МЕТОДИ ПОБУДОВИ ДИСКРЕТНИХ МОДЕЛЕЙ: НЕСТРУКТУРОВАНІ СІТКИ
Ключові слова:
дискретна модель, сітка, скінченний елемент, трикутний елемент, чотирикутний елемент, тетраедричний елемент, шестигранний елемент
Анотація
У статті проведено огляд актуальних підходів і методів автоматичної генерації неструктурованих дискретних моделей геометричних об’єктів. Зокрема, виконано аналіз методів генерації дискретних моделей з використанням трикутних або тетраедричних елементів, а також чотирикутних або шестигранних скінченних елементів.
Посилання
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5. Langelaar M. The use of convex uniform honeycomb tessellations in structural topology optimization / M. Langelaar // The 7th world congress on structural and multidisciplinary optimization : World Congress, Seoul, South Korea, 21-25 May 2007 : proceedings. – Seoul, 2007.
6. Saxena A. Combined Gradient-Stochastic Optimization with Negative Circular Masks for Large Deformation Topologies // International Journal for Numerical Methods in Engineering. – 2013. – Volume 93, Issue 6. – P. 635-663. – DOI : 10.1002/nme.4401.
7. Heikes R. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests / R. Heikes, D. Randall // Monthly Weather Review. – 1995. – Volume 123. – P. 1862-1880.
8. Heikes R. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy / R. Heikes, D. Randall // Monthly Weather Review. – 1995. – Volume 123. – P. 1881-1887.
9. Чопоров С. В. Методы построения дискретных моделей: структурированные и блочно-структурированные сетки / С. В. Чопоров, С. И. Гоменюк, Х. Х. Алатамнех, К. С. Оспищев // Вісник Запорізького національного університету: Збірник наукових статей. Фізико-математичні науки. – 2016. – № 1. – С. 272-284.
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21. Chew L. P. Constrained Delaunay Triangulations / L. P. Chew // Algorithmica. – 1989. – Volume 4, Issue 1. – P. 97-108.
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28. George P. L. Automatic Mesh Generator with Specified Boundary / P. L. George, F. Hecht, E. Saltel // Computer Methods in Applied Mechanics and Engineering. – 1991. – Volume 92, Issue 3. – P. 269-288.
29. Mavriplis D. J. An advancing front Delaunay triangulation algorithm designed for robustness / D. J. Mavriplis // Journal of Computational Physics. – 1995. – Volume 117, Issue 1. – P. 90-101.
30. Müller J.-D. A Frontal Approach for Internal Node Generation in Delaunay Triangulations / J.-D. Müller, P. L. Poe, H. Deconinck // International Journal for Numerical Methods in Fluids. – 1993. – Volume 17. – P. 241-255.
31. Silva C. T. Greedy Cuts: An Advancing Front Terrain Triangulation Algorithm / C. T. Silva, J. S. B. Mitchell // The 6th ACM International Symposium on Advances in Geographic Information Systems : International Conference, Washington, USA, 2-7 November 1998 : proceedings. – Washington : ACM, 1998. – P. 137-144. – DOI : 10.1145/288692.288717
32. Frey P. Delaunay tetrahedralization using an advancing-front approach / P. Frey, H. Borouchaki, P.-L. Geouge // The 5th International Meshing Roundtable : International Conference, Pittsburgh, Pennsylvania, USA, October 10-11, 1996 : proceedings. – Sandia : Sandia National Laboratories, 1996. – P. 31-48.
33. Frey P. 3D Delaunay mesh generation coupled with an advancing-front approach / P. Frey, H. Borouchaki, P.-L. Geouge // Computer methods in applied mechanics and engineering. – 1998. – Volume 157, Issue 1. – P. 115-131.
34. El-Hamalawi A. A 2D combined advancing front-Delaunay mesh generation scheme / A. El-Hamalawi // Finite Elements in Analysis and Design. – 2004. – Volume 40, No 9-10. – P. 967-989.
35. Kucwaj J. An Algorithm of Combining of Advancing Front and Delaunay Triangulation to 3-D Domain Tesselation / J. Kucwaj, B. Borowik // Annales UMCS Informatica AI IX. – 2009. – No 1. – P. 15-26.
36. Baker B. S. Nonobtuse Triangulation of Polygons / B. S. Baker, E. Grosse, C. S. Rafferty // Discrete and Computational Geometry. – 1988. – Volume 3, Issue 2. – P. 147-168.
37. Bern M. Provably good mesh generation / M. Bern, D. Eppstein, J. Gilbert // Journal of Computer and System Sciences. – 1994. – Volume 48, Issue 3. – P. 384-409.
