Measure theoretical approach for optimal shape design of a nozzle

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...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2005-03, Vol.17 (1-2), p.315-328
Main Authors: Farahi, M H, Borzabadi, A H, Mehne, H H, Kamyad, A V
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Boundary value problems
Computation
Domains
Linear programming
Mathematical analysis
Mathematical models
Nonlinearity
Nozzles
Operations research
Optimization
Studies
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Summary: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.
ISSN:1598-5865
1865-2085
DOI:10.1007/BF02936058