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The finite cell method for polygonal meshes: poly-FCM

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Abstract

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.

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Acknowledgments

The authors would like to thank the German Research Foundation (DFG) for its financial support under grant DU 1613/1-1. Furthermore, the authors acknowledge Prof. N. Sukumar (UC Davis) and Prof. M. Floater (University of Oslo) for making their source codes for the computation of generalized barycentric coordinates freely available and for their generous support. Finally, Prof. G. H. Paulino (Georgia Tech) and co-workers are gratefully mentioned for providing the mesh generation software PolyMesher.

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  1. Faculty of Mechanical Engineering, Computational Mechanics, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Sascha Duczek & Ulrich Gabbert

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  1. Sascha Duczek
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  2. Ulrich Gabbert
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Correspondence to Sascha Duczek.

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Duczek, S., Gabbert, U. The finite cell method for polygonal meshes: poly-FCM. Comput Mech 58, 587–618 (2016). https://doi.org/10.1007/s00466-016-1307-x

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  • DOI: https://doi.org/10.1007/s00466-016-1307-x

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