Multigrid methods for isogeometric analysis with THB-splines

In several numerical experiments, we study two-dimensional Poisson problems with singularities and employ a posteriori error estimators for the adaptive refinement of the hierarchical spline spaces. Using standard multigrid smoothers, we observe that using THB-spline bases consistently confers a dramatic advantage in terms of iteration numbers over the use of HB-spline bases, in particular for higher spline degrees. When used as a preconditioner for Conjugate Gradient iteration, the proposed multigrid method exhibits practical iteration numbers for two-dimensional problems up to the tested case of fourth-degree splines.