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From: wlrush@water.waterloo.edu (Wenchantress Wench Wendall)
Newsgroups: ont.events,uw.cs.grad,uw.talks
Subject: SCIENTIFIC COMPUTATION SEMINAR
Keywords: Dimpy Pathria, graduate student, Dept. of Computer Science,
Message-ID: <2629@water.waterloo.edu>
Date: 1 Sep 89 17:17:55 GMT
Distribution: ont
Organization: U of Waterloo, Ontario
Lines: 44

will speak on 
``Adaptive Mesh Methods for the Fourier Solution of 
Certain Wave Problems.''


DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES

SCIENTIFIC COMPUTATION SEMINAR

                    -Friday, September 8, 1989

Dimpy  Pathria,  graduate  student,  Dept.  of Computer
Science  will  speak on ``Adaptive Mesh Methods For The
Fourier Solution of Certain Wave Problems.''

TIME:                 10:30 a.m.

ROOM:                 DC 3540

ABSTRACT

In  a  previous  talk  we  described the pseudospectral
split-step   method   for   solving  certain  nonlinear
Schrodinger  equations.   Pseudospectral approximations
are  often  used for discretizing the spatial component
of  evolutionary  problems.   In  this talk we consider
enhancing  the  performance  of  such  methods  by  two
adaptive  grid  generation  schemes.   The first scheme
addresses the temporal nonuniformity commonly exhibited
by  solutions  of nonlinear evolutionary equations.  By
integrating  the  problem  independently on interleaved
grids   and   comparing  the  Fourier  coefficients  as
calculated   on  each,  it  provides  a  mechanism  for
automatically  varying  the degree of the interpolating
trigonometric  polynomial.  The second scheme addresses
the  spatial  nonuniformity  of the solutions, in which
the  resolution  requirements vary over the domain.  It
is   an   adaptive   meshing   algorithm   for  Fourier
interpolation,   where   the   collocation   nodes  are
dynamically located in accordance with the needs of the
problem.    Numerical   experiments   demonstrate   the
advantages of the adaptive discretization schemes.