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

TL;DR

This paper develops a convergence theory for IETI-DP solvers applied to discontinuous Galerkin isogeometric discretizations of the Poisson problem, providing explicit condition number bounds in terms of grid size and spline degree.

Contribution

It introduces a convergence analysis for IETI-DP solvers with explicit bounds depending on h and p, considering various primal degrees of freedom choices.

Findings

Condition number bounds are explicit in h and p.

Choosing vertex values or both vertices and edges yields bounds similar to conforming cases.

Using only edge averages causes the condition number to grow with patch size ratio.

Abstract

In this paper, we develop a convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin. The presented theory provides condition number bounds that are explicit in the grid sizes h and in the spline degrees p. 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.