Bisection.bib

1. Kossaczk$y$, I.. A recursive approach to local mesh refinement in two and three dimensions. Journal of Computational and Applied Mathematics, 55():275-288, 1994.
   Kossaczky.I1994   Google Scholar


2. Binev, P. and Dahmen, W. and DeVore, R.. Adaptive Finite Element Methods with Convergence Rates. Numerische Mathematik, 97(2):219-268, 2004.
   Binev.P;Dahmen.W;DeVore.R2004   Google Scholar


3. Zhang, Linbo. A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection. NUMERICAL MATHEMATICS: Theory, Methods and Applications, ():, 2008.
   Zhang.L2008   Google Scholar


4. B\"ansch, E.. Local Mesh Refinement in 2 and 3 Dimensions. Impact of Computing in Science and Engineering, 3():181--191, 1991.
   Bansch.E1991   Google Scholar


5. Stevenson, Rob. The completion of locally refined simplicial partitions created by bisection. Mathemathics of Computation, 77():227--241, 2008.
   Stevenson.R2008   Google Scholar


6. Arnold, Douglas N. and Mukherjee, Arup and Pouly, Luc. Locally adapted tetrahedral meshes using bisection. SIAM Journal of Scientific Computing, 22(2):431--448, 2000.
   Arnold.D;Mukherjee.A;Pouly.L2000   Google Scholar


7. Biedl, Therese C. and Bose, Prosenjit and Demaine, Erik D. and Lubiw, Anna. Efficient Algorithms for {Petersen}'s Matching Theorem. Symposium on Discrete Algorithms, ():130-139, 1999.
   Biedl.T;Bose.P;Demaine.E;Lubiw.A1999   Google Scholar


8. Arnold, D. N. and Mukherjee, A.. Tetrahedral bisection and adaptive finite elements. Grid Generation and Adaptive Algorithms, ():29--42, 1999.
   Arnold.D;Mukherjee.A1999   Google Scholar


9. Atalay, F. Betul and Mount, David M.. The Cost of Compatible Refinement of Simplex Decomposition Trees. Proceedings of the 15th International Meshing Roundtable, Birmingham, AL, September 2006, ():57--70, 2006.
   Atalay.F;Mount.D2006   Google Scholar


10. Bey, J.. Tetrahedral grid refinement. Computing, 55(4):355--378, 1995.
    Bey.J1995   Google Scholar


11. Bey, J\"urgen. Simplicial grid refinement: on Freudenthal's algorithm and the optimal number of congruence classes. Numerische Mathematik, 85(1):1--29, 2000.
    Bey.J2000   Google Scholar


12. Brandts, Jan and Korotov, Sergey and Kr\izek, Michal. Dissection of the path-simplex in {$\Bbb R\sp n$} into {$n$} path-subsimplices. Linear Algebra Appl., 421(2-3):382--393, 2007.
    Brandts.J;Korotov.S;Krivzek.M2007   Google Scholar


13. Chen, Long and Nochetto, Ricardo H. and Xu, Jinchao. Local Multilevel Methods on Graded Bisection Grids for {$H^1$} System. Submitted to JCM, ():, 2009.
    Chen.L;Nochetto.R;Xu.J2007   Google Scholar


14. Chen, Long and Zhang, Chen-Song. A coarsening algorithm on adaptive grids by newest vertex bisection and its applications. Submitted, ():, 2009.
    Chen.L;Zhang.C2007   Google Scholar


15. Chen, Long. Short implementation of bisection in {MATLAB}. Recent Advances in Computational Sciences -- Selected Papers from the International Workship on Computational Sciences and Its Education, ():318 -- 332, 2007.
    Chen.L2006a   Google Scholar


16. Gutierrez, Claudio and Gutierrez, Flavio and Rivara, Maria-Cecilia. A Geometric Approach to the Bisection Method. , ():, 2004.
    Gutierrez.C;Gutierrez.F;Rivara.M2004   Google Scholar


17. Horst, Reiner. On Generalized Bisection of $n$-Simplices. Mathemathics of Computation, 66(218):691--698, 1997.
    Horst.R1997   Google Scholar


18. Liu, A. and Joe, B.. Relationship between tetrahedron quality measures. BIT Numerical Mathematics, 34():268--287, 1994.
    Liu.A;Joe.B1994   Google Scholar


19. Liu, Anwei and Joe, Barry. On the shape of tetrahedra from bisection. Math. Comput., 63(207):141--154, 1994.
    Liu.A;Joe.B1994a   Google Scholar


