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Applied Shape Optimization for Fluids$
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Bijan Mohammadi and Olivier Pironneau

Print publication date: 2009

Print ISBN-13: 9780199546909

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199546909.001.0001

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Optimal shape design

Optimal shape design

Chapter:
(p.6) 2 Optimal shape design
Source:
Applied Shape Optimization for Fluids
Author(s):

Bijan Mohammadi

Olivier Pironneau

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199546909.003.0002

This chapter concerns optimal shape design by local shape variations for simple linear problems, discretized by the finite element method. The goal is to provide tools to do the same with the complex partial differential equations of CFD. It gives a general presentation of optimal shape design problems and of their solution by gradient algorithms. In particular, it discusses the existence of solutions, sensitivity analysis at the continuous, and discrete levels, and points out the implementation problems for each case. The chapter is therefore an introduction to the rest of the book. It summarizes the current knowhow for OSD (except topological optimization) as well as global optimization methods such as evolutionary algorithms.

Keywords:   optimal shape design, existence, solutions, discrete levels

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