SPECIAL PHYSICAL MATHEMATICS SEMINAR

TOPIC:		SECOND KIND INTEGRAL EQUATIONS FOR 
		SCATTERING BY OPEN SURFACES

SPEAKER:	SHIDONG JIANG
		Department of Computer Science
		Yale University

ABSTRACT:

Integral equations have been one of principal tools for the numerical
solution of scattering problems for more than 30 years, both in the
Helmholtz and Maxwell environments.  Historically, most of the equations
used have been of the first kind, since numerical instabilities associated
with such equations have not been critically important for the relatively
small-scale problems that could be handled at the time.

The combination of improved hardware with the recent progress in the
design of "fast" algorithms has changed the situation dramatically.  
Condition numbers of systems of linear algebraic equations resulting from
the discretization of integral equations of potential theory have become
critical, and the simplest way to limit such condition numbers is by
starting with second kind integral equations.  Hence, increasing interest
in reducing scattering problems to systems of second kind integral
equations on the boundaries of the scatterers.

During the last several years, satisfactory integral equation formulations
have been constructed in both acoustic (Helmholtz equation) and
electromagnetic (Maxwell's equations) environments, whenever all of the
scattering surfaces are "closed" (i.e. scatterers have well-defined
interiors, and have no infinitely thin parts).

In this talk, I will describe a stable second kind integral equation
formulation for the Dirichlet problem for the Laplace and Helmholtz
equations in two dimensions, with the boundary conditions specified on a
collection of "open" curves; the numerical performance of the scheme
will be illustrated with several numerical examples.

This is joint work with Prof. Vladimir Rokhlin at Yale University.


DATE:		FRIDAY, MARCH 12, 2004

TIME:		2:30 PM

LOCATION:	Building 2, Room 338

Refreshments at 3:30 PM in Room 2-349.


Massachusetts Institute of Technology, Department of Mathematics
Cambridge, MA  02139