Robustness of a multigrid solver for time-harmonic electromagnetic
problems
Tom Jonsthovel
Site of the project:
Shell
Hoekstede Building
Visseringlaan 26
2280AB Rijswijk
start of the project: September 2005
In December 2005 the
Interim
Thesis has been appeared
and a
presentation has been given.
The Master project has been finished in June 2006
by the completion of the
Masters Thesis and a final
presentation has been given.
For working address etc. we refer to our
alumnipage.
Summary of the master project:
The performance of a multigrid solver for time-harmonic
electromagnetic
problems occurring in geophysical exploration is investigated. The
frequencies considered are sufficiently small for the light-speed
waves to be
negligible, so that a diffusive problem remains. The discretization of
the
governing equations is based on the Finite-Integration-Technique,
which can
be viewed as a finite volume staggered grid discretization.
The accuracy of the discretization and the performance of the
iterative
multigrid solution method for solving the discrete equations degrade
when the
grid is stretched. Whereas the multigrid solver provides excellent
convergence rates with constant grid spacings, it performs far less
satisfactory when substantial grid stretching is applied.
The aim of this MSc project is to investigate whether known
techniques to
improve multigrid for a stretched grid discretization work well for
the
time-harmonic electromagnetic equations under consideration. We will
compare
line-wise smoothing methods in a standard grid coarsening sequence
with a
point-wise multigrid smoother in a semi-coarsened grid coarsening. The
staggered grid discretization poses here some initial difficulties.
The comparision between the two techniques will be done both from a
practical,
numerical point-of-view as from an analytical Fourier-analysis based
view
point.
Contact information:
Kees
Vuik
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