# Towards efficient geometric multigrid for isogeometric analysis

## Dr. Clemens Hofreither

**June 24, 2014, 1:30 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.