Multi Grid Methods And Applications
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| Author | : Wolfgang Hackbusch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 391 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662024276 |
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.
| Author | : William L. Briggs |
| Publisher | : SIAM |
| Total Pages | : 205 |
| Release | : 2000-01-01 |
| Genre | : Differential equations, Partial |
| ISBN | : 9780898719505 |
This second edition preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements. This introductory book is ideally suited as a companion textbook for graduate numerical analysis courses. It is written for computational mathematicians, engineers, and other scientists interested in learning about multigrid.
| Author | : Ulrich Trottenberg |
| Publisher | : Academic Press |
| Total Pages | : 652 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780127010700 |
Mathematics of Computing -- Numerical Analysis.
| Author | : Achi Brandt |
| Publisher | : SIAM |
| Total Pages | : 239 |
| Release | : 2011-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970753 |
This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
| Author | : Pieter Wesseling |
| Publisher | : R.T. Edwards, Inc. |
| Total Pages | : 300 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : |
Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.
| Author | : Are Magnus Bruaset |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2006-03-05 |
| Genre | : Mathematics |
| ISBN | : 3540316191 |
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.
| Author | : Taras Gerya |
| Publisher | : Cambridge University Press |
| Total Pages | : 359 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0521887542 |
This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.
| Author | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 537 |
| Release | : 2003-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898715342 |
Mathematics of Computing -- General.
| Author | : Ali Iftekhar Maswood |
| Publisher | : John Wiley & Sons |
| Total Pages | : 496 |
| Release | : 2019-01-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1119475864 |
A comprehensive survey of advanced multilevel converter design, control, operation and grid-connected applications Advanced Multilevel Converters and Applications in Grid Integration presents a comprehensive review of the core principles of advanced multilevel converters, which require fewer components and provide higher power conversion efficiency and output power quality. The authors – noted experts in the field – explain in detail the operation principles and control strategies and present the mathematical expressions and design procedures of their components. The text examines the advantages and disadvantages compared to the classical multilevel and two level power converters. The authors also include examples of the industrial applications of the advanced multilevel converters and offer thoughtful explanations on their control strategies. Advanced Multilevel Converters and Applications in Grid Integration provides a clear understanding of the gap difference between research conducted and the current industrial needs. This important guide: Puts the focus on the new challenges and topics in related areas such as modulation methods, harmonic analysis, voltage balancing and balanced current injection Makes a strong link between the fundamental concepts of power converters and advances multilevel converter topologies and examines their control strategies, together with practical engineering considerations Provides a valid reference for further developments in the multilevel converters design issue Contains simulations files for further study Written for university students in electrical engineering, researchers in areas of multilevel converters, high-power converters and engineers and operators in power industry, Advanced Multilevel Converters and Applications in Grid Integration offers a comprehensive review of the core principles of advanced multilevel converters, with contributions from noted experts in the field.
| Author | : Michael A. Heroux |
| Publisher | : SIAM |
| Total Pages | : 421 |
| Release | : 2006-01-01 |
| Genre | : Computers |
| ISBN | : 9780898718133 |
Parallel processing has been an enabling technology in scientific computing for more than 20 years. This book is the first in-depth discussion of parallel computing in 10 years; it reflects the mix of topics that mathematicians, computer scientists, and computational scientists focus on to make parallel processing effective for scientific problems. Presently, the impact of parallel processing on scientific computing varies greatly across disciplines, but it plays a vital role in most problem domains and is absolutely essential in many of them. Parallel Processing for Scientific Computing is divided into four parts: The first concerns performance modeling, analysis, and optimization; the second focuses on parallel algorithms and software for an array of problems common to many modeling and simulation applications; the third emphasizes tools and environments that can ease and enhance the process of application development; and the fourth provides a sampling of applications that require parallel computing for scaling to solve larger and realistic models that can advance science and engineering.
