Multigrid methods for Isogeometric Analysis (IGA)
Dr. Clemens HofreitherNov. 17, 2015, 2:30 p.m. S2 059
In this talk, we will discuss how to set up multigrid methods for linear systems arising from the discretization of a partial differential equation with an isogeometric discretization. As a model problem, we consider a Poisson equation, which is discretized with splines of maximum smoothness. The main focus of this talk is set on the construction of smoothers such that the convergence properties of the multigrid solver do not deteriorate if the polynomial degree is increased. This goal is achieved by modifying mass-matrix based smoothers by appropriate boundary corrections. We will provide convergence analysis and numerical experiments for this approach based on new approximation error estimates and inverse estimates for plines.
Joint work with Stefan Takacs.