Numerical Methods in Sensitivity Analysis and Shape Optimization

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, 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

• supplementary online source files and data; readers can test different solution strategies to determine their relevance and efficiency

• supplementary files also offer 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.

Contenu

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 Conclusions A: Subroutine cubspl B: Prototype Programmes for the Optimization Code C: Odyssee User's Manual (short version) D: A Subroutine computing the Gradient with respect to the Grid for the Steady Aerodynamic Example Bibliography Index