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Preconditioning the Advection-Diffusion Equation: the Green's Function Approach

Abstract:

We look at the relationship between efficient preconditioners (i.e., good approximations to the discrete inverse operator) and the generalized inverse for the (continuous) advection-diffusion operator -- the Green's function. We find that the continuous Green's function exhibits two important properties -- directionality and rapid downwind decay -- which are preserved by the discrete (grid) Green's functions, if and only if the discretization used produces non-oscillatory solutions. In partic...

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Publication date:
1997-10-05
URN:
uuid:94b480e7-0544-4735-8de8-23387688f4fe
Local pid:
oai:eprints.maths.ox.ac.uk:1312

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