did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

9780817643225

Numerical Methods in Sensitivity Analysis and Shape Optimization

by ;
  • ISBN13:

    9780817643225

  • ISBN10:

    0817643222

  • Edition: CD
  • Format: Hardcover
  • Copyright: 2002-12-01
  • Publisher: Birkhauser

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: $99.99 Save up to $81.43
  • Rent Book $90.24
    Add to Cart Free Shipping Icon Free Shipping

    TERM
    PRICE
    DUE
    SPECIAL ORDER: 1-2 WEEKS
    *This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.

Supplemental Materials

What is included with this book?

Summary

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.

Table of Contents

Outline and Notation ix
Acknowledgements xv
Basic Formulations
1(24)
A generic example
1(3)
Abstract formulation of a shape optimization problem
4(3)
General framework and notation
4(1)
Discretization
5(2)
Sensitivity analysis
7(1)
Shape parametrization
8(4)
Cubic spline interpolation
8(2)
Wing profile parametrization by cubic splines
10(1)
Parametrization of a shape deformation
11(1)
Mesh construction and deformation
12(7)
Mesh construction
13(2)
A simple mesh deformation algorithm
15(1)
A sophisticated mesh deformation algorithm
16(3)
Exercises
19(6)
Mesh generation around a wing profile
19(2)
A software package for mesh deformation
21(1)
Cubic spline shape parametrization
21(4)
Finite Dimensional Optimization
25(10)
Basic problem and notation
25(1)
Necessary conditions of optimality
26(2)
Optimality conditions of Euler--Lagrange
28(6)
Equality constraints
28(2)
Inequality constraints
30(4)
Exercises
34(1)
Newton's Algorithms
35(18)
The problem to solve
35(1)
Newton's algorithm
36(2)
Unconstrained optimization
38(3)
Basic algorithms
38(1)
Quasi-Newton variant
38(1)
GMRES solution
39(2)
Line search
41(1)
Constrained optimization
41(4)
Basic algorithm
41(1)
Han's penalized cost function
42(1)
Line search
43(2)
Complement: gradient based algorithms
45(2)
Complement: detailed description of the GMRES algorithm
47(4)
Description
47(1)
The main steps
47(2)
Final algorithm
49(1)
Convergence analysis
50(1)
Exercises
51(2)
Constrained Optimization
53(18)
Optimality conditions
53(1)
Interior point algorithms
54(2)
Introduction
54(1)
Basic philosophy
54(1)
A simplified interior point algorithm
55(1)
Interior point algorithms with deflection
56(8)
Introduction
56(3)
Central trajectories
59(1)
Centered trajectory algorithms
60(1)
Herskovits' algorithm without equality constraints
61(2)
Introduction of equality constraints
63(1)
Using an interior point algorithm
64(7)
Code's description
64(3)
Example
67(1)
Application to optimum design problems
67(1)
Exercises
68(3)
Automatic Differentiation
71(16)
Introduction
71(1)
Computing gradients by finite differences
71(1)
Schematic structure of a computer code
72(2)
Automatic differentiation
74(8)
Examples of automatic differentiation by Odyssee
82(2)
Exercises
84(3)
Computing Gradients by Adjoint States
87(10)
Structure of the cost function
87(1)
A Lagrangian approach
88(2)
Application to automatic differentiation in adjoint mode
90(1)
Numerical calculation of the gradient of the cost function
91(1)
Calculation of the Hessian
92(5)
Applications
97(40)
Introduction
97(1)
Inverse problem in diffusion
97(10)
Shape optimization in aerodynamics
107(17)
Navier--Stokes equations
107(1)
Euler's equations
108(1)
NSC2KE solver
109(3)
Input-Output data files
112(12)
Computing the gradient in aeroelasticity
124(13)
One Shot Methods
137(24)
Introduction
137(2)
Global algorithm
139(1)
Reduction of the linear systems
140(2)
Line search
142(2)
Detailed algorithm
144(5)
Numerical examples
149(3)
An example without inequality constraints
150(1)
Constrained torsion
151(1)
Conclusion
152(9)
Conclusions
161(2)
A Subroutine cubspl 163(2)
B Prototype Programmes for the Optimization Code 165(8)
Main programme
165(5)
Cost function and constraints
170(1)
Gradients
171(1)
Typical values of control parameters
172(1)
C Odyssee User's Manual (short version) 173(2)
D A Subroutine computing the Gradient with respect to the Grid for the Steady Aerodynamic Example 175(14)
A typical aerodynamic cost function
175(7)
A full subroutine for computing the gradient with respect to the grid
182(7)
Bibliography 189(4)
Index 193

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program