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- W2064301517 abstract "We propose and analyze a new relaxation scheme for the iterative solution of the linear system arising from the finite difference discretization of convection–diffusion problems. For problems that are convection dominated, the (nondimensionalized) diffusion parameter ϵ is usually several orders of magnitude smaller than computationally feasible mesh widths. Thus, it is of practical importance that approximation methods not degrade for small ϵ. We give a relaxation procedure that is proven to converge uniformly in ϵ to the solution of the linear algebraic system (i.e., “robustly”). The procedure requires, at each step, the solution of one 4 × 4 linear system per mesh cell. Each 4 × 4 system can be independently solved, and the result communicated to the neighboring mesh cells. Thus, on a mesh connected processor array, the communication requirements are four local communications per iteration per mesh cell. An example is given, which illustrates the robustness of the new relaxation scheme. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 91–110, 1999" @default.
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- W2064301517 date "1999-01-01" @default.
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- W2064301517 title "A robust and parallel relaxation method based on algebraic splittings" @default.
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- W2064301517 doi "https://doi.org/10.1002/(sici)1098-2426(199901)15:1<91::aid-num5>3.0.co;2-t" @default.
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