Multigrid analysis for isogeometric methods

MSc MTech Krishan Gahalaut

Jan. 17, 2012, 3:30 p.m. S2 046

In this talk the (geometric) multigrid methods for the isogeometric discreti-
zation of Poisson equation will be presented. The bound for condition number
of resulting sti ness 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 conver-
gence 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 proper-
ty, 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):