Nikolay Kirov
Research interests
Mesh generators and finite element solvers
Unstructured mesh generators and a finite element solver


[1] M. Batdorf, L. A. Freitag, C. Ollivier-Gooch, A Computational Study of the Effect of Unstructured Mesh Quality on Solution Efficiency, presented at 13th Annual Computational Fluid Dynamics Meeting, Snowmass Village, CO, 1997. Also Preprint ANL/MCS-P672-0697.
[2] J. Bey, AGM3D Manual, Report Nr. 50, SFB 382, Math. Inst. Univ. Tuebingen, 1996.
[3] J. Bey, Simplicial Grid Refinement: On Freudenthal's Algorithm and the Optimal Number of Congruence Classes, Report no. 151, Institut fuer Geometrie und Praktische Mathematik, RWTH Aachen, 1998.
[4] J. Bey, Tetrahedral Grid Refinement, Computing 55, pp. 355-378, 1995.
[5] J. Bey, G. Wittum, Downwind Numbering: A Robust Multigrid Method for Convection-Diffusion Problems on Unstructured Grids. In: Fast Solvers for Flow Problems. Proceedings of the 10th GAMM-Seminar Kiel, January 14 to 16, 1994. NNFM 49, W. Hackbusch, G. Wittum (eds.), Vieweg, pp. 63-73, 1995.
[6] G. Blelloch, G. L. Miller,  D. Talmor, Developing a Practical Projection-Based Parallel Delaunay Algorithm.
In Proceedings of the Annual ACM Symposium on Computational Geometry, May, 1996, Philadelphia, PA.
[7] F. Bornemann, B. Erdmann, R. Kornhuber, Adaptive multilevel-methods in three space dimensions, Int. J. Num. Eng, Vol. 36, 3187-3203 (1993).
[8] H. Borouchaki, F. Hecht, E. Saltel, P. L. George (INRIA), Reasonably efficient Delaunay based mesh generator in 3 dimensions, Proc. 4th International Meshing Roundtable, Albuquerque, New Mexico, October 16-17, 1995.
[9] S. A. Cannan, S. N. Muthukrishnan, R. K. Phillips, Topological refinement procedures for triangular finite element meshes, Engineering with Computers, 12, 243-255.
[10] S. A. Cannan, J. R. Tristano, M. L. Staten, An approach to combined Laplacian ans optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes, Proc.7th International Meshing Roundtable, Dearborn, Michigan, October 26-28, 1998.
[11] P. L. Chew, Guaranteed-quality triangular meshes, TR 89-983, Dep. Comp. Sci., Cornell Univ., Ithaca, NY, April 1989.
[12] Boris N. Delaunay, Sur la sphere, Vide. Izvestia Akademia Nauk SSSR, IIV seria, vol. 7, 793-800, 1934.
[13] J. Dompierre, P. Labbe, F. Guibault, R. Camarero, Proposal of benchmarks for 3D unstructured tetrahedral mesh optimization, Proc.7th International Meshing Roundtable, Dearborn, Michigan, October 26-28, 1998.
[14] D. A. Field, Laplacian smoothing and Delaunay triangulations, Comm. in Appl. Num. Methods, 4, 709-712, 1988.
[15] S. Fortune, A sweepline algorithm for Voronoi diagrams, Algoritmica 2(2), pp. 153-174,  1987.
[16] L. Freitag, M. Jones, P. Plassmann, An efficient parallel algorithm for mesh smoothing, Proc. 4th International Meshing Roundtable, Albuquerque, New Mexico, October 16-17, pp.47-58, 1995.
[17] L. Freitag, C. Ollivier-Gooch, A comparison of tetrahedral mesh improvement techniques, Proc. 5th International Meshing Roundtable, Sandia National Laboratories, pp. 87-106, October 1996.
[18] L. Freitag, C. Ollivier-Gooch, Tetrahedral Mesh Improvement Using Swapping and Smoothing, Preprint ANL/MCS-P657-0497.
[19] V. John, G. Matthies, F. Schieweck, L. Tobiska, A streamline-diffusion method for nonconforming finite approximations applied to convection-diffusion problems, Otto-fon-Guericke-Universitaet Magdeburg, Fakultaet fuer Mathematik, Preprint Nr. 35, 1997.
[20] M. T. Jones, P. E. Plassmann, Adaptive Refinement of Unstructured Finite-Element Refinement Meshes, J. of Finite Elements in  Analysis and Design, 25, (1997) pp. 41-60 (Also MSC  Preprint P562-0296).
