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Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
Many engineering and scientific problems in design, control, and
parameter estimation can be formulated as optimization problems
that are governed by partial differential equations (PDEs). The
complexities of the PDEs - and the requirement for rapid solution -
pose significant difficulties. A particularly challenging class of
PDE-constrained optimization problems is characterized by the need
for real-time solution, i.e., in time scales that are sufficiently
rapid to support simulation-based decision making. Real-Time
PDE-Constrained Optimization, the first book devoted to real-time
optimization for systems governed by PDEs, focuses on new
formulations, methods, and algorithms needed to facilitate
real-time, PDE-constrained optimization. In addition to presenting
state-of-the-art algorithms and formulations, the text illustrates
these algorithms with a diverse set of applications that includes
problems in the areas of aerodynamics, biology, fluid dynamics,
medicine, chemical processes, homeland security, and structural
dynamics. Despite difficulties, there is a pressing need to
capitalize on continuing advances in computing power to develop
optimization methods that will replace simple rule-based decision
making with optimized decisions based on complex PDE simulations.
This book offers a fundamental and practical introduction to the
use of computational methods, particularly finite element methods,
in the simulation of fluid flows in porous media. It is the first
book to cover a wide variety of flows, including single-phase,
two-phase, black oil, volatile, compositional, nonisothermal, and
chemical compositional flows in both ordinary porous and fractured
porous media. In addition, a range of computational methods are
used, and benchmark problems of nine comparative solution projects
organized by the Society of Petroleum Engineers are presented for
the first time in book form. It reviews multiphase flow equations
and computational methods to introduce basic terminologies and
notation. A thorough discussion of practical aspects of the subject
is presented in a consistent manner, and the level of treatment is
rigorous without being unnecessarily abstract. Each chapter ends
with bibliographic information and exercises.
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