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:
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
Download or read book Iterative Solution of Large Sparse Systems of Equations written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the description of the state of modern iterative techniques together with systematic analysis. The first chapters discuss the classical methods. Comprehensive chapters are devoted to semi-iterative techniques (Chebyshev methods), transformations, incomplete decompositions, gradient and conjugate gradient methods, multi-grid methods and domain decomposition techniques (including e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.
Download or read book Iterative Solution of Large Sparse Systems of Equations written by Wolfgang Hackbusch and published by Springer. This book was released on 1993-12-13 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c~ empfe~le 3~nen biegen IDlobu9 aur 9tac~a~mung. ec~werlic~ werben eie ie wieber bi reet eliminiren, wenigftens nic~t, wenn eie me~r als 2 Unbefannte ~aben. :Da9 inbirecte 93erfa~ren 109st sic~ ~alb im ec~lafe ausfii~ren, ober man fann wo~renb be9gelben an anbere :Dinge benfen. [CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.
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 Preconditioned Iterative Methods written by David J. Evans and published by Gordon & Breach Science Pub. This book was released on 1994 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Precondition Gradient Methods emerged in the early 1970s as the most impressive algorithm for the large sparse definite problems. The method has gained large acceptance throughout the world since then and undergone rapid development. The method has been generalized to non-symmetric and indefinite problems, domain decomposition, eigenvalue problems, and many other application areas. The analysis of the preconditioning strategy is both a mathematically fascinating and complex topic. Since the topic appears to be expanding in importance, it was felt opportune to present this volume containing papers on preconditioned iterative methods, Incomplete Factorisation and SSOR preconditioning and the Preconditioned Conjugate Gradient Method covering symmetric and non-symmetric systems on computers (vector and parallel) for finite element and computational fluid dynamic applications. This volume serves as a useful companion volume to the previously published "Preconditioning Methods: Theory and Application"
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 Parallel Iterative Methods for Solving Large Sparse Sets of Linear Equations written by L. C. W. Dixon and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Download or read book Solution Methods for Large Sparse Linear Systems written by H. A. van der Vorst and published by . This book was released on 1983 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discretisation of partial differential equations, by either finite element or finite difference techniques, often leads to large linear systems of equations with sparse matrices. Fast iterative solution methods, based upon the preconditioning of the conjugate gradients method, have been proposed for the symmetric positive definite case and also for more general situations. In this report we present new sharp upperbounds for the conjugate gradients residual. These upperbounds help us to understand and explain the convergence behaviour of the preconditioned conjugate gradients method. We also present a type of preconditioning that has almost the same convergence properties as those presented, but which admit- full vectorization on supercomputers like the CRAY-1 and the CYBER 205. For the nonsymmetric case we propose different types of preconditioning in connection with the Chebyshev iterative method. (Author).
Download or read book Iterative Methods for Large Linear Systems written by David Ronald Kincaid and published by . This book was released on 1990 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Download or read book Preconditioning Methods written by David J. Evans and published by Routledge. This book was released on 1983-01-01 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Parallel and Vector Solution of Linear Systems written by James M. Ortega and published by Springer Science & Business Media. This book was released on 1988-04-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
Download or read book Massively Parallel Iterative Methods Multiscale Preconditioners and Implicit Methods written by and published by . This book was released on 1995 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear and linear systems of equations often arise in scientific computation, for example in implicit methods in Computational Fluid Dynamics (CFD). It is important to find cost-effective and accurate methods to solve such systems. Iterative methods are among those widely used, especially for 3D problems. In this project, we consider iterative methods which are especially suited to massively parallel architectures. To accelerate convergence of these iterative methods, preconditioners are often used. Good preconditioners reduce the number of iterations and involves few arithmetic operations per iteration. Effective parallel preconditioners must account for the global coupling inherent in elliptic problems. On the other hand, efficient parallel implementation often favors local computations. Multiscale iterative methods represent a good compromise between these two conflicting goals. We focused our attention on two classes of multiscale preconditioners: multilevel basis preconditioners and domain decomposition preconditioners.
