Multigrid Methods for Isogeometric Analysis with THB-splines

Dr. Clemens Hofreither

May 12, 2015, 3:30 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