Adaptive Computational Methods for Partial Differential Equations PDF Download

Author: Ivo Babushka
Publisher: SIAM
ISBN: 9780898711912
Category : Mathematics
Languages : en
Pages : 272

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Book Description
List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.

Author: Ivo Babuska
Publisher: Springer Science & Business Media
ISBN: 1461242487
Category : Mathematics
Languages : en
Pages : 487

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Book Description
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.

Author: Jens Lang
Publisher: Springer Science & Business Media
ISBN: 3662044846
Category : Computers
Languages : en
Pages : 161

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Book Description
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.

Author: Andrey Smyshlyaev
Publisher: Princeton University Press
ISBN: 1400835364
Category : Mathematics
Languages : en
Pages : 344

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Book Description
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.

Author: Weizhang Huang
Publisher: Springer Science & Business Media
ISBN: 1441979166
Category : Mathematics
Languages : en
Pages : 446

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Book Description
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.

Author: Kenneth Eriksson
Publisher: Cambridge University Press
ISBN: 9780521567381
Category : Mathematics
Languages : en
Pages : 558

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Book Description
This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

Author: Wolfgang Bangerth
Publisher: Birkhäuser
ISBN: 303487605X
Category : Mathematics
Languages : en
Pages : 216

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Book Description
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.

Author: Alfio Quarteroni
Publisher: Springer
ISBN: 3319154311
Category : Mathematics
Languages : en
Pages : 305

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Book Description
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit

Author: Z. J. Wang
Publisher: World Scientific
ISBN: 9814313181
Category : Science
Languages : en
Pages : 471

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Book Description
This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

Author: P. Ladeveze
Publisher: Elsevier
ISBN: 0080525938
Category : Computers
Languages : en
Pages : 539

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Book Description
Mastering modelling, and in particular numerical models, is becoming a crucial and central question in modern computational mechanics. Various tools, able to quantify the quality of a model with regard to another one taken as the reference, have been derived. Applied to computational strategies, these tools lead to new computational methods which are called "adaptive". The present book is concerned with outlining the state of the art and the latest advances in both these important areas.Papers are selected from a Workshop (Cachan 17-19 September 1997) which is the third of a series devoted to Error Estimators and Adaptivity in Computational Mechanics. The Cachan Workshop dealt with latest advances in adaptive computational methods in mechanics and their impacts on solving engineering problems. It was centered too on providing answers to simple questions such as: what is being used or can be used at present to solve engineering problems? What should be the state of art in the year 2000? What are the new questions involving error estimators and their applications?