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Boundary Element & Linear Programming Method in Optimization of Partial Differential Equation Systems

  • T. Futagami
Part of the Boundary Elements book series (BOUNDARY, volume 3)

Abstract

By combining “boundary element method with linear programming, a new optimization technique (boundary element & linear programming method, or, the BE&LP method) is developed and systematized in order to control partial differential equation systems with both equality or inequality constraints and an objective function. The BE&LP method is applied to optimal control problems in heat conduction phenomena. Minimization of total of the controllable loads to meet with temperature requirements is performed by using simplex method of linear programming. The tractability in both the boundary conditions and the equality or inequality constraints makes sure that the method becomes a powerful technique for several new types of boundary value problems.

Keywords

Optimal Control Problem Boundary Element Boundary Element Method Inequality Constraint Controllable Load 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aguado, E. and Remson, I. (1974), “Ground-Water Hydraulics in Aquifer Management,” Journal of the Hydarualics Division, ASCE, Vol. 100, No. HY1, pp. 103–118.Google Scholar
  2. 2.
    Bolteus, L. and Tullberg, O. (1980), “Boundary Element Method Applied to Two-Dimensional Heat Conduction in Non-homogeneous Media,” Advances in Engineering Software, Vol. 2, No. 3, pp. 131–137.CrossRefMATHGoogle Scholar
  3. 3.
    Brebbia, C.A. (1978), “The Boundary Element Method for Engineers,” Pentech Press, London.Google Scholar
  4. 4.
    Brebbia, C.A. (1980), “Fundamental of Boundary Elements,” New Developments in Boundary Element Methods, Proceedings of the Second International Seminar on Recent Advances in Boundary Element Methods, CML Publications, pp. 3-33.Google Scholar
  5. 5.
    Dantzig, B.G. (1963), “Linear Programming and Extensions,” Princeton University Press.Google Scholar
  6. 6.
    Dubois, M. and Buysse, M. (1980), “Transient Heat Transfer Analysis by the Boundary Integral,” New Developments in Boundary Element Methods, Proceedings of the Second International Seminar on Recent Advances in Boundary Element Methods, CML Publications, 137-154.Google Scholar
  7. 7.
    Futagami, T. (1975), “Finite Element & Linear Programming Method and Water Pollution Control,” Proceedings of 16th Congress of the International Association for Hydraulics Research, Vol. 3, c7, pp. 54–61.Google Scholar
  8. 8.
    Futagami, T., Tamai, N. and Yatsuzuka, M. (1976), “FEM Coupled with LP for Water Pollution Control,” Journal of Hydraulic Division, ASCE, Vol. 102, Hy7, pp. 881–897.Google Scholar
  9. 9.
    Futagami, T. (1976), “Several Mathematical Methods in Water Pollution Control — THE FINITE ELEMENT & LINEAR PROGRAMMING METHOD and the Related Methods,” HIT-C-EH-1, Department of Civil Engineering, Hiroshima Institute of Technology.Google Scholar
  10. 10.
    Gass, I.S. (1969), “Linear Programming,” 3rd ed, McGraw-Hill Kogakusha.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • T. Futagami
    • 1
  1. 1.Hiroshima Institute of TechnologyItsukaichi, HiroshimaJapan

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