ISSN:
0749-159X
Keywords:
Mathematics and Statistics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
In solving unsteady problems,domain decomposition methods may be used either for iterative preconditioning each global implicit time-step or directly (noniteratively) within a blockwise implicit time-stepping procedure, in the latter case, the inner boundary values for the subproblems are generated by explicit time-extrapolation. The overlapping variants of this method have been proved to be efficient tools for solving parabolic and first-order hyperbolic problems on modern parallel computers, 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 model problems of convection and convection-diffusion. Favorable optimal and far-reaching estimates of the overlap required have been established 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 corresponding convection and diffusion problem to be considered independently. These results have been confirmed with several numerical test examples. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 387-406, 1998
Additional Material:
8 Ill.
Type of Medium:
Electronic Resource
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