Green's Functions Used as Preconditioner

W. D. Drenth, R. M. M. Mattheij and J. M. L. Maubach

Department of Mathematics and Computer Science
Eindhoven University of Technology, The Netherlands


The inverse of a boundary value problem operator can be expressed using Green's functions. In the discrete case this is also valid. With this in mind, a preconditioner is constructed using (approximate) Green's functions. The method is described in detail. Subsequently the method is tested for a 1-dimensional problem. For grids with local refinements the results are very good.