# 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.