20. Liu, A. and Joe, B.. Quality Local Refinement of Tetrahedral Meshes Based on Bisection. SIAM Journal on Scientific Computing, 16(6):1269--1291, 1995.
    Liu.A;Joe.B1995   Google Scholar


21. Liu, Anwei and Joe, Barry. Quality local refinement of tetrahedral meshes based on {$8$}-subtetrahedron subdivision. Math. Comp., 65(215):1183--1200, 1996.
    Liu.A;Joe.B1996   Google Scholar


22. Maubach, Joseph. Local Bisection Refinement for $N$-Simplicial Grids Generated by Reflection. SIAM Journal of Scientific Computing, 16(1):210--227, 1995.
    Maubach.J1995   Google Scholar


23. Maubach, Joseph M.. Space-filling curves for 2-simplicial meshes created with bisections and reflections. Appl. Math., 50(3):309--321, 2005.
    Maubach.J2005   Google Scholar


24. Mukherjee, Arup. An Adaptive Finite Element Code for Elliptic Boundary Value Problems in Three Dimensions with Applications in Numerical Relativity. , ():, 1996.
    Mukherjee.A1996   Google Scholar


25. Padron, Miguel A. and Suarez, Jose P. and Plaza, Angel. A comparative study between some bisection based partitions in 3D. Applied Numerical Mathematics, 55(3):357--367, 2005.
    Padron.M;Suarez.J;Plaza.A2005   Google Scholar


26. Plaza, A. and Carey, G. F.. Local refinement of simplicial grids based on the skeleton. Applied Numerical Mathematics, 32(2):195--218, 2000.
    Plaza.A;Carey.G2000   Google Scholar


27. Plaza, Angel and Padron, Miguel A. and Carey, Graham F.. A 3D refinement/derefinement algorithm for solving evolution problems. Applied Numerical Mathematics, 32(4):401--418, 2000.
    Plaza.A;Padron.M;Carey.G2000   Google Scholar


28. Plaza, Angel and Padrón, Miguel A. and Suárez, José P.. Non-degeneracy study of the 8-tetrahedra longest-edge partition. Appl. Numer. Math., 55(4):458--472, 2005.
    Plaza.A;Padron.M;Suarez.J2005   Google Scholar


29. Plaza, Angel and Rivara, Maria-Cecilia. Mesh Refinement based on the 8-tetrahedra longest-edge partition. 12th meshing roundtable, ():67--78, 2003.
    Plaza.A;Rivara.M2003   Google Scholar


30. Plaza, Angel. The eight-tetrahedra longest-edge partition and Kuhn triangulations. Computers \& Mathematics with Applications, 54(3):427--433, 2007.
    Plaza.A2007   Google Scholar


31. Rivara, Maria-Cecilia and Inostroza, Patricio. Using Longest-side Bisection Techniques for the Automatic Refinement fo {D}elaunay Triangulations. International Journal for Numerical Methods in Engineering, 40():581--597, 1997.
    Rivara.M;Inostroza.P1997   Google Scholar


32. Rivara, M. C. and Venere, M.. Cost Analysis of the longest-side (triangle bisection) Refinement Algorithms for Triangulations. Engineering with Computers, 12():224--234, 1996.
    Rivara.M;Venere.M1996   Google Scholar


33. Rivara, M. C.. Mesh refinement processes based on the generalized bisection of simplices. SIAM Journal on Numerical Analysis, 21():604-613, 1984.
    Rivara.M1984   Google Scholar


34. Suárez, J. P. and Carey, G. F. and Plaza, A.. Graph-based data structures for skeleton-based refinement algorithms. Comm. Numer. Methods Engrg., 17(12):903--910, 2001.
    Suarez.J;Carey.G;Plaza.A2001   Google Scholar


35. Suárez, José P. and Plaza, Ángel and Carey, Graham F.. The propagation problem in longest-edge refinement. Finite Elem. Anal. Des., 42(2):130--151, 2005.
    Suarez.J;Plaza.A;Carey.G2005   Google Scholar


36. Suarez, J. P. and Abad, P. and Plaza, A. and Padron, M. A.. Computational aspects of the refinement of {3D} complex meshes. ICCMSE '03: Proceedings of the international conference on Computational methods in sciences and engineering, ():615--618, 2003.
    Surez.J;Abad.P;Plaza.A;Padrn.M2003   Google Scholar


37. Traxler, C. T.. An algorithm for adaptive mesh refinement in {$n$} dimensions. Computing, 59(2):115--137, 1997.
    Traxler.C1997   Google Scholar


38. Zhang, Lin-bo. A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection. preprint, ():, 2005.
    Zhang.L2005   Google Scholar

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