hp-explicit convergence analysis for IETI-DP solvers for non-conforming multipatch decompositions

DI Rainer Schneckenleitner

Jan. 19, 2021, 3:30 p.m. ZOOM

We analyze a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-
DP) solver to compute solutions to the discretized Poisson problem where the
patches are coupled with a discontinuous Galerkin approach. Multipatch com-
putational domains at rest are usually constructed such that the single patches
form a conforming decomposition of the global domain. Moving computational
domains that use the same patch representations for each state lead to non-
conforming patch decompositions. We present a convergence theory for novel
IETI-DP algorithms that can deal with the non-conformity of the decompo-
sition. Our analysis also covers the case with coefficient jumps between the
patches. The fastest IETI-DP solver for conforming patch decompositions uses
vertex values as primal variables that form the global coarse grid problem. For
non-conforming patch decompositions, the vertex values are not available. We
generalize this idea to obtain a IETI-DP solver that maintains the condition
number bound of the conforming case with vertex values leading to a slightely
larger coarse grid problem. Moreover, we establish a bound for another IETI-
DP algorithm with a smaller coarse grid problem at the cost of an exponential
dependence of the condition number on the polynomial degree of the used basis
functions.