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Multi-level hp-adaptivity for transient discretizations of complex domains

The Finite Cell Method combines the idea of fictitious domain approaches with the advantageous approximation qualities of high-order FEM yielding a highly accurate, yet
flexible discretization strategy. This approach has proven to work well in the context of various linear and non-linear applications. However, local geometry features such as re-entrant corners, material interfaces, or small inclusions demand for a local refinement of the discretization.

In the current work, this challenge is addressed using the multi-level hp-formulation of the Finite Element Method [1]. The essential idea of this discretization scheme is to
increase the approximation accuracy by superposing coarse elements with a finer overlay mesh. As the compatibility of the approximation can be easily ensured by constraining
the overlay solution via homogeneous Dirichlet boundary conditions, hp-FEM like meshes can be created without the difficulties associated with hanging nodes. This allows to
define an agile data structure in which a change of the discretization in a transient simulation comes naturally without posing additional challenges.

In this work, previous studies will be extended by analyzing the convergence properties of the proposed method for three-dimensional examples in the presence of singularities. Furthermore, it will be shown that the new discretization method can be used to capture e.g the temperature distribution around moving three-dimensional objects on a fixed background mesh.

References
[1] N. Zander, T. Bog, S. Kollmannsberger, D. Schillinger, and E. Rank, “Multi-Level hp-Adaptivity: High-Order Mesh Adaptivity without the Difficulties of Constraining Hanging Nodes,” Computational Mechanics, vol. submitted, 2014.

Author(s):

Nils Zander    
Chair for Computation in Engineering, Technische Universität München
Germany

Bog Tino    
Chair for Computation in Engineering, Technische Universität München
Germany

Stefan Kollmannsberger    
Chair for Computation in Engineering, Technische Universität München
Germany

Martin Ruess    
Aerospace Structures and Computational Mechanics, Delft University of Technology
Netherlands

Dominik Schillinger    
Department of Civil Engineering, University of Minnesota
United States

Ernst Rank    
Chair for Computation in Engineering, Technische Universität München
Germany