Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Download or read book Adaptive Methods for Partial Differential Equations written by Ivo Babushka and published by SIAM. This book was released on 1989-01-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
Download or read book Adaptive Computational Methods for Partial Differential Equations written by Ivo Babushka and published by SIAM. This book was released on 1983-01-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.
Download or read book Adaptive Methods for Partial Differential Equations written by and published by . This book was released on 1994 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Control of Parabolic PDEs written by Andrey Smyshlyaev and published by Princeton University Press. This book was released on 2010-07-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.
Download or read book Adaptive Moving Mesh Methods written by Weizhang Huang and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Download or read book Multilevel Adaptive Methods for Partial Differential Equations written by Stephen F. McCormick and published by SIAM. This book was released on 1989-01-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques.
Download or read book Adaptive Methods for Partial Differential Equations written by United States. Army Research Office and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Method of Lines written by A, Vande Wouwer and published by CRC Press. This book was released on 2001-04-18 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's
Download or read book Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems written by Jens Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.
Download or read book Adaptive methods for partial differential equations proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations Rensselaer Polytechnic Institute October 13 15 1988 written by Joseph E. Flaherty and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations written by Ivo Babuska and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.
Download or read book ADAPT 03 Adaptive Methods for Partial Differential Equations written by Slimane Adjerid and published by . This book was released on 2005 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Self Adaptive Methods for Parabolic Partial Differential Equations written by Dennis B. Gannon and published by . This book was released on 1980 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Methods for Partial Differential Equations and Large Scale Computation written by Slimane Adjerid and published by . This book was released on 2005 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Final Report written by and published by . This book was released on 1998 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Download or read book ADAPT 03 Adaptive Methods for Partial Differential Equations and Large scale Computation 11 12 October 2003 Rensselaer Polytechnic Institute Troy New York written by ADAPT and published by . This book was released on 2005 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
