Delaunay decoupling method for parallel guaranteed quality planar mesh refinement

SIAM Journal on Scientific Computing

Volumn 27, Issue 4, 2006, Pages 1394-1423

  Linardakis, Leonidas ^a   Chrisochoides, Nikos ^a  

^a The College of William and Mary   (United States)

Author keywords

Delaunay triangulation; Distributed memory computers; Domain decomposition; Mesh generation; Parallel algorithms

Indexed keywords

CODES (SYMBOLS); DATA STRUCTURES; INFORMATION TECHNOLOGY; PROBLEM SOLVING; QUALITY CONTROL; TWO DIMENSIONAL;

DELAUNAY TRIANGULATION; DISTRIBUTED MEMORY COMPUTERS; DOMAIN DECOMPOSITION; MESH GENERATION;

PARALLEL PROCESSING SYSTEMS;

EID: 33746054942     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030602812     Document Type: Article

References (48)

1. C. ARMSTRONG, D. ROBINSON, R. MCKEAG, T. LI, S. BRIDGETT, R. DONAGHY, AND C. MCGLEENAN, Medials for meshing and more, in Proceedings of the 4th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 1995, pp. 277-288.
2. K. BARKER, N. CHRISOCHOIDES, A. CHERNIKOV, AND K. PINGALI, A framework for load balancing of adaptive and asynchronous applications, IEEE Trans. Parallel and Distributed Systems, 14 (2004), pp. 183-192
3. K. BARKER, N. CHRISOCHOIDES, J. DOBBELAERE, D. NAVE, AND K. PINGALI, Data movement and control substrate for parallel adaptive applications, Concurrency and Computation: Practice and Experience, 14 (2002), pp. 77-101.
4. S. T. BARNARD AND H. D. SIMON, A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems, Concurrency: Practice and Experience, 6 (1994), pp. 101-107.
5. A. BEGUELIN, J. DONGARRA, A. GEIST, R. MANCHEK, K. MOORE, AND V. SUNDERAM, PVM and HeNCE: Tools for heterogeneous network computing, in Software for Parallel Computation, Vol. 106, J. S. Kowalik and L. Grandinetti, eds., Springer-Verlag, Berlin, 1993.
6. G. E. BLELLOCH, G. L. MILLER, J. C. HARDWICK, AND D. TALMOR, Design and implementation of a practical parallel Delaunay algorithm, Algorithmica, 24 (1999), pp. 243-269.
7. H. BLUM, A transformation for extracting new descriptors of shape, in Models for the Perception of Speech and Visual Form, MIT Press, Cambridge, MA, 1967, pp. 362-380.
8. J. W. BRANDT, Convergence and continuity criteria for discrete approximations of the continuous planar skeleton, CVGIP: Image Understanding, 59 (1994), pp. 116-124.
9. J. W. BRANDT AND V. R. ALGAZI, Continuous skeleton computation by Voronoi diagram, CVGIP: Image Understanding, 55 (1992), pp. 329-338.
10. L. P. CHEW, Constrained Delaunay triangulations, Algorithmica, 4 (1989), pp. 97-108.
11. L. P. CHEW, Guaranteed Quality Triangular Meshes, Technical report TR-89-983, Department of Computer Science, Cornell University, Ithaca, NY, 1989.
12. L. P. CHEW, Guaranteed-quality mesh generation for curved surfaces, in 9th Annual Symposium on Computational Geometry, ACM, San Diego, CA, 1993, pp. 274-280.
13. L. P. CHEW, N. CHRISOCHOIDES, AND F. SUKUP, Parallel constrained Delaunay triangulation, in ASME/ASCE/SES Special Symposium on Trends in Unstructured Mesh Generation, Evanston, IL, 1997, pp. 89-96.
14. H. CHOI, S. CHOI, AND H. MOON, Mathematical theory of medial axis transform, Pacific J. Math., 181 (1997), pp. 57-88.
15. N. CHRISOCHOIDES, An alternative to data mapping for parallel PDE solvers: Parallel grid generation, in Scalable Parallel Libraries Conference, Mississippi State, MS, 1993.
16. N. CHRISOCHOIDES, A. FEDOROV, B. B. LOWEKAMP, M. ZANGRILLI, AND C. LEE, A case study of optimistic computing on the Grid: Parallel mesh generation, in Next Generation Systems Program Workshop, IPDPS'03, Nice, 2003.
17. N. CHRISOCHOIDES AND D. NAVE, Simultaneous mesh generation and partitioning, Math. Comput. Simulation, 54 (2000), pp. 321-339.
18. N. CHRISOCHOIDES AND D. NAVE, Parallel Delaunay mesh generation kernel, Internat. J. Numer. Methods Engrg., 58 (2003), pp. 161-176.
19. N. CHRISOCHOIDES AND F. SUKUP, Task parallel implementation of the BOWYER-WATSON algorithm, in Proceedings of Fifth International Conference on Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Mississippi State, MS, 1996.
20. H. DE COUGNY AND M. SHEPHARD, Parallel volume meshing using face removals and hierarchical repartitioning, Comput. Methods Appl. Mech. Engrg., 174 (1999), pp. 275-280.
21. R. DIEKMANN, D. MEYER, AND B. MONIEN, Parallel decomposition of unstructured FEM-meshes, Concurrency: Practice and Experience, 10 (1998), pp. 53-72.
