Towards a IETI-DP solver on non-matching multi-patch domains

TL;DR

This paper extends IETI-DP solvers for multi-patch domains in Isogeometric Analysis to handle T-junctions, increasing geometric flexibility by allowing patches to meet at non-edge interfaces using vertex-based primal degrees of freedom.

Contribution

It generalizes existing IETI-DP solvers to support non-matching interfaces with T-junctions, introducing the concept of 'fat vertices' for primal degrees of freedom.

Findings

Enables IETI-DP solvers to handle T-junctions in multi-patch domains.

Maintains solver robustness despite relaxed interface conditions.

Provides a flexible framework for complex geometric models.

Abstract

Recently, the authors have proposed and analyzed isogeometric tearing and interconnecting (IETI-DP) solvers for multi-patch discretizations in Isogeometric Analysis. Conforming and discontinuous Galerkin settings have been considered. In both cases, we have assumed that the interfaces between the patches consist of whole edges. In this paper, we present a generalization that allows us to drop this requirement. This means that the patches can meet in T-junctions, which increases the flexibility of the geometric model significantly. We use vertex-based primal degrees of freedom. For the T-junctions, we propose to follow the idea of "fat vertices".