Robust multigrid methods for biharmonic problems discretized with IGA

MSc Jarle Sogn

May 18, 2021, 3:30 p.m. ZOOM

In this talk we consider multigrid methods for biharmonic problems discretized with tensor-product B-splines.
We want a convergence result which is robust with respect to the grid size $h$ and spline degree $p$. For the Poisson problem this was achieved by \cite{HT}, using a subspace corrected mass smoother and it was analyzed using the ``Hackbusch'' framework. In \cite{ST}, this approach was, to a certain degree, carried over to a biharmonic problem.
There are some problems regarding this: First, the regularity requirement of the ``Hackbusch'' approach creates difficulties for biharmonic problems. Second, equidistant grids are required in the analysis of \cite{ST}. This last condition is rather restrictive and we are unable to relax it. For these reasons we consider the ``Bramble'' framework to show a robust convergence result. This framework does not require regularity and we are able relax the equidistant grids condition to quasi-uniform grids.