Multigrid analysis for isogeometric methods

MSc MTech Krishan Gahalaut

Jan. 17, 2012, 2:30 p.m. S2 046

In this talk the (geometric) multigrid methods for the isogeometric discretization of Poisson equation will be presented. The bound for condition number of resulting stiffness matrix will be discussed. The smoothing property of the relaxation methods, and the approximation property of the intergrid transfer operators are analyzed for two-grid cycle. It will be shown that the convergence of the two-grid solver is independent of the discretization parameter h, and that the overall solver is of optimal complexity. For two-grid and multigrid cycles supporting numerical results will be provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. The numerical results are complete up to polynomial degree $p = 4$, and from minimum smoothness $C^0$ to maximum smoothness $C^{(p-1)}$: