Large-Scale PDE-Constrained Optimization in Applications

1. Front Matter

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2. Introduction

   1. Introduction

      • Subhendu Bikash Hazra

      Pages 1-4

   2. Partial Differential Equations in Mathematical Modeling of Fluid Flow Problems

      • Subhendu Bikash Hazra

      Pages 5-18

   3. PDE-Constrained Optimization Methods

      • Subhendu Bikash Hazra

      Pages 19-25

3. Part I: Applications in Environmental Engineering

   1. Front Matter

      Pages 27-27

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   2. Mathematical Model of Multiphase Flow through Porous Media

      • Subhendu Bikash Hazra

      Pages 29-41

   3. Parameter Identification in Multiphase Flow through Porous Media

      • Subhendu Bikash Hazra

      Pages 43-62

4. Part II: Applications in Aerodynamics

   1. Front Matter

      Pages 63-63

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   2. Simultaneous Pseudo-Time-Stepping for PDE-Model Based Optimization Problems

      • Subhendu Bikash Hazra

      Pages 65-80

   3. Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping

      • Subhendu Bikash Hazra

      Pages 81-104

   4. Indirect Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping

      • Subhendu Bikash Hazra

      Pages 105-116

   5. Direct Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping

      • Subhendu Bikash Hazra

      Pages 117-133

   6. Multigrid One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization

      • Subhendu Bikash Hazra

      Pages 135-153

   7. Multigrid One-Shot Pseudo-Time-Stepping Method for State Constrained Aerodynamic Shape Optimization

      • Subhendu Bikash Hazra

      Pages 155-174

   8. One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization Using the Navier-Stokes Equations

      • Subhendu Bikash Hazra

      Pages 175-188

5. Back Matter

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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.

• Navier-Stokes equation
• RSI
• algorithm
• algorithms
• linear optimization
• mathematical modeling
• mechanical engineering
• model
• modeling
• numerical methods
• optimization
• porous media
• simulation
• fluid- and aerodynamics

From the reviews:

“This book is based on the habilitation thesis … of the author. It documents the author’s extensive experience with two classes of optimization algorithms applied to two particular PDE constrained optimization problems. … The book offers a wealth of practical information about the design and numerical performance of specific optimization algorithms in two specific application settings. Engineers ad practitioners who are experienced in computational design and who seek practical numerical recipes to solve optimization problems in these two application areas will find the monograph useful.” (Pavel B. Bochev, Mathematical Reviews, Issue 2012 b)

• FG Strömungsdynamik, FB Maschinenbau, TU Darmstadt, Darmstadt, Germany

  Subhendu Bikash Hazra

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