Advances In Numerical Partial Differential Equations And Optimization
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Advances In Numerical Partial Differential Equations And Optimization
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Author : Susana Gomez
language : en
Publisher:
Release Date : 1991
Advances In Numerical Partial Differential Equations And Optimization written by Susana Gomez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Advances In Numerical Partial Differential Equations And Optimization
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Author : Susana Gomez
language : en
Publisher: SIAM
Release Date : 1990-12-31
Advances In Numerical Partial Differential Equations And Optimization written by Susana Gomez and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-31 with Mathematics categories.
The papers in this volume emphasize the numerical aspects of three main areas: optimization, linear algebra and partial differential equations. Held in January, 1989, in Yucatan, Mexico, the workshop was organized by the Institute for Research in Applied Mathematics of the National University of Mexico in collaboration with the mathematical Sciences Department at Rice University.
Advances In Numerical Partial Differential Equations And Optimization Proceedings Of The Mexico United States Workshop Institute For Research In Applied Mathematics And Systems National University Of Mexico
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Author :
language : en
Publisher:
Release Date : 1989
Advances In Numerical Partial Differential Equations And Optimization Proceedings Of The Mexico United States Workshop Institute For Research In Applied Mathematics And Systems National University Of Mexico written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Real Time Pde Constrained Optimization
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Author : Lorenz T. Biegler
language : en
Publisher: SIAM
Release Date : 2007-01-01
Real Time Pde Constrained Optimization written by Lorenz T. Biegler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
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. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.
Petsc For Partial Differential Equations Numerical Solutions In C And Python
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Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22
Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Optimization And Control For Partial Differential Equations
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Author : Roland Herzog
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07
Optimization And Control For Partial Differential Equations written by Roland Herzog and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with Mathematics categories.
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Optimization With Pde Constraints
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Author : Michael Hinze
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-16
Optimization With Pde Constraints written by Michael Hinze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-16 with Mathematics categories.
Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
Computational Optimization Of Systems Governed By Partial Differential Equations
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Author : Alfio Borzi
language : en
Publisher: SIAM
Release Date : 2012-01-26
Computational Optimization Of Systems Governed By Partial Differential Equations written by Alfio Borzi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-26 with Mathematics categories.
This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.
Numerical Methods And Optimization
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Author : Éric Walter
language : en
Publisher: Springer
Release Date : 2014-07-22
Numerical Methods And Optimization written by Éric Walter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Technology & Engineering categories.
Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods – a Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to · discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; · understand the principles behind recognized algorithms used in state-of-the-art numerical software; · learn the advantages and limitations of these algorithms, to facilitate the choice of which pre-existing bricks to assemble for solving a given problem; and · acquire methods that allow a critical assessment of numerical results. Numerical Methods – a Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied mathematics.
Numerical Methods For Elliptic And Parabolic Partial Differential Equations
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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26
Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.