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Measure theoretical approach for optimal shape design of a nozzle

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Abstract

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain.

By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

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Authors and Affiliations

  1. Dept. of Mathematics, Ferdowsi University of Mashhad, 91775-1159, Mashhad, Iran

    M. H. Farahi & A. V. Kamyad

  2. Dept. of Mathematics, Damghan University of Basic Sciences, 36715-364, Damghan, Iran

    A. H. Borzabadi

  3. Aerospace Research Inst., 15875-3885, Tehran, Iran

    H. H. Mehne

Authors
  1. M. H. Farahi
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  2. A. H. Borzabadi
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  3. H. H. Mehne
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  4. A. V. Kamyad
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Corresponding author

Correspondence to M. H. Farahi.

Additional information

Mohammad Hadi Farahi received his B. Sc from Ferdowsi University of Mashhad, Mashhad, Iran, M. Sc from Brunel University, U. K. and Ph. D. at Leeds University, U. K. At the moment he is associate professor at the College of Mathematics, Ferdowsi University of Mashhad, Iran and his research area are optimal control, optimization, approximation theory and numerical analysis.

Akbar Hashemi Borzabadi received his B. Sc from Birjand University, Iran and his M. Sc from Ferdowsi University of Mashhad. He is lecturer in Damghan University of Basic Sciences and at the moment he is Ph. D student in Ferdowsi University of Mashhad. His research interests center on optimal control of distributed parameter systems and optimal path planning.

Hamed Hashemi Mehne received his B. Sc and M. Sc from Ferdowsi University of Mashhad, Iran. He is lecturer in Aerospace Research Inst. of Tehran, Iran and at the moment he is Ph. D student in Ferdowsi University of Mashhad. His research interests center on optimal shape design and optimal control.

Ali Vahidian Kamyad received his B. Sc from Ferdowsi University of Mashhad, Mashhad, Iran, M. Sc from Institute of Mathematics Tehran, Iran and Ph. D at Leeds University, Leeds, England under supervisior of J. E. Rubio. Since 1972 he has been at the Ferdowsi University of Mashhad, he is professor at the College of Mathematics, Ferdowsi University of Mashhad, Iran and his research interests are mainly on optimal control of distributed parameter systems and applications of fuzzy theory.

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Farahi, M.H., Borzabadi, A.H., Mehne, H.H. et al. Measure theoretical approach for optimal shape design of a nozzle. JAMC 17, 315–328 (2005). https://doi.org/10.1007/BF02936058

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  • DOI: https://doi.org/10.1007/BF02936058

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