unambiguously the partitioning of the actual space in which the simulation takes place, and we reserve the use of the expression data parallelism to those cases where no such spatially oriented partitioning of the problem is implied, such as the algorithms described in Chap. 8. Although the methods we describe here are conceptually straightforward they require, in general, a substantial increase in program length and complexity. The additional time that is required to write and test such programs can be kept to a minimum by careful planning of the program structure and communication procedures between the processors in relation to the underlying geometry of the system being simulated. The reward for such effort is a program that uses the machine effectively and delivers as much of the available computing power as possible, thereby enabling us to study problems of a size that would otherwise have been inaccessible.