Simple multidimensional integration of discontinuous functions with application to level set methods

Authors

  • B. Müller,

    Corresponding author
    1. Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany
    • Department of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt, Germany
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  • F. Kummer,

    1. Department of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt, Germany
    2. Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany
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  • M. Oberlack,

    1. Department of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt, Germany
    2. Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany
    3. Center of Smart Interfaces, Technische Universität Darmstadt, Darmstadt, Germany
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  • Y. Wang

    1. Department of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt, Germany
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Björn Müller, Department of Fluid Dynamics, Technische Universität Darmstadt, 64287 Darmstadt, Germany.

E-mail: mueller@fdy.tu-darmstadt.de

SUMMARY

We present a simple, tree-based approach for the numerical integration over volumes and surfaces defined by the zero iso-contour of a level set function. The work is motivated by a variant of the discontinuous Galerkin method that is characterized by discontinuous enrichments of the polynomial basis. Although numerical results suggest that the presently achieved accuracy is comparable with methods based on discretized delta functions and on the geometric reconstruction of the interface, the presented approach is conceptually simpler and applicable to almost arbitrary grid types, which we demonstrate by means of numerical experiments on triangular, quadrilateral, tetrahedral and hexahedral meshes. Copyright © 2012 John Wiley & Sons, Ltd.

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