A new data structure for handling efficiently polyhedral complexes

Alexandre Marin and Wassim Ahmed-Belkacem and Alexandra Bac and Laurent Astart. ( 2021 )
in: 2021 RING Meeting, ASGA

Abstract

This work is part of a PhD thesis about polyhedral mesh generation for simulation of geological phenomena. Two recent numerical methods enable us to use meshes containing polyhedra with any number of faces : on the one hand, we have non-linear finite volumes, for which orthogonality condition is no longer required, on the other hand, we can use the virtual elements method which generalizes FEMs and which does not have to consider simplicial meshes. Consequently, we need a reliable structure which is able to represent, to build, to travel and to modify polyhedral complexes having lots of generic polyhedra. Moreover, we want a compact and versatile structure to handle topology of potentially huge meshes, which help us write algorithms easily. First, after presenting how that structure caters to our needs, we will unveil its layout and some implementation details. Then, we will deal with space and time complexity. We will give several advantages and drawbacks of the structure, which will be highlighted by performance tests. We will compare our structure and other data structures for 3D meshes. Finally, we will show examples of meshes proving that the data structure is operational.

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BibTeX Reference

@INPROCEEDINGS{MARIN_RM2021,
    author = { Marin, Alexandre and Ahmed-Belkacem, Wassim and Bac, Alexandra and Astart, Laurent },
     title = { A new data structure for handling efficiently polyhedral complexes },
 booktitle = { 2021 RING Meeting },
      year = { 2021 },
 publisher = { ASGA },
  abstract = { This work is part of a PhD thesis about polyhedral mesh generation for simulation of geological phenomena. Two recent numerical methods enable us to use meshes containing polyhedra with any number of faces : on the one hand, we have non-linear finite volumes, for which orthogonality condition is no longer required, on the other hand, we can use the virtual elements method which generalizes FEMs and which does not have to consider simplicial meshes. Consequently, we need a reliable structure which is able to represent, to build, to travel and to modify polyhedral complexes having lots of generic polyhedra. Moreover, we want a compact and versatile structure to handle topology of potentially huge meshes, which help us write algorithms easily. First, after presenting how that structure caters to our needs, we will unveil its layout and some implementation details. Then, we will deal with space and time complexity. We will give several advantages and drawbacks of the structure, which will be highlighted by performance tests. We will compare our structure and other data structures for 3D meshes. Finally, we will show examples of meshes proving that the data structure is operational. }
}