[21] P. Knobloch, L. Tobiska, A streamline diffusion method for nonconforming finite element approximations applied to the linearized incompressible Navier-Stokes equation, Proceedings of NMA'98, 4-th Int. Conf. on Numerical Methods and Appl., August 19-23, 1998, Sofia, Bulgaria.
[22] C. Lawson, Software for C1 interpolation, Math. Software III, (John R. Rice, editor), pages 161-194. Academic Press, New York, 1977.
[23] D. T. Lee and B. J. Schachter, Two algorithms for constructing a Delaunay triangulation. International
Journal of Computer and Information Sciences 9(3), pp. 219-242, 1980.
[24] S. H. Lo, Volume discretization into tetrahedra, Computers and Structures, 39, 493-511, 1991.
[25] R. Lohner, P. Parokh, C. Gumbert, Interactive generation of unstructured grid for three dimensional problems,
Num. Grid Generation in Computational Fluid Mechanics'88, Pineridge Press, 687-697, 1988.
[26] D. L. Marcum, N. P. Weatherill, Unstructured grid generation using iterative point insertion and local reconnection, AIAA J., 33(9), 1619-1625, 1995.
[27] G. L. Miller, D. Talmor,  Shang-Hua Teng, Optimal Good-Aspect-Ratio Coarsening for Unstructured Meshes.
In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, January, 1997, New Orleans, LA.
[28] G. L. Miller, D. Talmor, Shang-Hua Teng, N. Walkington, On the Radius-Edge Condition in the Control Volume Method. Submitted to SIAM journal on Numerical Analysis, also a CMU math department TR.
[29] G. L. Miller, D. Talmor, Shang-Hua Teng, N.Walkington, A Delaunay Based Numerical Method for Three Dimensions: Generation, Formulation, and Partition." In Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing , May, 1995, Las Vegas, NV.
[30] S. A. Mitchell, Refining a Triangulation of a Planar Straight-Line Graph to Eliminate Large Angles, Thirty-fourth Annual Symposium on Foundations of Computer Science (FOCS '93), 583-591.
[31] S. A. Mitchell, S. A. Vavasis, Quality mesh generation in three dimensions, In Proc. 8th ACM symp. on Computational Geometry, pp. 212-221, 1992.
[32] S. A. Mitchell, S. A. Vavasis, Quality mesh generation in higher dimensions, Preprint, December 19, 1996.
[33] S. Mitchell and S. Vavasis, An aspect ratio bound for triangulating a d-grid cut by a hyperplane,  Extended abstract appeared in Proc. 1996 Symp. Comput. Geom.
[34] S. J. Owen, A survey of unstructured mesh generation technology, Proc. 7th International Meshing Roundtable, Dearborn, Michigan, October 26-28, 1998.
[35] Jim Ruppert, A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation. Journal of Algorithms 18(3):548-585, May 1995.
[36] J. Schoeberl, NETGEN -- User's manual
[37] J. Schoeberl,  NETGEN - An advancing front 2D/3D-mesh generator based on abstract rules. Comput.Visual.Sci, 1:41-52, 1997.
[38] J. R. Shewchuk, Triangle, A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator,
[39] J. R. Shewchuk, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, First Workshop on Applied Computational Geometry (Philadelphia, Pennsylvania), pages 124-133, ACM, May 1996.
[40] K. Shimada, Anisotropic triangular meshing of parametric surfaces via close packing of ellipsoidal bubbles,  Proc. 6th International Meshing Roundtable, Park City, Utah, October 13-15, 375-390, 1997.
[41] M. Stynes, L. Tobiska, Analysis of the streamline-diffusion finite element method on a Shishkin mesh for a convection-diffussion problem with exponential layers, Otto-fon-Guericke-Universitaet Magdeburg, Fakultaet fuer Mathematik, Preprint Nr. 17, 1998.
[41] L. Tobiska, G. Matthies, M. Stynes, Convergence properties of the streamline-diffusion finite element method on a Shishkin mesh for singularly perturbed elliptic equations with exponentiol layers, Proc. Workshop on Analytical and Computaional Methods for Convection-Dominated and Singular Perturbed Problems, Lozenetz, Bulgaria, August, 1998.
[43] S. A. Vavasis, QMG: mesh generation and related software,
[44] D. F. Watson, Computing the Delaunay tessalation with application to Voronoi polytopes, The Computer Journal, 24(2), 167-172, 1981.
[45] N. P. Weatherill, O. Hassan, Efficient tree-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints, Int. J. Num. Meth. Engineering, 37, 2005-2039, 1994.
[46] M. A. Yerry, M. S. Shephard, Three dimensional mesh generation by modified octree technique, Int. J. Num. Meth. in Engineering, 20, 1965-1990, 1984