This book results from the authors work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in his postdoctoral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and algorithms which lead to efficient 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 implementations are discussed at each level as the complexity of the problems increase, supporting with enough number of computational examples. It consists of two parts: first part deals with time dependent optimization problems with applications in environmental engineering and the second part deals with steady state optimization problems, in which the PDEs are solved using semi-iterative or pseudo-time-stepping techniques, with applications in aerodynamics.
This book will be useful for scientists and engineers who are looking for efficient numerical methods for PDE-constrained optimization problems. It will be helpful for graduate and Ph.D. students in applied mathematics, aerospace engineering, mechanical engineering, civil engineering and computational engineering during their training and research. This also will provide exciting research and development areas involving realistic applications.
Author(s): Subhendu Bikash Hazra
Series: Lecture Notes in Applied and Computational Mechanics 0049
Edition: 1st Edition.
Publisher: Springer
Year: 2010
Language: English
Pages: 214
3642015018......Page 1
Large-Scale
PDE-Constrained Optimization
in Applications......Page 4
Preface......Page 6
Acknowledgements......Page 8
Contents......Page 10
Introduction......Page 23
Introduction......Page 27
Turbulence and Its Modeling......Page 36
Analytic Aspects of the PDEs......Page 39
Unconstrained Optimization Problem......Page 41
Constrained Optimization Problem......Page 43
Introduction......Page 48
General form of the Multiphase Flow Equations......Page 49
The Forward Simulation Problem......Page 55
Discretization......Page 57
The Software System MUFTE UG......Page 60
Introduction......Page 61
The Multiple Shooting Parameter Estimation Approach......Page 62
A Reduced Generalized Gauss-Newton Method......Page 63
Computation of (Inexact) Derivatives......Page 65
Isothermal Case (Two-Phase flow)......Page 68
Conclusions......Page 79
Introduction......Page 81
The Optimization Problem and Pseudo-unsteady Formulation of the KKT Conditions......Page 83
Reduced SQP Methods......Page 85
Pseudo-Time-Stepping for Optimization Problems......Page 87
Application to a Model Problem......Page 88
Analysis of the Hessian......Page 89
Numerical Implementation......Page 91
Results and Discussion......Page 92
Conclusions......Page 96
Introduction......Page 97
Detailed Equations of the Aerodynamic Shape Optimization Problem in 2D......Page 99
Discretization......Page 102
Reduced Hessian Updates......Page 108
Numerical Results and Discussion......Page 111
Conclusions......Page 120
Pseudo-Time-Stepping for the Constrained Optimization Problem......Page 121
Numerical Results and Discussion......Page 125
Conclusions......Page 132
Introduction......Page 133
Scalar State Constraints......Page 134
Numerical Results and Discussion......Page 138
Conclusions......Page 148
Introduction......Page 150
The Multigrid Algorithm......Page 151
Numerical Results and Discussion......Page 152
Conclusions......Page 167
Introduction......Page 169
The Multigrid Algorithm......Page 170
Numerical Results and Discussions......Page 171
Conclusions......Page 187
Introduction......Page 189
Detailed Equations of the Aerodynamic Shape Optimization Problem......Page 190
Numerical Results and Discussion......Page 197
Conclusions......Page 202
References......Page 203
