15 June 2000
Dr Steven Benbow
The talk will focus on solution methods for augmented linear systems of the form \\ \\ $[ A B ][x] = [b] [ B' 0 ][y] $. \\ \\ Augmented linear systems of this type arise in several areas of numerical applied mathematics including mixed finite element / finite difference discretisations of flow equations (Darcy flow and Stokes flow), electrical network simulation and optimisation. The general properties of such systems are that they are large, sparse and symmetric, and efficient solution techniques should make use of the block structure inherent in the system as well as of these properties. \\ \\ Iterative linear solution methods will be described that attempt to take advantage of the structure of the system, and observations on augmented systems, in particular the distribution of their eigenvalues, will be presented which lead to further iterative methods and also to preconditioners for existing solution methods. For the particular case of Darcy flow, comments on properties of domain decomposition methods of additive Schwarz type and similarities to incomplete factorisation preconditioners will be made.
- Computational Mathematics and Applications Seminar