mwang@watmath.UUCP (mwang) (04/03/84)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES NUMERICAL ANALYSIS SEMINAR - Thursday, April 12, 1984. Dr. W. Liniger of IBM Thomas J. Watson Research Center will speak on ``Fast Finite Difference Algorithms for Solving Poisson's Equation on General Two-Dimensional Regions.'' TIME: 3:30 PM ROOM: MC 6091A ABSTRACT Fast finite difference algorithms are proposed for solving Poisson's equation on general two-dimensional regions. These algorithms are based on a variant of the marching method but are intrinsically much more stable than the latter and thus can be applied on rela- tively large grids without resorting to multiple shoot- ing. The algorithms are associated with a one- parameter family of factored second-order complex discretizations of the Laplace operator and the gain in stability is due to solving initial value problems for two first-order difference equations, rather than one second-order equation as in the conventional marching method. These initial value problems represent back- solves in a sparse Choleski decomposition. The stabil- ity and accuracy of the method can be further con- trolled by the choice of the parameter on which the discretization depends. The factored discretization lends itself well to an iterative implementation by means of the preconditioned conjugate gradient method, as well as for a direct implementation. The algorithms were tested successfully on regions with complicated geometries, including multiply connected ones.