Parallel Architectures for Iterative Methods on Adaptive, Block Structured Grids

Publisher Summary This chapter focuses on parallel architectures for iterative methods on adaptive, block structured grids. The development of larger and faster computers is being driven by a number of application areas where current computers are not adequate. One of the most important of these areas is the numerical solution of partial differential equations. No computer in existence could tackle the problem of accurately modeling air flow over realistic aircraft configurations. This is so even if all time dependent effects are neglected. Similar remarks are made about partial differential equations arising in a number of applications areas. While no major technological barriers impede the development of large memories, the speed of the switching elements used for sequential computation seems to have reached a plateau. The solution must lie in the use of parallelism. With device densities rising rapidly, and prices dropping correspondingly, computers having hundreds or thousands of processors will be practical within a decade. Such computers will present a challenge to both the computer architect and numerical analyst.