Computational aspects of the refinement of 3D tetrahedral meshes

Article type: Research Article

Authors: Suárez, J.P.^{a; *} | Abad, P.^a | Plaza, A.^b | Padrón, M.A.^c

Affiliations: [a] Department of Cartography and Graphic Engineering, University of Las Palmas de Gran Canaria, Spain | [b] Department of Mathematics, University of Las Palmas de Gran Canaria, Spain | [c] Department of Civil Engineering, University of Las Palmas de Gran Canaria, Spain

Correspondence: [*] Corresponding author. Tel.: +1 34 928 457268; Fax: +1 34 928 451872; E-mail: jsuarez@dcegi.ulpgc.es.

Abstract: The refinement of tetrahedral meshes is a significant task in many numerical and discretizations methods. The computational aspects for implementing refinement of meshes with complex geometry need to be carefully considered in order to have real-time and optimal results. In this paper we study some computational aspects of a class of tetrahedral refinement algorithms. For local adaptive refinement we give numerical results of the computational propagation cost of a general class of longest edge based refinement and show the implications of the geometry in the global process. Moreover we study the conformity process based on the longest edge bisection and give an algorithm and data structure to efficiently handle tetrahedral refinement.

Keywords: Tetrahedral meshes, refinement, finite element, 65M50, 65N50, 65Y20

DOI: 10.3233/JCM-2005-5401

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 5, no. 4, pp. 215-224, 2005