Numerical Methods in Sensitivity Analysis and Shape Optimization

By: James Penrice, E. Laporte, Emmanuel Laporte

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Hardcover | 13 December 2002

At a Glance

Hardcover
216 Pages

Dimensions(cm)
24.13 x 15.88 x 2.54

Hardcover

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Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book/interactive CD-ROM presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers.

Key features of this original, progressive, and comprehensive approach:

* description of mathematical background and underlying tools

* up-to-date review of grid construction and control, optimization algorithms, software differentiation and gradient calculations

* practical solutions for implementation in many real-life problems

* solution of illustrative examples and exercises

* basic mathematical programming techniques used to solve constrained minimization problems are presented; these fairly self-contained chapters can serve as an introduction to the numerical solution of generic constrained optimization problems

* companion CD-ROM contains source files and data; readers can test different solution strategies to determine their relevance and efficiency

* CD-ROM also offers software building, updating computational grids, performing automatic code differentiation, and computing basic aeroelastic solutions.

Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. The work is suitable as a textbook for graduate courses in any of the topics mentioned above, and as a reference text.

Industry Reviews

"The focus of this book is finite-dimensional constrained optimization problems which arise by discretizing shape optimization problems of [a particular] type.... In the major part of the book the authors recall the basic principles of constrained optimization, describe variants of Newton's algorithm to solve the necessary optimality conditions and discuss analytic and automatic techniques to calculate the derivative of j with respect to the design variable z." -Mathematical Reviews

"Many illustrative examples and numerical results clarify the presentation. The book will be of interest to graduate students involved in mathematical modeling and simulation, as well as to engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design." -Zentralblatt Math

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Outline and Notation
Acknowledgements
Basic Formulations Finite
Dimensional Optimization
Newton's Algorithms
Constrained Optimization
Automatic Differentiation
Computing Gradients by Adjoint States
Applications One Shot Methods

Prototype Programmes for the Optimization Code
Odyssee User's Manual (short version)
A Subroutine computing the Gradient with respect to the Grid for the Steady Aerodynamic
Example
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Numerical Methods in Sensitivity Analysis and Shape Optimization

At a Glance

Hardcover

Industry Reviews

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How to return your order

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