[ugrads] [Mathclub-members] Applied Math Welcome Luncheon and Colloquium

Michael Pelsmajer pelsmajer at iit.edu
Sun Aug 17 19:38:47 CDT 2008

Greetings everyone, and welcome back for the 2008-2009 school year!

Please join us for the Applied Math Welcome Luncheon, next Wednesday,
August 20 (that's one day before classes start) at 12 noon in E1 102.
We will gather together to see old friends, eat food, and kick off the
school year on the right foot. If you are a new or returning faculty
member, student, or math enthusiast, you are welcome to come!

Also, we will have the first colloquium of the new school year on
Tuesday, August 19 at 3:30 pm in E1 106.  The information is below,
and as always, refreshments will be served.
(For more about seminars, see <http://www.iit.edu/csl/am/colloquia>.)

Lorena Barba
Department of Mathematics
University of Bristol, UK

"Global Field Interpolation for Particle Methods"

When a particle representation is used as a numerical discretization
of a continuum problem, one often represents the field variable as a
linear combination of moving basis functions (the particles). In this
Lagrangian approach, the particles can become severely strained, which
for continuum representations results in a deterioration of spatial
accuracy. Thus, most workers face the need to remediate sets of
particles so that the basis functions do not cease to overlap in

While various investigators have developed means for replacing a set
of particles with another that is more uniform, this subject is rarely
addressed in the literature. The more general problem is that of
finding a set of basis functions such that the field of interest is
well represented by their superposition. We refer to this procedure as
field interpolation.  One approach is to formulate this as a radial
basis function interpolation problem, which with global methods, will
result in a dense and ill-conditioned system that needs to be solved.

In particle simulation of fluid flow, a recent advance incorporates
deforming basis functions to provide fourth-order accuracy in space.
The requirement of an accurate field interpolation scheme becomes more
stringent in this context, to maintain the overall high order. We have
developed methods for performing field interpolation in this
application, using custom preconditioning with iterative methods on
the one hand, and deblurring techniques from image processing on the

About the Speaker

Lorena Barba obtained her PhD in Aeronautics from California Institute
of Technology in 2004.  She then joined the Department of Mathematics
in the University of Bristol, UK.

Dr Barba is a computational scientist and a fluid dynamicist.  Her
research covers particle methods used for fluid simulation, the
development of fast and efficient algorithms, the use of novel
computer architectures, as well as fundamental and applied aspects of
fluid dynamics.

Michael J. Pelsmajer             http://www.iit.edu/~pelsmaje
Applied Mathematics, E1 Room 206       pelsmajer at iit.edu
Illinois Institute of Technology         (312)567-5344
Chicago, IL 60616
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