Large-Scale PDE-Constrained Optimization in Applications (Lecture Notes in Applied and Computational Mechanics, 49)

✍ Scribed by Subhendu Bikash Hazra

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 216
• Category: Library

✦ Synopsis

With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.

✦ Table of Contents

Title Page
Preface
Contents
List of Figures
List of Tables
Acronyms
Introduction
Partial Differential Equations in Mathematical Modeling of Fluid Flow Problems
Introduction
Non-dimensionalization
Turbulence and Its Modeling
Analytic Aspects of the PDEs
PDE-Constrained Optimization Methods
Unconstrained Optimization Problem
Constrained Optimization Problem
Part I Applications in Environmental Engineering
Mathematical Model of Multiphase Flow through Porous Media
Introduction
General form of the Multiphase Flow Equations
The Forward Simulation Problem
Discretization
The Software System MUFTE UG
Parameter Identification in Multiphase Flow through Porous Media
Introduction
Least-Squares Formulation
The Multiple Shooting Parameter Estimation Approach
A Reduced Generalized Gauss-Newton Method
Computation of (Inexact) Derivatives
Numerical Results and Discussion
Conclusions
Part II Applications in Aerodynamics
Simultaneous Pseudo-Time-Stepping for PDE-Model Based Optimization Problems
Introduction
The Optimization Problem and Pseudo-unsteady Formulation of the KKT Conditions
Reduced SQP Methods
Pseudo-Time-Stepping for Optimization Problems
Application to a Model Problem
Analysis of the Hessian
Numerical Implementation
Results and Discussion
Conclusions
Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping
Introduction
Pseudo-Time-Stepping for Optimization Problems
Detailed Equations of the Aerodynamic Shape Optimization Problem in 2D
Discretization
Reduced Hessian Updates
Numerical Results and Discussion
Conclusions
Indirect Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping
Introduction
Pseudo-Time-Stepping for the Constrained Optimization Problem
Numerical Results and Discussion
Conclusions
Direct Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping
Introduction
Scalar State Constraints
Numerical Results and Discussion
Conclusions
Multigrid One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization
Introduction
The Multigrid Algorithm
Numerical Results and Discussion
Conclusions
Multigrid One-Shot Pseudo-Time-Stepping Method for State Constrained Aerodynamic Shape Optimization
Introduction
The Multigrid Algorithm
Numerical Results and Discussions
Conclusions
One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization Using the Navier-Stokes Equations
Introduction
Detailed Equations of the Aerodynamic Shape Optimization Problem
Numerical Results and Discussion
Conclusions
References
Index