Download or read book Domain Decomposition written by Barry Smith and published by Cambridge University Press. This book was released on 2004-03-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.
Download or read book Parallel Multilevel Methods written by Gerhard Zumbusch and published by . This book was released on 2003-11-26 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Multilevel Methods written by Gerhard Zumbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Adaptive Parallel Multilevel Methods for Partial Differential Equations written by Gerhard Zumbusch and published by . This book was released on 2001 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Multilevel Methods for Transport Equations written by Suely Oliveira and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations written by Marc Alexander Schweitzer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.
Download or read book A Review of Numerous Parallel Multigrid Methods written by International Business Machines Corporation. Research Division and published by . This book was released on 1995 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Parallel multilevel methods are shown to be the natural precursors to standard multilevel methods based on the personnel computing era of earlier this century. They are also the natural successors to standard multilevel methods in the age of computers. What makes six parallel multilevel methods practical and impractical is discussed in the context of the three algorithms that encapsulate them."
Download or read book Parallel multilevel iterative methods written by Bi Roubolo Vona and published by . This book was released on 1992 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies in Domain Decomposition written by Xuejun Zhang and published by Forgotten Books. This book was released on 2017-10-13 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem Multilevel methods, such as multigrid methods, are among the most efficient methods for linear equations arising from elliptic problems; cf. Hackbusch mccormick [38] and the references therein. Recently, with the increasing interest in parallel computation, several new multilevel methods have been developed; cf. Yserentant Bank, Dupont and Yserentant Bramble, Pasciak and Xu and Dryja and Widlund In this thesis, we give improved results for a class of multilevel methods by showing that the condition number of the iteration Operator grows at most linearly with the number of levels in general, and is bounded by a constant independent of the mesh sizes and the number of levels if the elliptic problem is Hz - regular. This is an improvement on Dryja and Widlund's results on a multilevel additive Schwarz method as well as Bramble, P-asciak and Ku's results on the bpx algorithm. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Numerical Solution of Partial Differential Equations on Parallel Computers written by Are Magnus Bruaset and published by Springer Science & Business Media. This book was released on 2006-03-05 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Download or read book Multilevel Block Factorization Preconditioners written by Panayot S. Vassilevski and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Download or read book A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries written by M. J. Aftosmis and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Modeling in Plain Language written by Karen Robson and published by SAGE. This book was released on 2015-11-02 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you been told you need to do multilevel modeling, but you can′t get past the forest of equations? Do you need the techniques explained with words and practical examples so they make sense? Help is here! This book unpacks these statistical techniques in easy-to-understand language with fully annotated examples using the statistical software Stata. The techniques are explained without reliance on equations and algebra so that new users will understand when to use these approaches and how they are really just special applications of ordinary regression. Using real life data, the authors show you how to model random intercept models and random coefficient models for cross-sectional data in a way that makes sense and can be retained and repeated. This book is the perfect answer for anyone who needs a clear, accessible introduction to multilevel modeling.
Download or read book The SAGE Handbook of Multilevel Modeling written by Marc A. Scott and published by SAGE. This book was released on 2013-08-31 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this important new Handbook, the editors have gathered together a range of leading contributors to introduce the theory and practice of multilevel modeling. The Handbook establishes the connections in multilevel modeling, bringing together leading experts from around the world to provide a roadmap for applied researchers linking theory and practice, as well as a unique arsenal of state-of-the-art tools. It forges vital connections that cross traditional disciplinary divides and introduces best practice in the field. Part I establishes the framework for estimation and inference, including chapters dedicated to notation, model selection, fixed and random effects, and causal inference. Part II develops variations and extensions, such as nonlinear, semiparametric and latent class models. Part III includes discussion of missing data and robust methods, assessment of fit and software. Part IV consists of exemplary modeling and data analyses written by methodologists working in specific disciplines. Combining practical pieces with overviews of the field, this Handbook is essential reading for any student or researcher looking to apply multilevel techniques in their own research.
Download or read book Studies in Domain Decomposition Vol 255 written by Xuejun Zhang and published by . This book was released on 2015-08-05 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Studies in Domain Decomposition, Vol. 255: Multilevel Methods and the Biharmonic Dirichlet Problem A class of multilevel methods for second order problems is considered in the additive Schwarz framework. It is established that, in the general case, the condition number of the iterative operator grows at most linearly with the number of levels. The bound is independent of the mesh sizes and the number of levels under a regularity assumption. This is an improvement of a result by Dryja and Widlund on a multilevel additive Schwarz algorithm, and the theory given by Bramble, Pasciak and Xu for the BPX algorithm. Additive Schwarz and iterative substructuring algorithms for the biharmonic equation are also considered. These are domain decomposition methods which have previously been developed extensively for second order elliptic problems by Bramble, Pasciak and Schatz, Dryja and Widlund and others. Optimal convergence properties are established for additive Schwarz algorithms for the biharmonic equation discretized by certain conforming finite elements. The number of iterations for the iterative substructuring methods grows only as the logarithm of the number of degrees of freedom associated with a typical subregion. It is also demonstrateed that it is possible to simplify the basic algorithms. This leads to a decrease of the cost but not of the rate of convergence of the iterative methods. In the analysis, new tools are developed to deal with Hermitian elements. Certain new inequalities for discrete norms for finite element spaces are also used. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Scalable Parallel Multilevel Algorithms for Solving Partial Differential Equations written by Shaoying Lu and published by . This book was released on 2004 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Preconditioning Methods for the Parallel Iterative Solution of Large Sparse Systems of Equations written by Wesley D. Turner and published by . This book was released on 2001 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