38. Neugebauer F. Improved Mesh Generation: Not Simple but Good / F. Neugebauer, R. Diekmann // The 5th International Meshing Roundtable : International Conference, Pittsburgh, Pennsylvania, USA, October 10-11, 1996 : proceedings. – Sandia : Sandia National Laboratories, 1996. – P. 257-272.
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40. Mitchell S. A. Quality Mesh Generation in Higher Dimensions / S. A. Mitchell, S. A. Vavasis // SIAM Journal on Computing. – 2000. – Volume 29, Issue 4. – P. 1334-1370.
41. Blacker T. D. Paving: A new approach to automated quadrilateral mesh generation / T. D. Blacker, M. B. Stephenson // International Journal For Numerical Methods in Engineering. – 1991. – Volume 32, Issue 4. – P. 811-847. – DOI : 10.1002/nme.1620320410.
42. Park C. A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints / C. Park, J.-S. Noh, I.-S. Jang, J. M. Kang // Computer-Aided Design. – 2007. – Volume 39. – P. 258-267.
43. Zhao Y. A modified paving algorithm for quadrilateral mesh generation / Y. Zhao, B. Yu // Kung Cheng Je Wu Li Hsueh Pao/Journal of Engineering Thermophysics. – 2013. – Volume 34, Issue 4. – P. 728-732.
44. Blacker T. D. Seams and Wedges in Plastering:A 3D Hexahedral Mesh Generation Algorithm / T. D. Blacker, R. J. Meyers // Engineering with Computers. – 1993. – Volume 9, Issue 2. – P. 83-93.
45. Staten M. L. Unconstrained plastering – Hexahedral mesh generation via advancing-front geometry decomposition / M. L. Staten, S. J. Owen, T. D. Blacker, M. Supazzini, K. Shimada // International Journal for Numerical Methods in Engineering. – 2010. – Volume 81, Issue 2. – P. 135-171. – DOI : 10.1002/nme.2679.
46. Owen S. J. Q-Morph: An Indirect Approach to Advancing Front Quad Meshing / S. J. Owen, M. L. Staten, S. A. Canann, S. Saigal // International Journal for Numerical Methods in Engineering. – 1999. – Volume 44, Issue 9. – P. 1317-1340. – DOI : 10.1002/(SICI)1097-0207(19990330)44:9 <1317::AID-NME532>3.0.CO;2-N.
47. Сковпень А. В. Усовершенствованный алгоритм построения нерегулярных четырехугольных сеток / А. В. Сковпень // Журнал вычислительной математики и математической физики. – 2005. – Т. 45, № 8. – С. 1506-1528.
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2. Zienkiewicz O. C. The Finite Element Method: Its Basis and Fundamentals, Seventh Edition / O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. – London : Butterworth-Heinemann, 2013. – 756 P.
3. Zienkiewicz O. C. The Finite Element Method for Solid and Structural Mechanics, Seventh Edition / O. C. Zienkiewicz, R. L. Taylor, D. D. Fox. – London : Butterworth-Heinemann, 2013. – 672 P.
4. Zienkiewicz O. C. The Finite Element Method for Fluid Dynamics, Seventh Edition / O. C. Zienkiewicz, R. L. Taylor, P. Nithiarasu. – London : Butterworth-Heinemann, 2013. – 584 P.
5. Langelaar M. The use of convex uniform honeycomb tessellations in structural topology optimization / M. Langelaar // The 7th world congress on structural and multidisciplinary optimization : World Congress, Seoul, South Korea, 21-25 May 2007 : proceedings. – Seoul, 2007.
6. Saxena A. Combined Gradient-Stochastic Optimization with Negative Circular Masks for Large Deformation Topologies // International Journal for Numerical Methods in Engineering. – 2013. – Volume 93, Issue 6. – P. 635-663. – DOI : 10.1002/nme.4401.
7. Heikes R. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests / R. Heikes, D. Randall // Monthly Weather Review. – 1995. – Volume 123. – P. 1862-1880.
8. Heikes R. Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy / R. Heikes, D. Randall // Monthly Weather Review. – 1995. – Volume 123. – P. 1881-1887.
9. Чопоров С. В. Методы построения дискретных моделей: структурированные и блочно-структурированные сетки / С. В. Чопоров, С. И. Гоменюк, Х. Х. Алатамнех, К. С. Оспищев // Вісник Запорізького національного університету: Збірник наукових статей. Фізико-математичні науки. – 2016. – № 1. – С. 272-284.
10. Чопоров С. В. Сравнительный анализ треугольных и четырехугольных конечных элементов / С.В. Чопоров, С.И. Гоменюк, А.А. Лисняк // Вестник Херсонского национального технического университета. – 2013. – № 2(47). – С. 382-386.
