IETI-DP for conforming multi-patch Isogeometric Analysis in three dimensions

TL;DR

This paper investigates the extension of IETI-DP solvers for multi-patch geometries from 2D to 3D in Isogeometric Analysis, providing theoretical insights and numerical evidence for their convergence behavior.

Contribution

It extends the convergence analysis of IETI-DP solvers to three-dimensional multi-patch geometries in Isogeometric Analysis.

Findings

Numerical experiments suggest similar convergence properties in 3D as in 2D.

Revisits and confirms previous 2D convergence results.

Provides initial evidence for the applicability of IETI-DP in 3D geometries.

Abstract

We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a convergence analysis for those solvers that is explicit in both the grid size and the spline degree for conforming discretizations of two dimensional computational domains. In the present paper, we shortly revisit these results and provide numerical experiments that indicate that similar results may hold for three dimensional domains.