A neural network graph partitioning procedure for grid-based domain decomposition

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 5, 1999, Pages 593-613

  Pain, C C ^a   De Oliveira, C R E ^a   Goddard, A J H ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Domain decomposition; Graph partitioning; Mean field theorem; Multi grid; Neural network; Unstructured finite element

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; INTERPOLATION; NEURAL NETWORKS; OPTIMIZATION;

MEAN FIELD THEOREM; NEURAL NETWORK GRAPH PARTITIONING ALGORITHM; PARALLEL DOMAIN DECOMPOSITION SOLUTION METHOD;

GRAPH THEORY;

EID: 0033080238     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990220)44:5<593::AID-NME516>3.0.CO;2-0     Document Type: Article

References (33)

1. G. Karypis and V. Kumar, 'Parallel multi-level graph partitioning', Proc. Int. Parallel Processing Symp., April 1996.
2. C. C. Pain, C. R. E. de Oliveira and A. J. H. Goddard, 'Gradient annealing: an approach to combinatorial optimisation', submitted to Parallel Computing (1997).
3. C. Peterson and J. Anderson, 'Neural networks and NP-complete optimization problems; A performance study on the graph bisection problem', Complex Systems, 2, 59-89 (1988).
4. A. H. Gee, S. Aiyer and R. Prager, 'An analytical framework for optimizing neural networks', Neural Nets, 6, 77-97 (1993).
5. A. Bahreininejad, B. H. V. Topping and A. I. Khan, 'Finite element mesh partitioning using neural networks', Adv. Eng. Software, 27, 103-115 (1996).
6. C. Farhat, 'A simple and efficient automatic FEM domain decomposer', Comput. Struct., 28, 579-602 (1988).
7. W. Chen, M. F. M. Stallmann and E. F. Gehringer, 'Hypercube embedding heuristics: an evaluation', Int. J. Paral. Prog., 18(6), (1989).
8. B. Kernighan and S. Lin, 'An efficient heuristic procedure for partitioning graphs', Bell System Technical J., 291-307 (1970).
9. C. Greenough and R. F. Fowler, 'Partitioning methods for unstructured finite element meshes', Proc. 1994, World Transputer Cong., Como, Italy, 1994, pp. 748-762
10. G. Miller et al., A. George, J. Gilbert and J. Liu, 'Automatic mesh partitioning', in A. George, J. Gilbert and J. Liu (eds.), Sparse Matrix Computations: Graph Theory Issues and Algorithms, Springer, New York, 1993.
11. B. Nour-Omid et al., 'Solving finite element equations on concurrent computers', A. K. Noor, (ed.), Am. Soc. Mech. Engng., 291-307 (1986).
12. G. Bilbro, R. Mann, T. Miller, W. Snyder, D. Van den Bout and M. White, 'Mean field annealing and Neural networks', Advances in Neural Information Processing, Morgan-Kaufmann, 1989, 91-98.
13. J. I. Hopfield, 'Neurons with graded response have collective computational properties like those of two state neurons', Proc. Natl. Acad. Sci. USA, 81, 3088-3092 (1984).
14. J. J. Hopfield and D. W. Tank, 'Neural computations of decisions in optimization problems', Biol. Cybernet., 52, 141-152 (1985).
15. D. Van den Bout and T. Miller, 'Improving the performance of the Hopfield-Tank neural network with normalization and annealing', Biol. Cybernet., 62, 129-139 (1989).
16. D. E. Van Den Bout and T. K. Miller, 'Graph partitioning using annealed neural networks', IEE Trans. Neural Networks, 1 (1990).
17. A. Pothen, H. D. Simon and K. Liou, 'Partitioning sparse matrices with eigenvectors of graphs', SIAM J. Matrix Anal. Appl. 11(3), 430-452 (1990).
18. A. Pothen et al., 'Towards a fast implementation of spectral nested dissection', Proc. Supercomputing, 1992, pp. 42-51.
19. H. Muhlenbein, M. Schomisch and J. Born, 'The parallel genetic algorithm as function optimizer', Parallel Comput., 17, 619-632 (1991).
20. E. H. L. Aarts and P. J. M van Laarhoven, 'Simulated annealing: a pedestrian review of the theory and some applications', Pattern Recognition Theory and Applications', Springer, Berlin, 1987, pp. 179-192.
21. G. Karypis and V. Kumar, 'A fast and high quality multilevel scheme for partitioning irregular graphs', Int. Conf. Parallel Processing (1995).
22. C. Walshaw, M. Cross and M. Everett, 'A localised algorithm for optimising unstructured mesh partitions', Int. J. Supercomputer Appl., 9(4), 280-295 (1995).
23. Bruce Hendrickson and Rober Leland, The chaco user's guide, Technical Report SAND93-2339, Sandia National Laboratories, 1993.
24. C. Walshaw et al., 'Parallel dynamic load-balancing for adaptive unstructured meshes: Extended abstract', Proc. Parallel CFD 97, May 19 1997, Manchester England, 1997.
25. D. E. Keyes and W. G. Gropp, 'A comparison of domain decomposition techniques for elliptical partial differential equations and their parallel implementations', SIAM. J. Statist. Comp., 8, 166-202 (1987).
26. H. Muhlenbein, M. Gorges-Schleuter and O. Kramer, 'Evolution algorithms in combinatorial optimization', Parallel Computing, 7, 65-85 (1988).
27. R. Webster, 'An algebraic multigrid solver for Navier-Stokes problems', Int. J. Numer. Meth. FLuids, 18, 761-780 (1994).
28. M. Luby, 'A simple parallel algorithm for the maximal independent set problem', SIAM J. Comput., 15, 1036-1053 (1986).
29. F. J. Pineda, 'Generalization of backpropagation to recurrent and higher order neural networks', American Inst. Phys., 602-610 (1988).
30. Dan W. Patterson, Artificial Neural Networks - Theory and Applications, Prentice Hall, Englewood cliffs, N.J., ISBN 0-13-295353-6.
31. T. Chockalingam and S. Arunkumar, 'A randomized heuristics for the mapping problem: The genetic approach', Parallel Computing, 18, 1157-1165 (1992).
32. D. Whitley, T. Starkweather and C. Bogart, 'Genetic algorithms and neural networks optimizing connections and connectivity', Parallel Comput., 347-361 (1990).
33. G. Miller et al., 'A unified geometric approach to graph separators', Proc. 31st Annual Symp. on Foundations of Computer Science', 1991, pp. 538-547.