A Multigrid Tutorial

Second Edition


Author: William L. Briggs,Van Emden Henson,Steve F. McCormick

Publisher: SIAM

ISBN: 0898714621

Category: Mathematics

Page: 193

View: 4998

Mathematics of Computing -- Numerical Analysis.

Multiscale and Multiresolution Methods

Theory and Applications


Author: Timothy J. Barth,Tony Chan,Robert Haimes

Publisher: Springer Science & Business Media

ISBN: 9783540424208

Category: Mathematics

Page: 394

View: 3573

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.


Theory and Applications


Author: Gordon Erlebacher,M. Yousuff Hussaini,Leland M. Jameson

Publisher: Oxford University Press

ISBN: 0198025424

Category: Science

Page: 528

View: 3084

Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window". They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.

A First Course in the Numerical Analysis of Differential Equations


Author: A. Iserles

Publisher: Cambridge University Press

ISBN: 0521734908

Category: Mathematics

Page: 459

View: 5333

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

Multifield Problems

State of the Art


Author: Anna-Margarete Sändig,W. Schiehlen,W.L. Wendland

Publisher: Springer Science & Business Media

ISBN: 9783540675112

Category: Technology & Engineering

Page: 278

View: 4160

The simulation of complex engineering problems often involves an interaction or coupling of individual phenomena, which are traditionally related by themselves to separate fields of applied mechanics. Typical examples of these so- called multifield problems are the thermo-mechanical analysis of solids with coupling between mechanical stress analysis and thermal heat transfer processes, the simulation of coupled deformation and fluid transport mechanisms in porous media, the prediction of mass transport and phase transition phenomena of mixtures, the analysis of sedimentation proces- ses based on an interaction of particle dynamics and viscous flow, the simulation of multibody systems and fluid-structure interactions based on solid-to-solid and solid-to-fluid contact mechanisms.

Parallelization of a Multigrid Incompressible Viscous Cavity Flow Solver Using OpenMP


Author: Piyush Mehrotra

Publisher: N.A


Category: Multigrid methods (Numerical analysis)

Page: 8

View: 2424

Abstract: "We describe a multigrid scheme for solving the viscous incompressible driven cavity problem that has been parallelized using OpenMP. The incremental parallelization allowed by OpenMP was of great help during the parallelization process. Results show good parallel efficiencies for reasonable problem sizes on an SGI Origin 2000. Since OpenMP allowed us to specify the number of threads (and in turn processors) at runtime, we were able to improve performance when solving on smaller/coarser meshes. This was accomplished by giving each processor a more reasonable amount of work rather than having many processors work on very small segments of the data (and thereby adding significant overhead)."

Proceedings of the Fourth International Colloquium on Differential Equations

Plovdiv, Bulgaria, 18-22 August 1993


Author: Drumi D. Bainov,V. Covachev

Publisher: VSP

ISBN: 9789067641692

Category: Science

Page: 305

View: 6798

The Fourth International Colloquium on Differential Equations was organized by UNESCO and the Plovdiv Technical University, with the help of many international mathematical organizations, and was held in Plovdiv, Bulgaria, 18--22 August 1993. This proceedings volume contains selected invited talks which deal with the following topics: -- impulsive differential equations -- nonlinear differential equations -- differential equations with maxima -- applications of differential equations

Multi-Level Methods in Lubrication


Author: C.H. Venner,A A Lubrecht

Publisher: Elsevier

ISBN: 9780080537092

Category: Technology & Engineering

Page: 400

View: 5900

Efficient numerical solution of realistic and, therefore, complex equation systems occupies many researchers in many disciplines. For various reasons, but mainly in order to approximate reality, a very large number of unknowns are needed. Using classical techniques, the solution of such a system of equations would take too long, and so sometimes MultiLevel techniques are used to accelerate convergence. Over the last one and a half decades, the authors have studied the problem of Elastohydrodynamic Lubrication, governed by a complex integro-differential equation. Their work has resulted in a very efficient and stable solver. In this book they describe the different intermediate problems analyzed and solved, and how those ingredients finally come together in the EHL solver. A number of these intermediate problems, such as Hydrodynamic Lubrication and Dry Contact, are useful in their own right. In the Appendix the full codes of the Poisson problem, the Hydrodynamic Lubrication problem, the dry contact solver and the EHL solver are given. These codes are all written in 'C' language, based on the 'ANSI-C' version.

Multilevel Adaptive Methods for Partial Differential Equations


Author: Stephen F. McCormick

Publisher: SIAM

ISBN: 0898712475

Category: Mathematics

Page: 162

View: 8794

A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques.