On a bisection algorithm that produces conforming locally refined simplicial meshes

  • Authors:

  • Antti Hannukainen;Sergey Korotov;Michal Křížek

  • Affiliations:

  • Institute of Mathematics, Helsinki University of Technology, Espoo, Finland;Department of Mathematics, Tampere University of Technology, Tampere, Finland;Institute of Mathematics, Academy of Sciences, Prague 1, Czech Republic

  • Venue:
  • LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
  • Year:
  • 2009

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Abstract

First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the criterion function Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge Repeating this process, we construct a sequence of conforming nested simplicial meshes whose shape is determined by the mesh density function We prove that the corresponding mesh size of the sequence tends to zero for d=2, 3 as the bisection algorithm proceeds It is also demonstrated numerically that the algorithm seems to produce only a finite number of similarity-distinct triangles.