# Dual-Primal Isogeometric Tearing and Interconnecting solvers

## MSc Christoph Hofer

March 1, 2016, 3:30 p.m. S2 Z74

In this talk, we construct and investigate fast solvers for large-scale linear systems of algebraic equations arising from isogeometric analysis (IgA) of diffusion problems with heterogeneous diffusion coefficient on multipatch domains. In particular, we investigate the adaption of the Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) method to IgA, called Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We consider the cases where we have matching and non-matching meshes on the interfaces. In the latter case we use a discontinuous Galerkin (dG) method to couple the different patches. This requires a special extension of the IETI-DP method to the dG-IgA formulation. We use ideas from the finite element case in order to formulate the corresponding IETI-DP method, called dG-IETI-DP. We present numerical results for complicated two and three dimensional domains. We observe a quasi-optimal behavior of the condition number $\kappa$ of the preconditioned system with respect to the mesh-size $h$ and the patch-size $H$.

Abstract