Refinement based on longest-edge and self-similar four-triangle partitions

Mathematics and Computers in Simulation

Volumn 75, Issue 5-6, 2007, Pages 251-262

  Padrón, Miguel A ^a   Suárez, José P ^a   Plaza, Ángel ^a  

^a UNIVERSITY OF LAS PALMAS DE GRAN CANARIA   (Spain)

Author keywords

Longest edge based algorithms; Mesh quality; Uniform refinement

Indexed keywords

ALGORITHMS; ANGLE MEASUREMENT; FINITE ELEMENT METHOD; NUMERICAL METHODS;

MESH QUALITY; TRIANGLE PARTITIONS; UNIFORM REFINEMENT;

MESH GENERATION;

EID: 34547952406     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2006.12.010     Document Type: Article

References (19)

1. R.E. Bank, A.H. Sherman, A. Weiser, Refinement Algorithm and Data Structures for Regular Local Mesh Refinement, Scientific Computing, Amsterdam, 1983, pp. 3-17.
2. Becker E.B., Carey G.F., and Oden J.T. Finite Elements (1981), Prentice-Hall, New York
3. Carey G.F. A mesh refinement scheme for finite elements computations. J. Comput. Meth. Appl. Mech. Eng. 7 1 (1976) 93-105
4. Carey G.F. Computational Grids: Generation, Refinement and Solution Strategies (1997), Taylor and Francis, London
5. Ferragut L., Montenegro R., and Plaza A. Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems. Comm. Num. Meth. Eng. 10 5 (1994) 403-412
6. Graham R.L., Knuth D.E., and Patashnik O. Concrete Mathematics (1989), Addison Wesley
7. Kim H., Hong S., Choi K., Jung H., and Hahn S. A three dimensional adaptive finite element method for magnetostatic problems. IEEE Trans. Magn. 27 (1994) 4081-4084
8. Muthukrishnan M.C., Shiakolas P.S., Nambiar R.V., and Lawrence K.L. Simple algorithm for adaptive refinement of three-dimensional finite element tetrahedral meshes. AIAA J. 33 5 (1995) 928-932
9. Nambiar R.V., Valera R.S., Lawrence K.L., Morgan R.B., and Amil D. An algorithm for adaptive refinement of triangular meshes. Int. J. Num. Meth. Eng. 36 (1993) 499-4509
10. Plaza A., and Carey G.F. Refinement of simplicial grids based on the skeleton. Appl. Num. Math. 32 2 (2000) 195-218
11. Plaza A., Padrón M.A., and Carey G.F. A 3D refinement/derefinement algorithm for solving evolution problems. Appl. Num. Math. 32 4 (2000) 401-418
12. Plaza A., Padrón M.A., Suárez J.P., and Falcón S. The 8-tetrahedra longest-edge partition of right-type tetrahedra. Finit. Elem. Anal. Design. 41 3 (2004) 253-265
13. Plaza A., Suárez J.P., Padrón M.A., Falcón S., and Amieiro D. Mesh quality improvement and other properties in the four-triangles longest-edge partition. Comp. Aid. Geom. Design. 21 4 (2004) 353-369
14. Rivara M.C. Algorithms for refinement triangular grids suitable for adaptive and multigrid techniques. Int. J. Num. Meth. Eng. 20 (1984) 745-756
15. Rivara M.C., and Levin C. A 3-d refinement algorithm suitable for adaptive and multi-grid techniques. J. Comp. Appl. Math. 8 (1992) 281-290
16. Rivara M.C., and Iribarren G. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Math. Comp. 65 216 (1996) 1485-1502
17. Rosenberg I., and Stenger F. A lower bound on the angles of triangles constructed by bisecting the longest side. Math. Comp. 29 (1975) 390-395
18. Stamm C., Eidenbenz S., and Pajarola R. A modified longest side bisection triangulation. Proceedings of the 10th Canadian Conference on Computational Geometry'98 (1998) 1-6
19. Suárez J.P., Plaza A., and Carey G.F. The propagation problem in longest-edge refinement. Finit. Elem. Anal. Design. 42 2 (2005) 130-151