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, 4:15 p.m. ZOOM

In this presentation, we discuss a convergence theory for a Dual-Primal Isoge-
ometric Tearing and Interconnecting (IETI-DP) solver for isogeometric multi-
patch discretizations of the Poisson problem. We consider the case of patches
that are coupled with a discontinuous Galerkin (dG) formulation. dG ap-
proaches are very bene cial if the patch interfaces from two di erent geome-
try 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.