hp-explicit convergence analysis for IETI-DP solvers for non-conforming multipatch decompositions
DI Rainer SchneckenleitnerJan. 19, 2021, 2:30 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 computational 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 nonconforming patch decompositions. We present a convergence theory for novel IETI-DP algorithms that can deal with the non-conformity of the decomposition. 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 slightly 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.