Isogeometric analysis and domain decomposition methods

By Christian Hesch, Peter Betsch. 2012

101 citations recorded by the source corpus.

In the present work we use the mortar finite element method for the coupling of nonconforming discretized sub-domains in the framework of nonlinear elasticity. The mortar method has been shown to preserve optimal convergence rates (see Laursen (2002) [25] for details) and is variationally consistent. We show that the method can be applied to isogeometric analysis with little effort, once the framework of NURBS based shape functions has been implemented. Furthermore, a specific coordinate augmentation technique allows the design of an energy–momentum scheme for the constrained mechanical system under consideration. The excellent performance of the redesigned mortar method as well as the energy–momentum scheme is illustrated in representative numerical examples.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/907f534363ce7233e5ed0410ddc2b79d39c72368

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries (2017, methodology): “These include the discontinuous Galerkin method [20, 27], the use of Nitsche’s technique [1, 23], the mortar approach [3, 9, 12] and domain decomposition methods [13, 18].”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “A mortar method was firstly introduced in [12] in the analysis of 3D elasticity problems and in [13] in the context of contact problems.”