Chapter

Optimal shape design

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Second edition

Published in print September 2009 | ISBN: 9780199546909
Published online February 2010 | e-ISBN: 9780191720482 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199546909.003.0002

Series: Numerical Mathematics and Scientific Computation

 Optimal shape design

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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

Chapter.  9377 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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