Abstract
This paper presents an outline of a parallel algorithm for the identification of parameters in the Swartzendruber formula. This formula appears in the mathematical model of the prelinear filtration of ground water. The parameter inverse problem is formulated as an appropriate control problem. The idea of the proposed algorithm (called MSP) is to review large areas of the domain through proper, parallel investigation of many parts of it. The results of numerical tests are included. Some improvements to the algorithm are also proposed.
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R.H. Byrd, C.L. Dert, A.H.G. Rinnoy Kan and R.B. Schnabel. Concurrent stochastic methods for global optimization. Math. Programming 46 (1990) 1–30.
Z. Denkowski, S. Migórski, R. Schaefer and H. Telega. Theoretical and practical aspects of inverse problems for nonlinear filtration process. In H.D. Bui et al. (eds), Inverse Problems in Engineering Mechanics, A.A. Balkema, Rotterdam, (1994) 403–409.
Z. Denkowski, R. Schaefer and H. Telega. On identification problems for prelinear filtration of ground water. In K. Morgan et al. (eds), Finite Elements in Fluids, Barcelona, Pineridge Press, (1993) 878–886.
H. S. Morse Practical parallel computing. AP Professional, Cambridge USA 1994.
Pranay Chaudhuri Parallel Algorithms Design and Analysis. Prentice Hall of Australia Pty Ltd 1992.
A.H.G. Rinnoy Kan and G.T. Timmer. Stochastic methods for global optimization, Amer. J. Math. Management Sci. (1984) 7–40.
A.H.G. Rinnoy Kan and G.T. Timmer. Global optimization. Handbooks in Operations Research and Management Science, Vol. I: Optimization, G.L. Nemhauser, A.H.J. Rinnoy Kan and M.J. Todd, eds. North-Holland, (1989) 631–662.
R. Schaefer. Numerical models of the prelinear filtration. Jagiellonian University Press, Cracow, 1991 (in polish).
R. Schaefer and S. Sedziwy. Filtration in cohesive soils: modeling and solving. In K. Morgan et al. (eds), Finite Elements in Fluids, Barcelona, Pineridge Press, (1993) 887–891,.
R. Schaefer and H. Telega. A hybrid genetic approach to the hydraulic conductivity identification in earthen dams. In J. Arabas (ed) Warsaw University of Technology, Algorytmy ewolucyjne (Evolution algorithms), Proc. of I Polish Conference on Evolution Algorithms, Murzasihle, 1996.
R. B. Schnabel. A view of the limitations, opportunities, and challenges in parallel nonlinear optimization. Parallel Computing, 21 (1995) 875–905.
D. Swartzendruber. Modification of Darcy's law for the flow of water in soils. Soil. Sci. 93, (1961) 23–29.
H. Telega. Nonlinear programming approach to the inverse problem of water percolation through cohesive soils. In K. Morgan et al. (eds), Finite Elements in Fluids, Barcelona, Pineridge Press, (1993) 892–899.
H. Telega. Distributed and Parallel computations for solving identification problems. In M. Kasiak et al. (eds), Proc. of XII Polish Conference on Computer Methods in mechanics, Warsaw-Zegrze (1995).
A.A. Törn. Cluster analysis using seed points and density-determined hyperspheres as an aid to global optimization. IEEE Transactions on Systems, Man, and Cybernetics, p. 610, (1977).
R. Wit. Metody programowania nieliniowego (Methods of Nonlinear Programming). WNT, Warszawa, (1986) (in Polish).
W. Wolski, A. Szymański, A. Mirecki, Z. Lechowicz, R. Larson, J. Hartlen, K. Garbulewski, U. Bergdahl. Two stage — constructed embankment on organic soils, Swedish Geotechnical Institute Reports, no 32, Linköping, (1988).
R. Zieliński, P. Neumann. Stochastische Verfahren zur Suche nach dem Minimum einer Funktion. Akademie-Verlag, Berlin (1983) (Polish translation Stochastyczne metody poszukiwania minimum funkcji, WNT Warszawa 1986).
MINUIT, Function Minimization and Error Analysis. Reference Manual, CERN Program Library Long Writeup D506 Geneva (1992).
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Telega, H. (1997). Parallel and distributed computations in a parameter inverse problem. In: Palma, J.M.L.M., Dongarra, J. (eds) Vector and Parallel Processing — VECPAR'96. VECPAR 1996. Lecture Notes in Computer Science, vol 1215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62828-2_120
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DOI: https://doi.org/10.1007/3-540-62828-2_120
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