Large-Scale PDE-Constrained Optimization in Applications

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.

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.

Partial Differential Equations in Mathematical Modeling of Fluid Flow Problems.- PDE-Constrained Optimization Methods.- I: Applications in Environmental Engineering.- Mathematical Model of Multiphase Flow through Porous Media.- Parameter Identification in Multiphase Flow through Porous Media.- II: Applications in Aerodynamics.- Simultaneous Pseudo-Time-Stepping for PDE-Model Based Optimization Problems.- Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping.- Indirect Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping.- Direct Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping.- Multigrid One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization.- Multigrid One-Shot Pseudo-Time-Stepping Method for State Constrained Aerodynamic Shape Optimization.- One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization Using the Navier-Stokes Equations.