IGA: Multigrid method for the biharmonic problem
MSc Jarle SognJan. 23, 2018, 2:30 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.