ABSTRACT
This chapter reviews the parallel shooting process, primarily for the purpose of establishing notation and terminology. It seeks to timing estimates for each of the four phase/decomposition combinations. The chapter aims to use these estimates to discuss the relative advantages of using domain decomposition for both phases, as opposed to using column decomposition for both phases. The parallel shooting method perhaps should be considered a class of methods, with the particular method within this class depending upon the precise selection of “shooting” points from among the mesh points. Numerical solution of two-point boundary-value problems on basically sequential computers is a highly developed field, with a number of well tested codes available for this specialized purpose. At this early juncture it seems appropriate to consider the circumstances under which one might reasonably wish to consider using a hypercube, or any other type of computer having a high degree of explicit user-accessible parallelism, to solve a linear two-point boundary-value problem.
