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Optimal shape design for a nozzle problem

Published online by Cambridge University Press:  17 February 2009

R. Butt
R. Butt
Affiliation:
Centre for Advanced Studies in Pure & Appl. Maths, Bahauddin Zakaryia University, Pakistan
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Abstract

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In this paper, a gradient method is developed for the optimal shape design in a nozzle problem described by variational inequalities. It is known that this method can be used for the optimal shape design for systems described by partial differential equations (Pironneau [6]); it is used here for differential inequalities by taking limits of the expression resulting from an approximations scheme. The computations are done by the finite element method; the gradient of the criteria as a function of the coordinates nodes is computed, and the performance criterion is then minimised by the gradient method.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 1 , July 1993 , pp. 71 - 86
Copyright
Copyright © Australian Mathematical Society 1993

References

[1] Angrand, F., “Numerical method for optimal shape design in aerodynamics”, 3 Cycle Thesis, University of Paris 6, 1980.Google Scholar
[2] Butt, R., “Optimal shape design for differential inequalities”, Ph. D. Thesis, Leeds University, U.K., 1988.Google Scholar
[3] Ciarlet, P., The finite element method (North Holland, Amsterdam, 1979).Google Scholar
[4] Glowinski, R., Lions, J. L. and Tremolieres, R., Theory of variational inequalities (North Holland, Amsterdam, 1981).Google Scholar
[5] Lions, J. L., “Some topics on variational inequalities and applications”, in New developments in differential equations (ed. Eckaus, W.), (North-Holland Publishing Company, 1976) 1–38.Google Scholar
[6] Pironneau, O., Optimal shape design for elliptic systems (Springer-Verlag, New York, 1984).Google Scholar