Patrick Le Tallec - Böcker

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

A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator splitting methods such as alternating methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics.This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator splitting methods (coupled to finite element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods traditionally used to study them. These ideas are then applied to specific classes of mechanical problems.