ABSTRACT
This chapter develops a dynamic domain decomposition algorithm for the solution of advection-diffusion equations. The traditional computer consists of three basic units: the control unit, the processing unit, and the main memory. This chapter concentrates only on the multiprocessor. Multiprocessors take on two forms: the loosely coupled or distributed memory multiprocessors and the tightly coupled or shared-memory multiprocessors. The chapter reexamines the basic formulation put forth by Schwarz with the goal of redefining it to achieve a faster iteration. The advection-diffusion equations are first advanced on a coarse mesh subject to the hyperbolic stability condition. Significant parabolic regions are identified with a parabolic threshold criterion, and the coarse mesh is dynamically decomposed and refined. The clustering algorithm is used to create nonoverlapping meshes. The parallel performance of this idea was studied on an Alliant FX/8 multiprocessor.