22. S. DONG AND G. KARNIADAKIS, DNS of flow past a stationary and oscillating rigid cylinder at RE = 10,000, in Flow Induced Vibrations, E. de Langre and F. Axisa, eds., Ecole Polytechnique, Paris, 2004.
23. P. J. FREY AND P.-L. GEORGE, Mesh Generation, Hermes Science Publishing, Oxford, UK, 2000.
24. J. GALTIER AND P.-L. GEORGE, Prepartitioning as a way to mesh subdomains in parallel, in 5th International Meshing Roundtable, Pittsburgh, PA, 1996, pp. 107-122.
25. P. L. GEORGE AND H. BOROUCHAKI, Delaunay Triangulation and Meshing: Applications to Finite Element, Hermes, Paris, 1998.
26. H. N. GURSOY AND N. M. PATRIKALAKIS, An automatic coarse and fine surface mesh generation scheme based on medial axis transform: Part I. Algorithms, Engineering with Computers, 8 (1992), pp. 121-137.
27. B. HENDRICKSON AND R. W. LELAND, An improved spectral graph partitioning algorithm for mapping parallel computations, SIAM J. Sci. Comput., 16 (1995), pp. 452-469.
28. B. HENDRICKSON AND R. W. LELAND, A multilevel algorithm for partitioning graphs, in Proceedings of ACM/IEEE Conference on Supercomputing, San Diego, CA, 1995.
29. C. KADOW AND N. WALKINGTON, Design of a projection-based parallel Delaunay mesh generation and refinement algorithm, in 4th Symposium on Trends in Unstructured Mesh Generation, 2003.
30. G. KARYPIS AND V. KUMAR, A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs, Technical report TR 95-035, Department of Computer Science, University of Minnesota, Minneapolis, MN, 1995.
31. G. KARYPIS AND V. KUMAR, METIS: Unstructured Graph Partitioning and Sparse Matrix Ordering System, Version 2.0, 1995.
32. B. W. KERNIGHAN AND S. LIN, An efficient heuristic procedure for partitioning graphs, Bell Syst. Tech. J., 49 (1970), pp. 291-307.
33. D. T. LEE, Medial axis transformation of a planar shape, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI 4 (1982), pp. 363-369.
34. R. LOHNER AND J. CEBRAL, Parallel advancing front grid generation, in International Meshing Roundtable, Sandia National Labs, Albuquerque, NM, 1999.
35. B. MAERTEN, D. ROOSE, A. BASERMANN, J. FINGBERG, AND G. LONSDALE, DRAMA: A library for parallel dynamic load balancing of finite element applications, in European Conference on Parallel Processing, Toulouse, 1999, pp. 313-316.
36. D. NAVE, N. CHRISOCHOIDES, AND L. P. CHEW, Guaranteed-quality parallel Delaunay refinement for restricted polyhedral domains, in Proceedings of the 18th ACM Symposium on Computational Geometry, ACM Press, New York, 2002, pp. 135-144.
37. P. P. PEBAY AND J. F. PASCAL, A-priori Delaunay-conformity, in 7th International Meshing Roundtable, 1998, Sandia National Labs, pp. 321-333.
38. F. P. PREPARATA AND M. I. SHAMOS, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
39. M. PRICE, C. STOPS, AND G. BUTLIN, A medial object toolkit for meshing and other applications, in Proceedings of 4th International Meshing Roundtable, 1995, Sandia National Labs, pp. 219-229.
40. J. RUPPERT, A Delaunay refinement algorithm for quality 2-dimensional mesh generation, J. Algorithms, 18 (1995), pp. 548-585.
41. R. SAID, N. WEATHERILL, K. MORGAN, AND N. VERHOEVEN, Distributed parallel Delaunay mesh generation, Comput. Methods Appl. Mech. Engrg., 177 (1999), pp. 109-125.
42. E. C. SHERBROOKE, N. M. PATRIKALAKIS, AND F.-E. WOLTER, Differential and topological properties of medial axis transforms, Graphical Models and Image Processing, 55 (1996), pp. 574-592.
43. J. R. SHEWCHUK, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in Applied Computational Geometry: Towards Geometric Engineering, Lecture Notes in Comput. Sci. 1148, M. C. Lin and D. Manocha, eds., Springer-Verlag, 1996, pp. 203-222.
44. J. R. SHEWCHUK, Delaunay Refinement Mesh Generation, Ph.D. thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1997.
45. T. K. H. TAM AND C. ARMSTRONG, 2D finite element mesh generation by medial axis subdivision, Adv. Engrg. Software, 56 (1991), pp. 313-324.
46. C. WALSHAW AND M. CROSS, Mesh partitioning: A multilevel balancing and refinement algorithm, SIAM J. Sci. Comput., 22 (2000), pp. 63-80.
47. C. WALSHAW, M. CROSS, AND M. G. EVERETT, Parallel dynamic graph partitioning for adaptive unstructured meshes, J. Parallel Distributed Comput., 47 (1997), pp. 102-108.
48. F.-E. WOLTER, Cut Locus and Medial Axis in Global Shape Interrogation and Representation, Technical report, Department of Ocean Engineering, Design Laboratory, MIT, Cambridge, MA, 1993.