Condition number bounds for IETI-DP methods that are explicit in h and p

TL;DR

This paper analyzes the convergence of IETI-DP methods for multi-patch isogeometric analysis, providing condition number bounds that depend explicitly on mesh size h and spline degree p, with implications for large-scale Poisson problems.

Contribution

It offers a comprehensive convergence analysis of IETI-DP methods with various primal degrees of freedom, deriving explicit condition number bounds in terms of h and p.

Findings

Condition number bounds are quasi-linear in spline degree p.

Convergence behavior depends on the choice of primal degrees of freedom.

The analysis applies to large-scale 2D Poisson problems.

Abstract

We study the convergence behavior of Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for solving large-scale algebraic systems arising from multi-patch Isogeometric Analysis. We focus on the Poisson problem on two dimensional computational domains. We provide a convergence analysis that covers several choices of the primal degrees of freedom: the vertex values, the edge averages, and the combination of both. We derive condition number bounds that show the expected behavior in the grid size h and that are quasi-linear in the spline degree p.