Thursday, November 10, 9:30 am in room MTH 3206, University of Maryland,
College Park
On the numerical solution of the heat equation in unbounded domains
Prof. Leslie Greengard
Department of Mathematics
New York University-Courant Institute
251 Mercer Street
New York, NY 10012-1110
greengar@greengard.cims.nyu.edu
Many problems in applied mathematics require the
solution of the heat equation in unbounded domains. Integral
equation methods are particularly appropriate for the solution of
such problems for several reasons: they are unconditionally stable,
they are insensitive to the complexity
of the geometry, and they do not require the artificial truncation
of the computational domain as do finite difference and finite
element techniques.
Methods of this type, however, have not become widespread due to
the high cost of evaluating heat potentials.
When m points are used in the discretization of the initial data,
M points are used in the discretization of the boundary and
N time steps are computed, an amount of work of the order
O(N^2 M^2 + NM m)
has traditionally been required.
In this talk, we present an algorithm which requires an amount of work
of the order O(NM log M + m) and which is based on the evolution
of the continuous spectrum of the solution.
The method is a generalization of the technique developed by
Greengard and Strain for evaluating layer potentials in bounded
domains.
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