Speaker
Sven Gross, RWTH Aachen
Abstract
In this talk we consider iterative solution techniques for linear systems stemming from CutFEM discretizations of Poisson and Stokes interface problems.
For the solution of the discrete Poisson interface problem, an optimal preconditioner is proposed which is based on a subspace splitting motivated by the XFEM approach. As the splitting is uniformly stable w.r.t. mesh size and interface location, the preconditioner is uniformly spectrally equivalent to the stiffness matrix. Furthermore, we present a geometric multigrid method for the Poisson interface problem using a special interface smoother which performs reasonably well in numerical experiments.
For the generalized Stokes problem several iterative solution techniques are discussed. We introduce a Schur complement preconditioner of Cahouet-Chabard type. Numerical experiments show the performance of the preconditioner for different choices of numerical and material parameters.