mwang@watmath.UUCP (mwang) (03/20/84)
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- Thursday, March 29, 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: 2:30 PM
ROOM: MC 5158
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.
March 20, 1984