Defect Correction Methods
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Defect Correction Methods
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Author : K. Böhmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Defect Correction Methods written by K. Böhmer 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 2012-12-06 with Mathematics categories.
Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.
Defect Correction Methods For Fluid Flows At High Reynolds Numbers
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Author : Alexander E. Labovsky
language : en
Publisher: CRC Press
Release Date : 2025-07-17
Defect Correction Methods For Fluid Flows At High Reynolds Numbers written by Alexander E. Labovsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-17 with Mathematics categories.
Defect Correction Methods for Fluid Flows at High Reynold’s Numbers presents the mathematical development of defect correction methods (DCM) in application to fluid flow problems in various settings. We will show several approaches to applying the DCM ideas in computational fluid dynamics (CFD) – from a basic idea of controlling the flow by the means of increased diffusion, to the state-of-the-art family of novel, DCM-based turbulence models. The main idea of the methods presented in this book, is to use defect correction in turbulence modelling; additionally, several methods will also be presented, that aim at reducing the time discretization error. Features · Provides a road map, starting from the ideas of minimally invasive controlling of turbulent flows, to the ways of improving the existing regularization techniques with DCM, to the ideas of ‘full defect correction’ in both space and time and, finally, to the more complex embedding of the DCM into turbulence modelling by the ‘correction’ of the whole turbulence model · Can be used for teaching a topics course on a Masters or Ph.D. level. It is even more suitable as a reference for CFD theorists and practitioners, with most of the methods being minimally invasive and, therefore, easy to implement in the existing/legacy codes · Discusses the current challenges in turbulence modelling with defect correction, showing several possible directions for future developments. Two source codes are provided – one for a regularization technique and another for a novel turbulence model – in order to give an interested researcher a quick start to the topic of DCM in CFD.
Domain Decomposition Methods In Science And Engineering
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Author : Ralf Kornhuber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Domain Decomposition Methods In Science And Engineering written by Ralf Kornhuber 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 2006-03-30 with Mathematics categories.
Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.
Multigrid Methods
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Author : Ulrich Trottenberg
language : en
Publisher: Academic Press
Release Date : 2001
Multigrid Methods written by Ulrich Trottenberg and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Multigrid Methods
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Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1987-12-01
Multigrid Methods written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-01 with Mathematics categories.
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
Numerical Treatment Of Coupled Systems
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Numerical Treatment Of Coupled Systems written by Wolfgang Hackbusch 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 2013-04-17 with Technology & Engineering categories.
The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1995, January 20-22, with the 11th Kiel-Seminar on the special topic Numerical Treatment of Coupled Systems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two survey lectures. Different kinds of couplings are considered in this volume. The coupling of different components may occur in the physical model. On the other hand, a coupling of subsystems can be generated by the numerical solution technique. General examples of the latter kind are the domain decomposition (see p. 128) or subspace decomposition (p. 117). The local defect correction method couples different discretizations of the same problem in order to improve the results, although the basic linear system to be solved remains unchanged (p. 47). In general, the aim of the numerical coupling is to make use of (efficient) subsystem solvers (p. 1). The combination of different discretization techniques is mentioned on page 59.
Error Estimation And Adaptive Discretization Methods In Computational Fluid Dynamics
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Author : Timothy J. Barth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Error Estimation And Adaptive Discretization Methods In Computational Fluid Dynamics written by Timothy J. Barth 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 2013-04-17 with Mathematics categories.
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Multi Grid Methods And Applications
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Multi Grid Methods And Applications written by Wolfgang Hackbusch 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 2013-03-09 with Mathematics categories.
Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
The Method Of Approximate Inverse Theory And Applications
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Author : Thomas Schuster
language : en
Publisher: Springer
Release Date : 2007-04-26
The Method Of Approximate Inverse Theory And Applications written by Thomas Schuster and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.
This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.
Computational Solution Of Nonlinear Systems Of Equations
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Author : Eugene L. Allgower
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-04-03
Computational Solution Of Nonlinear Systems Of Equations written by Eugene L. Allgower and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-03 with Mathematics categories.
Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.