November 11, 2005: Leslie Greengard, CIMS
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. I will discuss an optimal
time algorithm which is based on a novel spectral representation of the heat
kernel.
