# Multigrid Methods for Isogeometric Analysis with THB-splines

## Dr. Clemens Hofreither

**May 12, 2015, 1:30 p.m. S2 059**

We present a multigrid algorithm for the solution of the large, sparse linear systems arising in isogeometric analysis of elliptic partial differential equations when using hierarchical spline spaces as the discretization spaces.

We describe the construction of the geometric multigrid algorithm and of the sequence of nested hierarchical spaces which serve as the levels in the multigrid algorithm. We employ two different bases for the construction of the hierarchical spline spaces: hierarchical B-splines and truncated hierarchical B-splines. We mention how to compute the grid transfer matrices in the setting of hierarchical spline spaces. Finally, we give several numerical examples, where we put particular emphasis on a comparison between the performance of multigrid when applied in the HB-spline basis and the THB-spline basis. It is found that using THB-splines always leads to a reduction of iteration numbers compared to HB-splines, often significantly so.

Joint work with Bert Juettler, Gabor Kiss, Walter Zulehner