11. Thompson J. F. Handbook of grid generation / J. F. Thompson, Bh. Sony, N. Weatherill. – New York : CRC Press, 1999. – 1136 p.
12. Делоне Б. Н. О пустой сфере / Б. Н. Делоне // Известия АН СССР. ОМЕН. – 1934. – № 4. – С. 793-800.
13. Watson D. F. Computing the n-dimensional Delaunay tesselation with applications to Voronoi polytopes / D. F. Watson // The Computer Journal. – 1981. – Volume 24, Issue 2. – P. 167-172.
14. Скворцов А. В. Триангуляция Делоне и её применение / А. В. Скворцов. – Томск : Издательство Томского университета, 2002. – 128 с.
15. Скворцов А. В. Обзор алгоритмов построения триангуляции Делоне / А. В. Скворцов // Вычислительные методы и программирование. – 2002. – № 3. – С. 14-39.
16. Скворцов А. В. Алгоритмы построения и анализа триангуляции / А. В. Скворцов, Н. С. Мирза. – Томск : Издательство Томского университета, 2006. – 168 с.
17. Su P. A comparison of sequential Delaunay triangulation algorithms / P. Su, R. L. S. Drysdale // Computational Geometry. – 1997. – Volume 7, Issues 5-6. – P. 361-385.
18. Joe B. Construction of k-Dimensional Delaunay Triangulations using Local Transformations / B. Joe // SIAM Journal on Scientific Computing. – 1993. – Volume 14, Issue 6. – P. 1415-1436.
19. Joe B. Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations / B. Joe // SIAM Journal on Scientific Computing. – 1995. – Volume 16, Issue 6. – P. 1192-1307.
20. Ruppert J. A Delaunay refinement algorithm for quality 2-dimensional mesh generation / J. Ruppert // Journal of Algorithms. – 1995. – Volume 18, Issue 3. – P. 548-585.
21. Chew L. P. Constrained Delaunay Triangulations / L. P. Chew // Algorithmica. – 1989. – Volume 4, Issue 1. – P. 97-108.
22. Cohel-Steiner D. Conforming Delaunay Triangulations in 3D / D. Cohen-Steiner, É. C. de Verdière, M. Yvinec // Computational Geometry: Theory and Applications. – 2004. – Volume 28. – P. 217-233.
23. Jamin C. CGALmesh: a Generic Framework for Delaunay Mesh Generation / C. Jamin, P. Alliez, M. Yvinec, J.-D. Boissonnat // ACM Transactions on Mathematical Software. – 2014. – Volume 1, No 1. – P. 1-26.
24. Frey W. H. Selective Refinement: A New Strategy for Automatic Node Placement in Graded Triangular Meshes / W. H. Frey // International Journal for Numerical Methods in Engineering. – 1987. – Volume 24, Issue 11. – P. 2183-2200. – DOI : 10.1002/nme.1620241111.
25. Nigel P. W. Delaunay Triangulation in Computational Fluid Dynamics / P. W. Nigel // Computers and Mathematics with Applications. – 1992. – Volume 24, No 5/6. – P. 129-150.
26. Du Q. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations / Q. Du, D. Wang // International Journal for Numerical Methods in Engineering. – 2003. – Volume 56, Issue 9. – P. 1355-1373. – DOI : 10.1002/nme.616.
27. Du Q. Recent progress in robust and quality Delaunay mesh generation / Q. Du, D. Wang // Journal of Computational and Applied Mathematics. – 2006. – Volume 195, Issues 1-2. – P. 8-23.
28. George P. L. Automatic Mesh Generator with Specified Boundary / P. L. George, F. Hecht, E. Saltel // Computer Methods in Applied Mechanics and Engineering. – 1991. – Volume 92, Issue 3. – P. 269-288.
29. Mavriplis D. J. An advancing front Delaunay triangulation algorithm designed for robustness / D. J. Mavriplis // Journal of Computational Physics. – 1995. – Volume 117, Issue 1. – P. 90-101.
30. Müller J.-D. A Frontal Approach for Internal Node Generation in Delaunay Triangulations / J.-D. Müller, P. L. Poe, H. Deconinck // International Journal for Numerical Methods in Fluids. – 1993. – Volume 17. – P. 241-255.
31. Silva C. T. Greedy Cuts: An Advancing Front Terrain Triangulation Algorithm / C. T. Silva, J. S. B. Mitchell // The 6th ACM International Symposium on Advances in Geographic Information Systems : International Conference, Washington, USA, 2-7 November 1998 : proceedings. – Washington : ACM, 1998. – P. 137-144. – DOI : 10.1145/288692.288717
32. Frey P. Delaunay tetrahedralization using an advancing-front approach / P. Frey, H. Borouchaki, P.-L. Geouge // The 5th International Meshing Roundtable : International Conference, Pittsburgh, Pennsylvania, USA, October 10-11, 1996 : proceedings. – Sandia : Sandia National Laboratories, 1996. – P. 31-48.
