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Volumn 19, Issue 6, 1998, Pages 2091-2110

Geometric mesh partitioning: Implementation and experiments

Author keywords

Centerpoints; Conformal mapping; Geometric sampling; Graph and geometric algorithms; MATLAB; Mesh partitioning; Moment of inertia; Parallel processing; Separators

Indexed keywords

CENTERPOINTS; GEOMETRIC MESH PARTITIONING; GEOMETRIC SAMPLING; MOMENT OF INERTIA;

EID: 0032204161     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594275339     Document Type: Article
Times cited : (89)

References (47)
  • 1
    • 0003839905 scopus 로고
    • Cutting down on fill using nested dissection: Provably good elimination orderings
    • A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, Berlin, New York
    • A. AGRAWAL AND P. KLEIN, Cutting down on fill using nested dissection: Provably good elimination orderings, in Graph Theory and Sparse Matrix Computation, A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, Berlin, New York, 1993.
    • (1993) Graph Theory and Sparse Matrix Computation
    • Agrawal, A.1    Klein, P.2
  • 2
    • 0024984223 scopus 로고
    • A separator theorem for graphs with an excluded minor and applications
    • ACM, New York
    • N. ALON, P. SEYMOUR, AND R. THOMAS, A separator theorem for graphs with an excluded minor and applications, in Proc. 22nd Symp. on Theory of Computing, ACM, New York, 1990.
    • (1990) Proc. 22nd Symp. on Theory of Computing
    • Alon, N.1    Seymour, P.2    Thomas, R.3
  • 3
    • 0028419680 scopus 로고
    • A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems
    • 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. 101-117.
    • (1994) Concurrency: Practice and Experience , vol.6 , pp. 101-117
    • Barnard, S.T.1    Simon, H.D.2
  • 4
    • 0001259868 scopus 로고
    • An algorithm for partitioning the nodes of a graph
    • E. R. BARNES, An algorithm for partitioning the nodes of a graph, SIAM J. Matrix Anal. Appl., 3 (1982), pp. 541-550.
    • (1982) SIAM J. Matrix Anal. Appl. , vol.3 , pp. 541-550
    • Barnes, E.R.1
  • 6
    • 21844517139 scopus 로고
    • Linear-size nonobtuse triangulation of polygons
    • M. BERN, S. MITCHELL, AND J. RUPPERT, Linear-size nonobtuse triangulation of polygons, Discrete Comput. Geom., 14 (1995), pp. 411-428.
    • (1995) Discrete Comput. Geom. , vol.14 , pp. 411-428
    • Bern, M.1    Mitchell, S.2    Ruppert, J.3
  • 8
    • 85034285354 scopus 로고
    • On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method
    • University California at Los Angeles
    • T. F. CHAN, P. CIARLET JR., AND W. K. SZETO, On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method, Tech. Report CAM 93-14, University California at Los Angeles, 1993.
    • (1993) Tech. Report CAM 93-14
    • Chan, T.F.1    Ciarlet Jr., P.2    Szeto, W.K.3
  • 10
    • 6044229291 scopus 로고
    • A sign cut version of the recursive spectral bisection graph partitioning algorithm
    • Snowbird, UT, June
    • T. F. CHAN AND W. K. SZETO, A sign cut version of the recursive spectral bisection graph partitioning algorithm, in Proc. Fifth SIAM Symp. on Applied Linear Algebra, Snowbird, UT, June 1994, pp. 562-566.
    • (1994) Proc. Fifth SIAM Symp. on Applied Linear Algebra , pp. 562-566
    • Chan, T.F.1    Szeto, W.K.2
  • 11
    • 11744303716 scopus 로고
    • On the Validity of a Front-oriented Approach to Partitioning Large Sparse Graphs with a Connectivity Constraint
    • University California at Los Angeles
    • P. CIARLET JR. AND F. LAMOUR, On the Validity of a Front-oriented Approach to Partitioning Large Sparse Graphs with a Connectivity Constraint, Tech. Report CAM 94-37, University California at Los Angeles, 1994.
    • (1994) Tech. Report CAM 94-37
    • Ciarlet Jr., P.1    Lamour, F.2
  • 12
    • 11744318272 scopus 로고
    • Recursive Partitioning Methods and Greedy Partitioning Methods: A Comparison on Finite Element Graphs
    • University California at Los Angeles
    • P. CIARLET JR. AND F. LAMOUR, Recursive Partitioning Methods and Greedy Partitioning Methods: A Comparison on Finite Element Graphs, Tech. Report CAM 94-9, University California at Los Angeles, 1994.
