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IBHM: index-based data structures for 2D and 3D hybrid meshes

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Abstract

We propose new topological data structures for the representation of 2D and 3D hybrid meshes, i.e., meshes composed of elements of different types. Hybrid meshes are playing an increasingly important role in all fields of modeling, because elements of different types are frequently considered either because such meshes are easier to construct or because they produce better numerical results. The proposed data structures are designed to achieve a balance between their memory requirements and the time complexity necessary to answer topological queries while accepting cells (elements) of different types. Additionally these data structures are easy to implement and to operate, because they are based on integer arrays and on basic arithmetic rules. A comparison with other existing data structures regarding their memory requirements and of the time complexities for the algorithms to answer general topological queries is also presented. The comparison shows that the overhead required to accept arbitrary cell types is small.

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Notes

  1. In this context, Hybrid refers to a finite element model where additional fields are discretized on the interfaces of the elements.

  2. A map container is a type of fast key lookup data structure that offers a flexible means of indexing into its individual elements. It stores key-value pairs and there cannot be duplicate keys. Maps are useful in situations where a key can be viewed as a unique identifier for the object.

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Acknowledgments

Part of the work described in this paper was developed during a sabbatical period of the second author at Instituto Superior Técnico, during the first semester of 2012, which was possible thanks to the support by PUC-Rio (Pontifícia Universidade Católica do Rio de Janeiro), CNPq (Brazilian National Council for Scientific and Technological Development), and the European Union through project NUMSIM—“Numerical simulation in technical sciences” of the Marie Curie Actions (FP7-PEOPLE-2009-IRSES), Project No. 246977. Hélio Lopes would like to thank CNPq and FINEP (Brazilian Funding Authority for Studies and Projects) for supporting his research. Marcos Lage would like to thank FAPERJ (Rio de Janeiro Research Funding Agency) for supporting his research.

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Authors and Affiliations

  1. Universidade Federal Fluminense, Niterói, Brazil

    Marcos Lage

  2. Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil

    Luiz Fernando Martha & Hélio Lopes

  3. Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    J. P. Moitinho de Almeida

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  1. Marcos Lage
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  2. Luiz Fernando Martha
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  3. J. P. Moitinho de Almeida
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  4. Hélio Lopes
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Correspondence to Luiz Fernando Martha.

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Lage, M., Martha, L.F., Moitinho de Almeida, J.P. et al. IBHM: index-based data structures for 2D and 3D hybrid meshes. Engineering with Computers 33, 727–744 (2017). https://doi.org/10.1007/s00366-015-0395-0

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