Green's Functions for Preconditioning
نویسنده
چکیده
In this paper we look at the connection between Green's functions and preconditioners for systems of equations arising through the discretization of linear partial diierential equations. We nd that Green's functions, as generalized inverses of diierential operators, can sometimes ooer a useful insight into the properties of the discrete inverse operator. More precisely, their properties (singularity, decay etc.) translate into a particular matrix structure of the discrete inverse, which should be approximated by a good preconditioner. In the case of the advection-diiusion operator it is found that eecient preconditioning is achieved with block lower triangular matrices (including the Gauss-Seidel matrix) under a ow-oriented numbering of the variables.
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