Towards efficient geometric multigrid for isogeometric analysis

Dr. Clemens Hofreither

June 24, 2014, 3:30 p.m. S2 059

We consider geometric multigrid methods for the solution of the large,
sparse linear
systems arising in isogeometric analysis of elliptic partial
differential equations.
Previous studies have shown that geometric multigrid is independent of
the mesh
size in this setting, but the iteration numbers are highly dependent on
the space
dimension as well as the spline degree if standard smoothers are used.
We investigate
more sophisticated smoothers with the goal to obtain, as far as
possible, iteration
numbers which are robust in all mentioned parameters. It turns out that
smoothers which make use of the mass matrix seem to be good candidates
towards this goal. This is confirmed by some numerical experiments.