Weak Cn coupling for multipatch isogeometric analysis in solid mechanics

• Published in: International journal for numerical methods in engineering Vol. 118; no. 11; pp. 678 - 699
• Main Authors: Dittmann, M., Schuß, S., Wohlmuth, B., Hesch, C.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 15-06-2019
• Subjects: Basis functions; basis modification approach; Continuity; Coupling; domain decomposition; Domain decomposition methods; extended mortar method; higher‐order; IGA; Mortars (material); Partial differential equations; Saddle points; Solid mechanics
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6032

Summary
The objective of this contribution is to design a novel methodology to enforce interface conditions preserving higher‐order continuity across the interface. In recent years, isogeometric methods using NURBS as basis functions have gained increasing attention, especially in the context of higher‐order partial differential equations. They require, in general, higher continuity across interfaces, and thus, new methodologies for domain decomposition constraints capable to deal with those requirements have to be developed. In this contribution, we introduce, in a first step, the coupling constraints using a Euclidean norm on the interface and construct new basis functions. A reformulation as saddle point system allows for a comparison with classical mortar approaches and leads finally to an extended mortar method to enforce Cn continuity.