33. Frey P. 3D Delaunay mesh generation coupled with an advancing-front approach / P. Frey, H. Borouchaki, P.-L. Geouge // Computer methods in applied mechanics and engineering. – 1998. – Volume 157, Issue 1. – P. 115-131.
34. El-Hamalawi A. A 2D combined advancing front-Delaunay mesh generation scheme / A. El-Hamalawi // Finite Elements in Analysis and Design. – 2004. – Volume 40, No 9-10. – P. 967-989.
35. Kucwaj J. An Algorithm of Combining of Advancing Front and Delaunay Triangulation to 3-D Domain Tesselation / J. Kucwaj, B. Borowik // Annales UMCS Informatica AI IX. – 2009. – No 1. – P. 15-26.
36. Baker B. S. Nonobtuse Triangulation of Polygons / B. S. Baker, E. Grosse, C. S. Rafferty // Discrete and Computational Geometry. – 1988. – Volume 3, Issue 2. – P. 147-168.
37. Bern M. Provably good mesh generation / M. Bern, D. Eppstein, J. Gilbert // Journal of Computer and System Sciences. – 1994. – Volume 48, Issue 3. – P. 384-409.
38. Neugebauer F. Improved Mesh Generation: Not Simple but Good / F. Neugebauer, R. Diekmann // The 5th International Meshing Roundtable : International Conference, Pittsburgh, Pennsylvania, USA, October 10-11, 1996 : proceedings. – Sandia : Sandia National Laboratories, 1996. – P. 257-272.
39. Mitchell S. A. Quality Mesh Generation in Three Dimensions / S. A. Mitchell, S. A. Vavasis // The Eighth Annual Symposium on Computational Geometry : International Conference, Berlin, Germany, June 10-12, 1992 : proceedings. – New York : Cornell University, 1992. – P. 92-104.
40. Mitchell S. A. Quality Mesh Generation in Higher Dimensions / S. A. Mitchell, S. A. Vavasis // SIAM Journal on Computing. – 2000. – Volume 29, Issue 4. – P. 1334-1370.
41. Blacker T. D. Paving: A new approach to automated quadrilateral mesh generation / T. D. Blacker, M. B. Stephenson // International Journal For Numerical Methods in Engineering. – 1991. – Volume 32, Issue 4. – P. 811-847. – DOI : 10.1002/nme.1620320410.
42. Park C. A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints / C. Park, J.-S. Noh, I.-S. Jang, J. M. Kang // Computer-Aided Design. – 2007. – Volume 39. – P. 258-267.
43. Zhao Y. A modified paving algorithm for quadrilateral mesh generation / Y. Zhao, B. Yu // Kung Cheng Je Wu Li Hsueh Pao/Journal of Engineering Thermophysics. – 2013. – Volume 34, Issue 4. – P. 728-732.
44. Blacker T. D. Seams and Wedges in Plastering:A 3D Hexahedral Mesh Generation Algorithm / T. D. Blacker, R. J. Meyers // Engineering with Computers. – 1993. – Volume 9, Issue 2. – P. 83-93.
45. Staten M. L. Unconstrained plastering – Hexahedral mesh generation via advancing-front geometry decomposition / M. L. Staten, S. J. Owen, T. D. Blacker, M. Supazzini, K. Shimada // International Journal for Numerical Methods in Engineering. – 2010. – Volume 81, Issue 2. – P. 135-171. – DOI : 10.1002/nme.2679.
46. Owen S. J. Q-Morph: An Indirect Approach to Advancing Front Quad Meshing / S. J. Owen, M. L. Staten, S. A. Canann, S. Saigal // International Journal for Numerical Methods in Engineering. – 1999. – Volume 44, Issue 9. – P. 1317-1340. – DOI : 10.1002/(SICI)1097-0207(19990330)44:9 <1317::AID-NME532>3.0.CO;2-N.
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Опубліковано
2016-12-20
Як цитувати
Чопоров, С. В., Лісняк, А. О., Борисовська, Ю. О., Козлова, О. С., & Снєжкова, Л. С. (2016). МЕТОДИ ПОБУДОВИ ДИСКРЕТНИХ МОДЕЛЕЙ: НЕСТРУКТУРОВАНІ СІТКИ. Computer Science and Applied Mathematics, (2), 237-250. вилучено із http://journalsofznu.zp.ua/index.php/comp-science/article/view/1394
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