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Unsteady convection and convection‐diffusion problems via direct overlapping domain decomposition methods
Author(s) -
Hebeker F. K.,
Kuznetsov Yu. A.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199805)14:3<387::aid-num7>3.0.co;2-i
Subject(s) - mathematics , domain decomposition methods , convection , extrapolation , diffusion , convection–diffusion equation , upwind scheme , boundary (topology) , partial differential equation , function (biology) , domain (mathematical analysis) , exponential function , mathematical analysis , mechanics , finite element method , physics , discretization , evolutionary biology , biology , thermodynamics
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