Boundary conforming Delaunay mesh generation

Computational Mathematics and Mathematical Physics

Volumn 50, Issue 1, 2010, Pages 38-53

  Si, H ^a   Gartner K ^a   Fuhrmann, J ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Delaunay mesh; Partitions of polyhedres; Voronoi partitions

Indexed keywords

EID: 76649143449     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: 10.1134/S0965542510010069     Document Type: Article

References (29)

1. R. H. Macneal, "An Asymmetrical Finite Difference Network," Quart. Math. Appl. 11, 295-310 (1953).
2. G. Voronoi, "Nouvelles Applications des Paramètres Continus à la Théorie des Formes Quadratiques," Reine Angew. Math. 133, 97-178 (1907).
3. D. Allen and R. Southwell, "Relaxation Methods Applied to Determine the Motion, in Two Dimensions, of a Viscous Fluid Past a Fixed Cylinder," Quart. J. Mech. and Appl. Math. 8, 129-145 (1955).
4. A. M. Il'in, "A Difference Scheme for a Differential Equation with a Small Parameter Multiplying the Second Derivative," Mat. Zametki 6(2), 237-248 (1969).
5. D. L. Scharfetter and H. K. Gummel, "Large signal analysis of a silicon Read diode," IEEE Trans. Electron. Dev. 16, 64-77 (1969).
6. R. Eymard, J. Fuhrmann, and K. Gärtner, "A Finite Volume Scheme for Nonlinear Parabolic Equations Derived from One-dimensional Local Dirichlet Problems," Numer. Math. 102(3), 463-495 (2006).
7. R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, 1962).
8. R. Eymard, T. Gallouët, and R. Herbin, "The Finite Volume Method," Handbook Numer. Analys. North-Holland 7, 715-1022 (2000).
9. J. Fuhrmann and H. Langmach, "Stability and Existence of Solutions of Time Implicit Finite Volume Schemes for Viscous Nonlinear Conservation Laws," Appl. Numer. Math. 37(1-2), 201-230 (2001).
10. H. Gajewski and K. Gärtner, "On the Discretization of van Roosbroeck's Equations with Magnetic Field," Z. angew. Math. and Mech. 76(5), 247-264 (1996).
11. K. Gärtner, "Existence of Bounded Discrete Steady State Solutions of the van Roosbroeck System on Boundary Conforming Delaunay Grids," SIAM J. Sci. Comput. 31, 1347-1362 (2009).
12. A. Glitzky and K. Gärtner, "Energy Estimates for Continuous and Discretized Electro-reaction-diffusion Systems," Preprint No. 1222, WIAS (Techn. Rep. WIAS, 2007). To appear in SIAM J. Math. Anal.
13. A. Linke, Divergence-free Mixed Finite Elements for the Incompressible Navier-Stokes Equation. PhD Thesis (Univ. Erlangen, 2008).
14. B. N. Delaunay, "Sur la Sphere Vide," Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 793-800 (1934).
15. K. R. Gabriel and R. R. Sokal, "A New Statistical Approach to Geographic Analysis," Systematic Zoology 18(3), 259-278 (1969).
16. P. L. Chew, "Guaranteed-quality Triangular Meshes," Techn. Rept. TR 89-983 (Dept. Comput. Sci. Cornell Univ., 1989).
17. J. Ruppert, "A Delaunay rEfinement Algorithm for Quality 2-dimensional Mesh Generation," J. Algorithms. 18(3), 548-585 (1995).
18. J. R Shewchuk, "Tetrahedral Mesh Generation by Delaunay Refinement," in Proceedings of 14th Ann. Symp. Comput. Geom. (1998), pp. 86-95.
19. H. Si, Three Dimensional Boundary Conforming Delaunay Mesh Generation. PhD Thesis (Inst. Math. Techn. Univ., Berlin, 2008).
20. H. Si, "An Analysis of Shewchuk's Delaunay Refinement Algorithm," in Proc of 18th Intern. Mesh. Rountable, 2009.
21. S.-W. Cheng, T. Dey, H. Edelsbrunner, et al., "Sliver Exudation," J. Assoc. Comput. Mack. 47, 883-904 (2000).
22. J. Erickson, "Nice Point Sets Can Have Nasty Delaunay Triangulations," Discreta Comput. Geometry 30(1), 109-132 (2003).
23. H. Si and K. Gärtner, "Meshing Piecewise Linear Complexes by Constrained Delaunay Tetrahe-dralizations," in Proceedings of 14th Internat. Mesh. Roundtable (2005), pp. 147-163.
24. X.-Y. Li and S. H. Teng, "Generating Well-shaped Delaunay Meshes in 3D," in Proceedings of 12th Ann. ACMSIAM Symp. on Disc. Algo (2001), pp. 28-37.
25. H. Si, TetGen-a Quality Tetrahedral Mesh Generator and a 3D Delaunay Triangulator. http://tetgen. berlios. de, 2009. Last retrieved 2009-12-14.
26. H. Si, "Adaptive Tetrahedral Mesh Generation by Constrained Delaunay refinement," Inter. J. Numer. Meth. Engin. 75(7), 856-880 (2008).
27. S.-W. Cheng, T. K. Dey, E. A. Ramos, and T. Ray, "Quality Meshing for Polyhedra with Small Angles," Inter. J. Comput. Geometry Appl. 15, 421-461 (2005).
28. S. E. Pav and N. J. Walkington, "Robust Three Dimensional Delaunay Refibement," in Proceedings of 13th Internat. Mesh. Roundtable (Sandia Nation. Lab., 2004).
29. S. E. Pav, Delaunay refinement algorithm: PhD Thesis (Carnegie Mellon Univ., 2003).