# IGA: Multigrid method for the biharmonic problem

## MSc Jarle Sogn

Jan. 23, 2018, 3:30 p.m. S2 416-1

In this talk, I present multigrid solvers for the biharmonic problem in the
framework of isogeometric analysis (IgA). In IgA, one typically sets up B-splines on a
unit square or cube and transforms them to the domain of interest by a global smooth
geometry function. With this approach, it is feasible to set up $H^2$-conforming discretizations.
We will propose two multigrid methods for such a discretization, one based on Gauss
Seidel smoothing and one based on mass smoothing. We will prove that both are robust
in the grid size, the latter is also robust in the spline degree. Numerical experiments
illustrate the convergence theory and indicate the efficiency of the Gauss Seidel based
multigrid approach, particularly in cases with non-trivial geometries.