Frontiers in Mortar Methods for Isogeometric Analysis

TL;DR

This paper reviews recent advancements in mortar methods tailored for isogeometric analysis, focusing on coupling techniques for complex multi-patch geometries in high-order PDE computations.

Contribution

It provides an overview of current mortar technology developments specifically designed for isogeometric analysis in complex geometries.

Findings

Enhanced coupling techniques for multi-patch geometries.

Application of mortar methods to higher-order PDEs.

Progress in analysis-suitable spline-based models.

Abstract

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric analysis is directly based on the spline parametrization and nowadays used for the calculation of higher-order partial differential equations. The computational, or more general, the engineering analysis necessitates suitable coupling techniques between the different patches. Mortar methods have been successfully applied for coupling of patches and for contact mechanics in recent years to resolve the arising issues within the interface. We present here current achievements in the design of mortar technologies in isogeometric analysis within the Priority Program SPP 1748, Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis.