Multigrid Methods VI

Multigrid Methods VI
Title Multigrid Methods VI PDF eBook
Author Erik Dick
Publisher Springer Science & Business Media
Pages 306
Release 2012-12-06
Genre Mathematics
ISBN 3642583121

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This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.

Numerical Solution of Partial Differential Equations on Parallel Computers

Numerical Solution of Partial Differential Equations on Parallel Computers
Title Numerical Solution of Partial Differential Equations on Parallel Computers PDF eBook
Author Are Magnus Bruaset
Publisher Springer Science & Business Media
Pages 491
Release 2006-03-05
Genre Mathematics
ISBN 3540316191

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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.

A Multigrid Tutorial

A Multigrid Tutorial
Title A Multigrid Tutorial PDF eBook
Author William L. Briggs
Publisher SIAM
Pages 318
Release 2000-07-01
Genre Mathematics
ISBN 9780898714623

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Mathematics of Computing -- Numerical Analysis.

Multigrid Methods

Multigrid Methods
Title Multigrid Methods PDF eBook
Author Ulrich Trottenberg
Publisher Academic Press
Pages 652
Release 2001
Genre Mathematics
ISBN 9780127010700

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Mathematics of Computing -- Numerical Analysis.

Multigrid Methods IV

Multigrid Methods IV
Title Multigrid Methods IV PDF eBook
Author P.W. Hemker
Publisher Birkhäuser
Pages 360
Release 2012-12-06
Genre Mathematics
ISBN 3034885245

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This volume contains a selection from the papers presented at the Fourth European Multigrid Conference, held in Amsterdam, July 6-9,1993. There were 78 registered participants from 14 different countries, and 56 presentations were given. The preceding conferences in this series were held in Cologne (1981, 1985) and in Bonn (1990). Also at the other side of the Atlantic special multigrid conferences are held regularly, at intervals of two years, always in Copper Mountain, Colorado, US. The Sixth Copper Mountain Conference on Multigrid Methods took place in April, 1993. Circumstances prevented us from putting a larger time interval between the Copper and Amsterdam meetings. The next European meeting is planned in 1996, a year later than the next Copper Meeting. When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists. The past twenty years have shown a rapid growth in theoretical understanding, useful applications and widespread acceptance of multi grid in the applied disciplines. Hence, one might ask whether there is still a need today for conferences specially dedicated to multigrid. The general consensus is that the answer is affirmative. New issues have arisen that are best addressed or need also be addressed from a special multigrid point of view.

An Introduction to Multigrid Methods

An Introduction to Multigrid Methods
Title An Introduction to Multigrid Methods PDF eBook
Author Pieter Wesseling
Publisher R.T. Edwards, Inc.
Pages 300
Release 2004
Genre Mathematics
ISBN

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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.

Multigrid Methods for Process Simulation

Multigrid Methods for Process Simulation
Title Multigrid Methods for Process Simulation PDF eBook
Author Wolfgang Joppich
Publisher Springer Science & Business Media
Pages 327
Release 2012-12-06
Genre Technology & Engineering
ISBN 3709192536

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It was about 1985 when both of the authors started their work using multigrid methods for process simulation problems. This happened in dependent from each other, with a completely different background and different intentions in mind. At this time, some important monographs appeared or have been in preparation. There are the three "classical" ones, from our point of view: the so-called "1984 Guide" [12J by Brandt, the "Multi-Grid Methods and Applications" [49J by Hackbusch and the so-called "Fundamentals" [132J by Stiiben and Trottenberg. Stiiben and Trottenberg in [132J state a "delayed acceptance, resent ments" with respect to multigrid algorithms. They complain: "Nevertheless, even today's situation is still unsatisfactory in several respects. If this is true for the development of standard methods, it applies all the more to the area of really difficult, complex applications." In spite of all the above mentioned publications and without ignoring important theoretical and practical improvements of multigrid, this situa tion has not yet changed dramatically. This statement is made under the condition that a numerical principle like multigrid is "accepted", if there exist "professional" programs for research and production purposes. "Professional" in this context stands for "solving complex technical prob lems in an industrial environment by a large community of users". Such a use demands not only for fast solution methods but also requires a high robustness with respect to the physical parameters of the problem.