Convergence theory for IETI-DP solvers for dis- continuous Galerkin Isogeometric Analysis that is explicit in h and p

DI Rainer Schneckenleitner

Nov. 17, 2020, 3:15 p.m. ZOOM

In this presentation, we discuss a convergence theory for a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver for isogeometric multipatch discretizations of the Poisson problem. We consider the case of patches that are coupled with a discontinuous Galerkin (dG) formulation. dG approaches are very beneficial if the patch interfaces from two different geometry mappings are not identical or if the meshes on the interfaces do not agree.

The presented theory gives condition number bounds that are explicit in the grid sizes and in the spline degrees. We give an analysis that holds for various choices for the primal degrees of freedom: vertex values, edge averages, and a combination of both. If only the vertex values or both vertex values and edge averages are taken as primal degrees of freedom, the condition number bound is the same as for the conforming case. If only the edge averages are taken, both the convergence theory and the experiments show that the condition number of the preconditioned system grows with the ratio of the grid sizes on neighboring patches.