UNSTEADY CONVECTION AND CONVECTION-DIFFUSION PROBLEMS VIA DIRECT OVERLAPPING DOMAIN DECOMPOSITION METHODS

In solving unsteady problems, domain decomposition methods may be used either for iterative preconditioning each global implicit time-step o r directly (noniteratively) within a blockwise implicit time-stepping procedure. In the latter case, the inner boundary values for the subpr oblems are generated by explicit time-extrapolation. The overlapping v ariants of this method have been proved to be efficient tools for solv ing parabolic and first-order hyperbolic problems on modern parallel c omputers, because they require global communication only once per time -step. The mechanism making this possible is the exponential decay in space of the time-discrete Green's function. We investigate several mo del problems of convection and convection-diffusion Favorable optimal and far-reaching estimates of the overlap required have been establish ed in the case of exemplary standard upwind finite-difference schemes. In particular, it has been shown that the overlap for the convection- diffusion problem is the additive function of overlaps for the corresp onding convection and diffusion problem to be considered independently . These results have been confirmed with several numerical test exampl es. (C) 1998 John Wiley & Sons, Inc.