Multigrid methods for Isogeometric Analysis (IGA)

Dr. Clemens Hofreither

Nov. 17, 2015, 3:30 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 splines.
Joint work with Stefan Takacs.