Design Sensitivity Analysis: No. 25: Computational Issues of Sensitivity Equation Methods (Frontiers in Applied Mathematics) Book

Recent and ongoing improvements in computer technology have increased the need for efficient and reliable design tools; computational methods have opened the door to making sensitivity analysis a tractable design tool for industries that design and manufacture high-performance products. These industries are increasingly interested in exploiting the advantages of computer-aided design, numerical analysis, and optimal design methods. This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations. The authors use basic models to illustrate the computational issues that one might encounter when applying the SEM in a laboratory or research setting, while providing an overview of applications and computational issues regarding sensitivity calculations performed by way of continuous sensitivity equation methods. Here they focus on the construction and analysis of algorithms for computing sensitivities. For readers already acquainted with the concept of a sensitivity equation, the authors include mathematical background for a deeper understanding of their approach. Finally, the book explores the use of SEMs for applications in the area of computational fluid dynamics, demonstrating that the early examples readers encounter in the book can be observed in the context of a more realistic physical setting. Several color figures are included. Audience This book is intended for advanced undergraduate and graduate students in the areas of numerical analysis, applied and computational mathematics, and for other scientists and engineers interested in modeling, design, control, and optimization of physical systems. Contents Preface; Chapter 1: Introduction; Chapter 2: Mathematical Framework for Linear Elliptic Problems; Chapter 3: Model Problems; Chapter 4: Computational Algorithms; Chapter 5: Numerical Results; Chapter 6: Mathematical Framework for Navier-Stokes Equations; Chapter 7: Two-Dimensional Flow Problems; Chapter 8: Adaptive Mesh Refinement Strategies; Bibliography; IndexRead More