[PDF] Full Splitting Extrapolation Methodthe A New Technique In Numerical Solution Of Multidimensional Prob Download eBook

Splitting Extrapolation Method,the: A New Technique In Numerical Solution Of Multidimensional Prob

Author: C B Liem

Publisher: World Scientific

Published: 1995-09-30

Total Pages: 337

ISBN-13: 9814500593

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.

Sparse Grids and Applications - Stuttgart 2014

Author: Jochen Garcke

Publisher: Springer

Published: 2016-03-16

Total Pages: 348

ISBN-13: 331928262X

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This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.

Advances in Software Tools for Scientific Computing

Author: Hans P. Langtangen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 362

ISBN-13: 3642571727

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To make full use of the ever increasing hardware capabilities of modern com puters, it is necessary to speedily enhance the performance and reliability of the software as well, and often without having a suitable mathematical theory readily available. In the handling of more and more complex real-life numerical problems in all sorts of applications, a modern object-oriented de sign and implementation of software tools has become a crucial component. The considerable challenges posed by the demand for efficient object-oriented software in all areas of scientific computing make it necessary to exchange ideas and experiences from as many different sources as possible. Motivated by the success of the first meeting of this kind in Norway in 1996, we decided to organize another International Workshop on Modern Software Tools for Scientific Computing, often referred to as SciTools'98. This workshop took place in Oslo, Norway, September 14-16, 1998. The ob jective was again to provide an open forum for exchange and discussion of modern, state-of-the-art software techniques applied to challenging numerical problems. The organization was undertaken jointly by the research institute SINTEF Applied Mathematics, the Departments of Mathematics and Infor matics at the University of Oslo, and the company Numerical Objects AS.

Parallel Multilevel Methods

Author: Gerhard Zumbusch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 215

ISBN-13: 3322800636

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Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.

Polynomial Sequences

Author: Francesco Aldo Costabile

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-12-18

Total Pages: 526

ISBN-13: 3110757249

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Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.

Computational Statistics

Author: James E. Gentle

Publisher: Springer Science & Business Media

Published: 2009-07-28

Total Pages: 732

ISBN-13: 0387981446

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Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

Computational Statistics

Author:

Publisher: Springer Science & Business Media

Published: 2010-04-29

Total Pages: 732

ISBN-13: 0387981454

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Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

Domain Decomposition Methods in Sciences and Engineering

Author: R. Glowinski

Publisher:

Published: 1997-04-30

Total Pages: 602

ISBN-13:

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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.