The 4-triangles longest-side partition of triangles and linear refinement algorithms

Mathematics of Computation

Volumn 65, Issue 216, 1996, Pages 1485-1502

  Rivara, María Cecilia ^a   Iribarren, Gabriel ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030505602     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-96-00772-7     Document Type: Article

References (22)

1. I. Babuška, O.C. Zienkiewcz, J. Gago and E. R. de A. Oliveira (eds.), Accuracy estimates and adaptive refinements in finite clement computations, John Wiley & Sons, Chichester (1986). MR 87j:65004
2. S.W. Bova and G. F. Carey, Mesh generation/refinement using jractal concepts and iterated function systems. Internat. J. Numer. Meth. in Engrg., 33 (1992), 287-305. MR 92j:65137
3. P. Dierckx, S. Van Leemput and T. Vermeire, Algorithms for surface fitting using Powell-Sabin splines, IMA J. Numer. Anal., 12(1992), 271-299. MR 93b:65026
4. W. Hackbush, Multi-grid methods and applications, Springer-Verlag, Berlin (1985). MR 87e:65082
5. H. Kim, S. Hong, K. Choi, H. Jung and S. Hahn, A three dimensional adaptive finite element method for magnetostatic problems, IEEE Trans. Magnetics, 27(1991), 4081-4084.
6. L. Freitag, M. Jones and P. Plassmann, New techniques for parallel simulation of high-temperature superconductors, Argonne National Laboratory 1994 Preprint MCS-P44-0594.
7. S.N. Muthukrishnan, P.S. Shiakolas, R. V. Nambiar and K.L. Lawrence, A simple algorithm for the adaptive refinement of three dimensional finite element tetrahedral meshes, to appear AIAA Journal.
8. R.V. Nambiar, R.S. Valera, K.L. Lawrence, R. B. Morgan and D. Amil, An algorithm for adaptive refinement of triangular meshes, Internat. J. Numer. Meth. Engrg. 36 (1993), 499-509.
9. J. O'Rourke, Computational Geometry Column 23, Internat. J. Comput. Geom. Appl. 4(1994), 239-242. MR 95j:52030
10. J. Penman and M.D. Grieve, Self-adaptive mesh generation technique for the finite element method, IEE Proceedings, 134(1987), 634-650.
11. M.-C. Rivara, Mesh refinement processes based on the generalized bisection of simplices, SIAM J. Numer. Anal. 21(1984), 604-613. MR 85i:65159
12. _, Algorithms for refining triangular grids suitable for adaptive and multigrid techniques, Internat. J. Numer. Methods Engrg., 20(1984), 745-756. MR 85h:65258
13. _, Design and data structure for fully adaptive, multigrid finite-element software, ACM Trans. Math. Software, 10(1984), 242-264. MR 86f:65207
14. _, Adaptive finite element refinement and fully irregular and conforming triangulations, In Accuracy Estimates and Adaptive Refinements in Finite Element Computations, I. Babuška, O.C. Zienkiewicz, J. Gago and E.R. de A. Oliveira (eds.), John Wiley & Sons, Chichester (1986), pp. 359-370.
15. _, A grid generator based on 4-triangles conforming mesh refinement algorithms, Internat. J. Numer. Meth. Engrg., 24 (1987), 1343-1354.
16. _, Selective refinement/derefinement algorithms for sequences of nested triangulations, Internat. J. Numer. Meth. Engrg., 28(1989), 2889-2906. MR 90j:57018
17. _, A discussion on the triangulation refinement problem, Proceedings of the Fifth Canadian Conference on Computational Geometry, University of Waterloo (1993), pp. 42-47.
18. M.-C. Rivara and C. Levin, A 3D refinement algorithm for adaptive and multigrid techniques, Comm. Appl. Numer. Methods, 8 (1992), 281-290.
19. M.-C. Rivara and M. Venere, Cost analysis of the longest-side (triangle bisection) refinement algorithms for triangulations (1994), to appear Engineering with Computers.
20. I. Rosenberg and F. Stenger, A lower bound on the angles of triangles constructed by bisecting the longest side, Math. Comp. 29(1975), 390-395. MR 51:11264
21. M. Stynes, On faster convergence of the bisection method for all triangles, Math. of Comp. 36 (1980), 1195-1201. MR 81j:51023
22. R. Williams, Adaptive parallel meshes with complex geometry, In Numerical Grid Generation in Computational Fluid Dynamics and Related Fields (A.S. Arcilla, J. Hauser, P.R. Eiseman, J.F. Thompson, eds.), Elsevier Science Publishers B.V. (North-Holland) (1991). CMP 91:16