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.

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.