    • (1994) Tech. Report CAM 94-9
    • Ciarlet Jr., P.1    Lamour, F.2
  • 14
    • 0001751998 scopus 로고
    • Helly's theorem and its relatives
    • AMS, Providence, RI
    • L. DANZER, J. FONLUPT, AND V. KLEE, Helly's theorem and its relatives, in Proc. Sympos. Pure Math. 7, AMS, Providence, RI, 1963, pp. 101-180.
    • (1963) Proc. Sympos. Pure Math. , vol.7 , pp. 101-180
    • Danzer, L.1    Fonlupt, J.2    Klee, V.3
  • 15
  • 17
    • 0027556252 scopus 로고
    • Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics
    • C. FARHAT AND M. LESOINNE, Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics, Internat. J. Numer. Methods Engrg., 36 (1993), pp. 745-764.
    • (1993) Internat. J. Numer. Methods Engrg. , vol.36 , pp. 745-764
    • Farhat, C.1    Lesoinne, M.2
  • 18
    • 0003513369 scopus 로고
    • TOP/DOMDEC - A Software Tool for Mesh Partitioning and Parallel Processing
    • Moffett Field, CA
    • C. FARHAT AND H. SIMON, TOP/DOMDEC - A Software Tool for Mesh Partitioning and Parallel Processing, Tech. report, NASA Ames Research Center, Moffett Field, CA, 1993.
    • (1993) Tech. Report, NASA Ames Research Center
    • Farhat, C.1    Simon, H.2
  • 19
    • 0003631872 scopus 로고
    • A Linear-Time Heuristic for Improving Network Partitions
    • Corporate Research and Development Center, General Electric Co., Schenectady, NY
    • C. M. FIDUCCIA AND R. M. MATTHEYSES, A Linear-Time Heuristic for Improving Network Partitions, Tech. report 82CRD130, Corporate Research and Development Center, General Electric Co., Schenectady, NY, 1982.
    • (1982) Tech. Report 82CRD130
    • Fiduccia, C.M.1    Mattheyses, R.M.2
  • 20
    • 0001350119 scopus 로고
    • Algebraic connectivity of graphs
    • M. FIEDLER, Algebraic connectivity of graphs, Czechoslovak. Math. J., 23 (1973), pp. 298-305.
    • (1973) Czechoslovak. Math. J. , vol.23 , pp. 298-305
    • Fiedler, M.1
  • 21
    • 0016485958 scopus 로고
    • Expected time bounds for selection
    • R. W. FLOYD AND R. L. RIVEST, Expected time bounds for selection, Comm. ACM, 18 (1975), pp. 165-172.
    • (1975) Comm. ACM , vol.18 , pp. 165-172
    • Floyd, R.W.1    Rivest, R.L.2
  • 22
    • 0000114384 scopus 로고
    • An automatic nested dissection algorithm for irregular finite element problems
    • A. GEORGE AND J. W. H. LIU, An automatic nested dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal., 15 (1978), pp. 1053-1069.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1053-1069
    • George, A.1    Liu, J.W.H.2
  • 24
    • 0001345696 scopus 로고
    • A separator theorem for graphs of bounded genus
    • J. R. GILBERT, J. P. HUTCHINSON, AND R. E. TARJAN, A separator theorem for graphs of bounded genus, J. Algorithms, 5 (1984), pp. 391-407.
    • (1984) J. Algorithms , vol.5 , pp. 391-407
    • Gilbert, J.R.1    Hutchinson, J.P.2    Tarjan, R.E.3
  • 25
  • 27
    • 21844512522 scopus 로고
    • A Cartesian nested dissection algorithm
    • M. T. HEATH AND P. RAGHAVAN, A Cartesian nested dissection algorithm, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 235-253.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 235-253
    • Heath, M.T.1    Raghavan, P.2
  • 29
    • 0003223128 scopus 로고
    • A multilevel algorithm for partitioning graphs
    • ACM, San Diego
    • B. HENDRICKSON AND R. LELAND, A multilevel algorithm for partitioning graphs, in Proc. Supercomputing '95, ACM, San Diego, 1995.
    • (1995) Proc. Supercomputing '95
    • Hendrickson, B.1    Leland, R.2
  • 30
    • 0000063845 scopus 로고
    • An improved spectral graph partitioning algorithm for mapping parallel computations
    • B. HENDRICKSON AND R. LELAND, An improved spectral graph partitioning algorithm for mapping parallel computations, SIAM J. Sci. Comput., 16 (1995), pp. 452-469.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 452-469
    • Hendrickson, B.1    Leland, R.2
  • 31
    • 0348164422 scopus 로고
    • Algorithm 63 (PARTITION) and Algorithm 65 (FIND)
    • C. A. R. HOARE, Algorithm 63 (PARTITION) and Algorithm 65 (FIND), Comm. ACM, 4 (1961), p. 321.
    • (1961) Comm. ACM , vol.4 , pp. 321
    • Hoare, C.A.R.1
