wikipedia isogeometric analysis
J. Austrin Cottrell, Thomas J. R. Hughes, Yuri Bazilevs, Isogeometric analysis: toward integration of CAD and FEA, 2009
Jarle Sogn, Stefan Takacs, Robust multigrid solvers for the biharmonic problem in isogeometric analysis, arxiv/1802.00220
In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the 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 H2-conforming discretizations. We propose two multigrid methods for such a discretization, one based on Gauss Seidel smoothing and one based on mass smoothing. We 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 proposed multigrid approaches, particularly of a hybrid approach combining both smoothers.
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