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A grid generator based on 4‐triangles conforming mesh‐refinement algorithms
Author(s) -
Rivara MariaCecilia
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620240710
Subject(s) - algorithm , grid , triangulation , polygon mesh , generator (circuit theory) , computer science , set (abstract data type) , mesh generation , subdivision , delaunay triangulation , geometry , mathematics , finite element method , computer graphics (images) , history , power (physics) , physics , archaeology , quantum mechanics , programming language , thermodynamics
Abstract A procedure to generate 2D meshes of triangles in a quite general fashion allowing for local and selective mesh‐refinement is presented and discussed. The grid generator is based on the iterative application of 4‐triangles conforming mesh‐refinement algorithms for triangulations, which are also introduced in this paper. These algorithms are modified versions of those proposed in Int. j. numer. methods eng. , 20 , 745–756 (1984), and they can be used for global refinement of a grid, as well as for local refinement. The grid generator works in the following way: given any initial coarse triangulation which properly defines the geometry of the problem, a set of user‐defined refinement subregions R i , i = 1,2,…, N , and an associated set of tolerance parameters h i , an irregular and conforming final triangulation is automatically constructed in such a way that the diameter of all the triangles contained in R i is smaller than h i , i = 1,2,…, N . Moreover, all angles in the final triangulation are greater than or equal to half the smallest angle in the initial, coarse one. The refinement is propagated only to assure the conformity and smoothness of the grid, and consequently, the number of involved nodes will be minimized. The refinement of the final mesh will be determined by the subregions R i and the parameters N i and will be essentially independent of the initial coarse grid. The 4‐triangles conforming mesh‐refinement algorithms are presented and their properties discussed. The implementation of these techniques is discussed and examples of the application of the grid generator are given.