  • 32
    • 84990479742 scopus 로고
    • An effective heuristic procedure for partitioning graphs
    • B. W. KERNIGHAN AND S. LIN, An effective heuristic procedure for partitioning graphs, The Bell System Tech. J., 49 (1970), pp. 291-308.
    • (1970) The Bell System Tech. J. , vol.49 , pp. 291-308
    • Kernighan, B.W.1    Lin, S.2
  • 33
    • 0003657590 scopus 로고
    • Computer Science and Information Processing 3, Addison-Wesley, Reading, MA
    • D. E. KNUTH, The Art of Computer Programming, 2nd ed., Computer Science and Information Processing 3, Addison-Wesley, Reading, MA, 1981.
    • (1981) The Art of Computer Programming, 2nd Ed.
    • Knuth, D.E.1
  • 34
    • 0024135198 scopus 로고
    • An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms
    • White Plains, NY
    • F. T. LEIGHTON AND S. RAO, An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms, in 29th IEEE Symp. on Foundations of Computer Sci., White Plains, NY, 1988, pp. 422-431.
    • (1988) 29th IEEE Symp. on Foundations of Computer Sci. , pp. 422-431
    • Leighton, F.T.1    Rao, S.2
  • 35
    • 0018457301 scopus 로고
    • A separator theorem for planar graphs
    • R. J. LIPTON AND R. E. TARJAN, A separator theorem for planar graphs, SIAM J. Appl. Math., 36 (1979), pp. 177-189.
    • (1979) SIAM J. Appl. Math. , vol.36 , pp. 177-189
    • Lipton, R.J.1    Tarjan, R.E.2
  • 36
    • 0022733785 scopus 로고
    • Finding small simple cycle separators for 2-connected planar graphs
    • G. L. MILLER, Finding small simple cycle separators for 2-connected planar graphs, J. Comput. System Sci., 32 (1986), pp. 265-279.
    • (1986) J. Comput. System Sci. , vol.32 , pp. 265-279
    • Miller, G.L.1
  • 39
    • 0000812783 scopus 로고
    • Partitioning sparse matrices with eigenvectors of graphs
    • A. POTHEN, H. D. SIMON, AND K.-P. LIOU, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 430-452.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 430-452
    • Pothen, A.1    Simon, H.D.2    Liou, K.-P.3
  • 40
    • 0005809076 scopus 로고
    • Spectral Nested Dissection
    • Department of Computer Science, Pennsylvania State University, State College, PA
    • A. POTHEN, H. D. SIMON, AND L. WANG, Spectral Nested Dissection, Tech. report CS-92-01, Department of Computer Science, Pennsylvania State University, State College, PA, 1992.
    • (1992) Tech. Report CS-92-01
    • Pothen, A.1    Simon, H.D.2    Wang, L.3
  • 42
    • 0042387610 scopus 로고
    • A Projection Technique for Partitioning the Nodes of a Graph
    • University of Waterloo
    • F. RENDL AND H. WOLKOWICZ, A Projection Technique for Partitioning the Nodes of a Graph, Tech. report CORR 90-20, University of Waterloo, 1990.
    • (1990) Tech. Report CORR 90-20
    • Rendl, F.1    Wolkowicz, H.2
  • 43
    • 44949282112 scopus 로고
    • Partitioning of unstructured problems for parallel processing
    • H. D. SIMON, Partitioning of unstructured problems for parallel processing, Comput. Syst. Engrg., 2 (1991), pp. 135-148.
    • (1991) Comput. Syst. Engrg. , vol.2 , pp. 135-148
    • Simon, H.D.1
  • 46
    • 0004922245 scopus 로고
    • Non-deterministic heuristics for automatic domain decomposition in direct parallel finite element calculations
    • R. F. Sincovec et al., ed., SIAM, Philadelphia
    • D. VANDERSTRAETEN, O. ZONE, R. KEUNINGS, AND L. A. WOSLEY, Non-deterministic heuristics for automatic domain decomposition in direct parallel finite element calculations, in Parallel Processing for Scientific Computing, R. F. Sincovec et al., ed., SIAM, Philadelphia, 1993, pp. 929-932.
    • (1993) Parallel Processing for Scientific Computing , pp. 929-932
    • Vanderstraeten, D.1    Zone, O.2    Keunings, R.3    Wosley, L.A.4
  • 47
    • 84990643496 scopus 로고
    • Performance of dynamic load balancing algorithms for unstructured mesh calculations
    • R. D. WILLIAMS, Performance of dynamic load balancing algorithms for unstructured mesh calculations, Concurrency: Practice and Experience, 3 (1991), pp. 457-481.
    • (1991) Concurrency: Practice and Experience , vol.3 , pp. 457-481
    • Williams, R.D.1


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