A robust Nitsche’s formulation for interface problems

By Chandrasekhar Annavarapu, M. Hautefeuille, John Dolbow. 2012

227 citations recorded by the source corpus.

Abstract In this work, we propose a novel weighting for the interfacial consistency terms arising in a Nitsche variational form. We demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method. Consequently, we propose a weighting that results in an estimate for the stabilization parameter such that the method remains well behaved in varied settings; ranging from the configuration of embedded interfaces resulting in arbitrarily small elements to such cases where a large contrast in material properties exists. An important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of (a) elements with arbitrarily small volume fractions, (b) large material heterogeneities and (c) both large heterogeneities as well as arbitrarily small elements. We then highlight the accuracy and efficiency of the proposed formulation through numerical examples, focusing particular attention on interfacial quantities of interest.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ba2d96eb1b20075bbba62c81caed3b4ed0d4620b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Dominik Schillinger
2. Martin Ruess
3. Yujie Guo
4. Erik Burman
5. Thomas J. R. Hughes
6. Mats G. Larson
7. I. Harari
8. Peter Hansbo

In Electrical and Electronic Engineering

1. Dominik Schillinger
2. Martin Ruess
3. Erik Burman
4. Peter Hansbo
5. Mats G. Larson
6. Yujie Guo
7. André Massing
8. Susanne Claus

In Mechanics of Materials

1. Dominik Schillinger
2. Martin Ruess
3. Erik Burman
4. Yujie Guo
5. Ashesh Sharma
6. Mats G. Larson
7. I. Harari
8. Kurt Maute

Citations in the corpus

• The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, background): “We note that a different weighting of the interface terms can improve the stability in the presence of arbitrarily small elements and largely differing material parameters [5].”
• A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, background): “[42,46,44], designed for superior performance in interface problems.”
• Stress-based topology optimization using spatial gradient stabilized XFEM (2017, methodology): “Following the work of Annavarapu et al. (2012) we define these constants as”
• CutFEM: Discretizing geometry and partial differential equations (2015, background): “Consider the penalty parameter for the choice (6) proposed in [21].”
• The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “For interface problems, an additional weighting of consistency terms at the interface can improve the accuracy with respect to Nitsche’s classical formulation [1, 2, 38].”