Loghin, Daniel and Wathen, A. J. (1997) Preconditioning the AdvectionDiffusion Equation: the Green's Function Approach. Technical Report. Unspecified. (Submitted)

PDF
800kB 
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) advectiondiffusion 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 nonoscillatory solutions. In particular, the downwind decay ensures the locality of the grid Green's functions. Hence, a finite element formulation which produces a good solution will typically use a coefficient matrix with almost lower triangular structure under a "withtheflow" numbering of the variables. It follows that the block GaussSeidel matrix is a first candidate for a preconditioner to use with an iterative solver of Krylov subspace type.
Item Type:  Technical Report (Technical Report) 

Subjects:  D  G > Functional analysis H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1312 
Deposited By:  Lotti Ekert 
Deposited On:  09 Jun 2011 07:23 
Last Modified:  29 May 2015 19:00 
Repository Staff Only: item control page