A Multigrid Tutorial
Author: William L. Briggs
Publisher: SIAM
Published: 2000-07-01
Total Pages: 318
ISBN-13: 9780898714623
DOWNLOAD EBOOK →Mathematics of Computing -- Numerical Analysis.
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˜Aœ Multigrid Tutorial
Multi-Grid Methods and Applications
Author: Wolfgang Hackbusch
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 391
ISBN-13: 3662024276
DOWNLOAD EBOOK →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.
An Introduction to Multigrid Methods
Author: Pieter Wesseling
Publisher: R.T. Edwards, Inc.
Published: 2004
Total Pages: 300
ISBN-13:
DOWNLOAD EBOOK →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.
Solving PDEs in Python
Author: Hans Petter Langtangen
Publisher: Springer
Published: 2017-03-21
Total Pages: 152
ISBN-13: 3319524623
DOWNLOAD EBOOK →This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.
Multigrid Techniques
Author: Achi Brandt
Publisher: SIAM
Published: 2011-01-01
Total Pages: 239
ISBN-13: 9781611970753
DOWNLOAD EBOOK →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.
A Tutorial on Elliptic PDE Solvers and Their Parallelization
Author: Craig C. Douglas
Publisher: SIAM
Published: 2003-01-01
Total Pages: 153
ISBN-13: 9780898718171
DOWNLOAD EBOOK →This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.
Multiscale and Multiresolution Methods
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 396
ISBN-13: 3642562051
DOWNLOAD EBOOK →Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
Numerical Solution of Partial Differential Equations on Parallel Computers
Author: Are Magnus Bruaset
Publisher: Springer Science & Business Media
Published: 2006-03-05
Total Pages: 491
ISBN-13: 3540316191
DOWNLOAD EBOOK →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.
Applied Numerical Linear Algebra
Author: James W. Demmel
Publisher: SIAM
Published: 1997-08-01
Total Pages: 426
ISBN-13: 0898713897
DOWNLOAD EBOOK →This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
