The Splitting Extrapolation Method
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The Splitting Extrapolation Method
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Author : C. B. Liem
language : en
Publisher: World Scientific
Release Date : 1995
The Splitting Extrapolation Method written by C. B. Liem and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The splitting extrapolation method is a newly developed technique for solving multidimensional mathematical problems. It overcomes the difficulties arising from Richardson's extrapolation when applied to these problems and obtains higher accuracy solutions with lower cost and a high degree of parallelism. The method is particularly suitable for solving large scale scientific and engineering problems.This book presents applications of the method to multidimensional integration, integral equations and partial differential equations. It also gives an introduction to combination methods which are relevant to splitting extrapolation. The book is intended for those who may exploit these methods and it requires only a basic knowledge of numerical analysis.
Splitting Extrapolation Method The A New Technique In Numerical Solution Of Multidimensional Prob
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Author : C B Liem
language : en
Publisher: World Scientific
Release Date : 1995-09-30
Splitting Extrapolation Method The A New Technique In Numerical Solution Of Multidimensional Prob written by C B Liem and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 with Mathematics categories.
The splitting extrapolation method is a newly developed technique for solving multidimensional mathematical problems. It overcomes the difficulties arising from Richardson's extrapolation when applied to these problems and obtains higher accuracy solutions with lower cost and a high degree of parallelism. The method is particularly suitable for solving large scale scientific and engineering problems.This book presents applications of the method to multidimensional integration, integral equations and partial differential equations. It also gives an introduction to combination methods which are relevant to splitting extrapolation. The book is intended for those who may exploit these methods and it requires only a basic knowledge of numerical analysis.
Difference Methods And Their Extrapolations
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Author : G.I. Marchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Difference Methods And Their Extrapolations written by G.I. Marchuk 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.
The stimulus for the present work is the growing need for more accurate numerical methods. The rapid advances in computer technology have not provided the resources for computations which make use of methods with low accuracy. The computational speed of computers is continually increasing, while memory still remains a problem when one handles large arrays. More accurate numerical methods allow us to reduce the overall computation time by of magnitude. several orders The problem of finding the most efficient methods for the numerical solution of equations, under the assumption of fixed array size, is therefore of paramount importance. Advances in the applied sciences, such as aerodynamics, hydrodynamics, particle transport, and scattering, have increased the demands placed on numerical mathematics. New mathematical models, describing various physical phenomena in greater detail than ever before, create new demands on applied mathematics, and have acted as a major impetus to the development of computer science. For example, when investigating the stability of a fluid flowing around an object one needs to solve the low viscosity form of certain hydrodynamic equations describing the fluid flow. The usual numerical methods for doing so require the introduction of a "computational viscosity," which usually exceeds the physical value; the results obtained thus present a distorted picture of the phenomena under study. A similar situation arises in the study of behavior of the oceans, assuming weak turbulence. Many additional examples of this type can be given.
Parallel Multilevel Methods
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Author : Gerhard Zumbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Multilevel Methods written by Gerhard Zumbusch 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.
Numerical simulation promises new insight in science and engineering. In ad dition to the traditional ways to perform research in science, that is laboratory experiments and theoretical work, a third way is being established: numerical simulation. It is based on both mathematical models and experiments con ducted on a computer. The discipline of scientific computing combines all aspects of numerical simulation. The typical approach in scientific computing includes modelling, numerics and simulation, see Figure l. Quite a lot of phenomena in science and engineering can be modelled by partial differential equations (PDEs). In order to produce accurate results, complex models and high resolution simulations are needed. While it is easy to increase the precision of a simulation, the computational cost of doing so is often prohibitive. Highly efficient simulation methods are needed to overcome this problem. This includes three building blocks for computational efficiency, discretisation, solver and computer. Adaptive mesh refinement, high order and sparse grid methods lead to discretisations of partial differential equations with a low number of degrees of freedom. Multilevel iterative solvers decrease the amount of work per degree of freedom for the solution of discretised equation systems. Massively parallel computers increase the computational power available for a single simulation.
Advanced Numerical Methods For Complex Environmental Models Needs And Availability
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Author : István Faragó
language : en
Publisher: Bentham Science Publishers
Release Date : 2013-12-10
Advanced Numerical Methods For Complex Environmental Models Needs And Availability written by István Faragó and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-10 with Nature categories.
High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.
Domain Decomposition Methods In Sciences And Engineering
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Author : R. Glowinski
language : en
Publisher:
Release Date : 1997-04-30
Domain Decomposition Methods In Sciences And Engineering written by R. Glowinski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-30 with Mathematics categories.
Domain Decomposition Methods are receiving significant attention in scientific and engineering computing. They provide a broad class of effective numerical methods for the solution of large scale mathematical-physical problems from sciences and engineering. This book contains invited and contributed papers from the 8th Domain Decomposition Methods Conference. The topics addressed range from basic theoretical research to industrial applications: basic algorithms, multilevel methods, parallel computing, transport, wave and flow problems. Applications include problems from fluid and structural mechanics, electromagnetics and petroleum engineering.
Scale Space And Variational Methods In Computer Vision
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Author : Xue-Cheng Tai
language : en
Publisher: Springer
Release Date : 2009-05-24
Scale Space And Variational Methods In Computer Vision written by Xue-Cheng Tai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-24 with Computers categories.
This book contains 71 original, scienti?c articles that address state-of-the-art researchrelatedto scale space and variationalmethods for image processing and computer vision. Topics covered in the book range from mathematical analysis of both established and new models, fast numerical methods, image analysis, segmentation, registration, surface and shape construction and processing, to real applications in medical imaging and computer vision. The ideas of scale spaceandvariationalmethodsrelatedtopartialdi?erentialequationsarecentral concepts. The papers re?ect the newest developments in these ?elds and also point to the latest literature. All the papers were submitted to the Second International Conference on Scale Space and Variational Methods in Computer Vision, which took place in Voss, Norway, during June 1–5, 2009. The papers underwent a peer review process similar to that of high-level journals in the ?eld. We thank the authors, the Scienti?c Committee, the Program Committee and the reviewers for their hard work and helpful collaboration. Their contribution has been crucial for the e?cient processing of this book, and for the success of the conference.
Applied Mathematics Reviews Volume 1
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2000-06-09
Applied Mathematics Reviews Volume 1 written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-09 with Mathematics categories.
Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world.This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.
Large Scale Scientific Computing
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Author : Ivan Lirkov
language : en
Publisher: Springer
Release Date : 2009-03-26
Large Scale Scientific Computing written by Ivan Lirkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Computers categories.
Coverage in this proceedings volume includes robust multilevel and hierarchical preconditioning methods, applications for large scale computations and optimization of coupled engineering problems, and applications of metaheuristics to large-scale problems.
Richardson Extrapolation
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Author : Zahari Zlatev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-07
Richardson Extrapolation written by Zahari Zlatev 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 2017-11-07 with Mathematics categories.
Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions