[BANANA] LAPACK seminar next week

[Ming Gu]

               Math 290, Section 16, CS 298, Section 6,
                          Spring 2008
         (Matrix Computations and Scientific Computing)


We meet WEDNESDAYS 11:10 - noon in Room 380 Soda Hall, Berkeley campus.
The coordinators are Profs. J. Demmel (demmel at cs.berkeley.edu), 
M. Gu (mgu at math.berkeley.edu), and B. N. Parlett (parlett at math.berkeley.edu). 
The program will be a mixture of research talks and tutorials.
The tutorials will provide a partial sequel to Math 221.

Date: Mar. 12
Speaker: John Strain
Title: Locally-corrected spectral boundary integral methods for elliptic systems

Abstract: Classical potential theory converts linear constant-coefficient elliptic
problems in complex domains into integral equations on interfaces, and
generates robust, efficient numerical methods.  The conversion is
usually carried out for a particular situation such as the Poisson
equation in dimension 2, and the efficiency of the resulting methods
then depends on detailed analysis of the appropriate special functions.

We present a general conversion scheme which leads naturally to a fast
general algorithm: arbitrary elliptic problems in arbitrary dimension
are converted to first-order systems, a periodic fundamental solution is
mollified for convergence, and the mollification is locally corrected
via Ewald summation. Local linear algebra and the elementary theory of
distributions yield a simple boundary integral equation.  With the aid
of a new nonequidistant fast Fourier transform for piecewise polynomial
functions, the resulting numerical methods provide highly accurate
solutions to general elliptic systems in complex domains.