This second edition preserves the introductory spirit of the first edition while roughly doubling the amount of material covered.
Author: William L. Briggs
Category: Differential equations, Partial
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.
Brandt, A., Multilevel computations: Review and recent developments, in:
Multigrid Methods: Theory, Applications and ... Brandt, A., Proceedings of the multigrid tutorial, with applications to molecular dynamics, Weizmann Institute of
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
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.
The series of such seminars was continued in 1994, January 14-16, with the 10th Kiel-Seminar on the special topic Fast Solvers for Flow Problems at the Christian-Albrechts-University of Kiel.
Author: Wolfgang Hackbusch
Publisher: Vieweg + Teubner Verlag
The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organises seminars on subjects concerning the algorithmic treatment of par tial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1994, January 14-16, with the 10th Kiel-Seminar on the special topic Fast Solvers for Flow Problems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two invited survey lectures. The central topic of most of the contributions are the Navier-Stokes equations. The authors discuss robust methods, parallel implementations, defect correction techniques, adaptive methods including error estimators, domain decompositions and FEM-BEM coupling. The invited lectures concern the hierarchical multigrid method for unstruc tured grids and structured adaptive finite-volume multigrid for compressible flows.
There exist a number of good introductory texts on multigrid techniques, e.g.
Briggs (1987); Hackbusch (1985) and Wesseling (1992). Convergence and ...
Briggs, W.L. (1987), A Multigrid Tutorial, SIAM, Philadelphia. Hackbusch, W. (
Author: A. Iserles
Publisher: Cambridge University Press
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.
... 0 if f(x) — xm for m = 0, ...M — 1. A multigrid method, likewise, refines the
approximation subspace based on the error of local polynomial interpolation. ...
conditions on the interval." Wavelets: A tutorial in theory and applications, Ed.
C. K. ...
Author: Gordon Erlebacher
Publisher: Oxford University Press
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.
Author: Anna-Margarete SändigPublish On: 2000-06-15
Bastian, P., Hackbusch, W., Wittum, G. (1998) Additive and Multiplicative Multi-
Grid - a Comparison, Computing 60, ... Briggs, W. L. (1987) A multigrid tutorial. ...
Fish, J., Belsky, V. (1995) Multigrid method for periodic heterogeneous media.
Author: Anna-Margarete Sändig
Publisher: Springer Science & Business Media
Category: Technology & Engineering
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.
Multigrid Techniques: 1984 Guide, with Applications to Fluid Dynamics, 1984,
191 pages, ISBN-3-88457-081-1; GMD-Studien ... “Wave-ray multigrid method for
standing wave equations”, Electronic Trans. ... A Multigrid Tutorial, 2nd Ed., SIAM.
Author: Jacob Fish
Publisher: OUP Oxford
Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness? The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of error estimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biological systems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.
The book is intended to be an intermediate level MultiGrid book, somewhere
between an introduction to MultiGrid as 'A MultiGrid Tutorial by W.L. Briggs 
and the advanced “MultiGrid Techniques: 1984 Guide with Applications to Fluid ...
Author: C.H. Venner
Category: Technology & Engineering
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.
Brigg% W., A Multigrid Tutorial, SIAM, Philadelphia, Pennsylvania, 1987. 15.
Curran, M.C. and Allen, M.B., "A multigrid-bascd solver for mixed finite-element
approximations to groundwater flow," in Computational Methods in Water Re-
Author: Drumi D. Bainov
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
Author: Stephen F. McCormickPublish On: 1989-01-01
Chapter 3 Multigrid Methods 3.1 Basic Concepts Multigrid (MG) serves as a basic
component of fast adaptive ... An excellent source for this purpose is A Multigrid Tutorial [Briggs 1987], which cites references for more advanced topics.
Author: Stephen F. McCormick
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.
Chapter 7 introduces briefly a multigrid solver that is an optimal solver in the
sense that it is 10 times as expensive with respect to both memory requirements
and solution time for 10 times as many unknowns. Thanks to the previous
Author: Craig C. Douglas
Category: Differential equations, Elliptic
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.
This is true regardless of whether MyLab access is purchased standalone or packaged with a physical book. "MyLab Access Code" is for the life of the edition.
Author: William L. Briggs
For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. T he most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs' Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLab(tm) Math content from over 140 instructors and an Engineering Review Panel. This thorough and extensive review process, paired with the authors' own teaching experiences, helped create a text that was designed for today's calculus instructors and students. Also available with MyLab Math MyLab Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134995996 / 9780134995991 Calculus: Early Transcendentals and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e Package consists of: 0134763645 / 9780134763644 Calculus: Early Transcendentals 0134856929 / 9780134856926 MyLab Math with Pearson eText - Standalone Access Card - for Calculus: Early Transcendentals
The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows. * This book is an expanded version of Calculus by the same authors, with an entire chapter ...
Author: Lyle Cochran
Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' years of teaching experience resulted in a text that reflects how students generally use a textbook: they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows. * This book is an expanded version of Calculus by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections. See the "Features" section for more details.
Author: Society for Industrial and Applied MathematicsPublish On: 1989
Society for Industrial and Applied Mathematics. Books from SIAM A Multigrid Tutorial William L . Briggs ix + 88 pages Softcover 54 illustrations ISBN 0 - 89871
- 221 - 1 List Price $ 13 . 50 SIAM Member Price $ 10 . 80 Assuming little
Author: Society for Industrial and Applied Mathematics
Guide to multigrid development, in Multigrid Methods: Proceedings of the 1st
European Conference on Multigrid Methods, W. Hackbusch and U. Trottenberg,
eds., Berlin, 1981, Springer-Verlag.  W. L. BRIGGs, A Multigrid Tutorial, SLAM,
Briggs , W . L . ( 1987 ) A multigrid tutorial , SIAM , Philadelphia . Briggs , W . L .
and McCormick , S . F . ( 1987 ) Introduction , Multigrid Methods , S . F .
McCormick ( ed . ) ( Frontiers in Applied Mathematics 3 ) SIAM , Philadelphia ,
Author: Pieter Wesseling
Publisher: R T Edwards Incorporated
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.
( 3 ] W. Auzinger and H. J. Stetter , “ Defect corrections and multigrid iterations , ”
in Multigrid Methods , Lecture Notes in Mathematics , vol . 960 , 1982 . [ 4 ] T. J.
Barth and ... [ 9 ] W. L. Briggs , A Multigrid Tutorial . SIAM , Philadelphia , PA ,
A Multigrid Tutorial . SIAM Philadelphia , 1987 . [ 2 ] K. Riemslagh and E. Dick . A
multigrid method for steady Euler equations on unstructured adaptive grids . In
Sixth Copper Mountain Conference on Multigrid Methods , pages ...
Author: E. Morano
Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = delta(y)/delta(x) “1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed. (AN).