Guest Speaker - mention unusual day and time


                  Numerical Analysis Seminar
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CNLS Conference Room, Tuesday  July 18, 9.00 am - 10.00 am
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        Multigrid for H(curl)-Elliptic Boundary Value Problems

                          R. Hiptmair
                  Sonderforschungsbereich 382
                    Universitaet Tuebingen
                             Germany

                    e-mail:ralf@hiptmair.de

           URL:http://na.uni-tuebingen.de/~hiptmair


The focus of this talk is on boundary value problems whose variational
statement involves a (weighted) H(curl)-inner product. Most
prominently, such problems occur as part of magnetoquasistatic models
for electromagnetic phenomena.

First, I am going to deal with discretization from the perspective of
discrete differential forms, which covers many approaches ranging from
finite elements to finite differences on staggered grids. It turns out
that the particular properties of discrete differential forms
are fundamental for the construction of the multigrid scheme.

Standard multigrid fails when applied to the discretized problem. The reason
is revealed by local mode analysis for a finite difference scheme: The culprit
is the kernel of the curl-operator, on which conventional local smoothers
are inefficient. Local mode analysis also suggests a remedy in the form of
an enhanced local relaxation.

The new relaxation scheme can be translated into a finite element setting
and viewed as additional relaxation in the space of discrete potentials.
This paves the way for a general theory in the framework of subspace
correction.

Finally, I am going to present the results of several numerical experiments
that confirm that "textbook multigrid efficiency" can be achieved both for
model problems and practical settings.

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Dr. Hiptmair will be here on July 17 and July 18 (Monday and Tuesday).
If you want to talk with him please let me know.



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For schedule and abstracts of future talks
look at
http://cnls.lanl.gov/~shashkov/NUMSEM/numsem.html

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If you want to make presentation, please contact:
Dr. Mikhail Shashkov
MS-B284, Group T-7, Theoretical Division,
Los Alamos National Laboratory,
Los Alamos, New Mexico, USA, 87545

phone:(505)-667-4400
fax:  (505)-665-5757

e-mail:misha@t7.lanl.gov

webpage: http://cnls.lanl.gov/~shashkov
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