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Author : William L. Briggs
Publisher : SIAM
ISBN 13 : 9780898714623
Total Pages : 318 pages
Book Rating : 4.7/5 (146 download)
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author :
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (727 download)
Download or read book Adaptive Algebraic Multigrid Methods written by and published by . This book was released on 2004 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Author : Karsten Kahl
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (724 download)
Download or read book Adaptive Algebraic Multigrid Methods for Lattice QCD Computations written by Karsten Kahl and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William L. Briggs
Publisher : SIAM
ISBN 13 : 0898714621
Total Pages : 196 pages
Book Rating : 4.8/5 (987 download)
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Are Magnus Bruaset
Publisher : Springer Science & Business Media
ISBN 13 : 3540316191
Total Pages : 491 pages
Book Rating : 4.5/5 (43 download)
Download or read book Numerical Solution of Partial Differential Equations on Parallel Computers written by Are Magnus Bruaset and published by Springer Science & Business Media. This book was released on 2006-03-05 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
ISBN 13 : 3642587348
Total Pages : 344 pages
Book Rating : 4.6/5 (425 download)
Download or read book Multigrid Methods V written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1996. All contributions were carefully refereed. The conference was organized by the Institute for Computer Applications (ICA) of the University of Stuttgart, in cooperation with the GAMM Committee for Scientific Computing, SFB 359 and 404 and the research network WiR Ba-Wü. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks focused on algebraic multigrid methods.
Author : R. D. Falgout
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (316 download)
Download or read book Filtering Algebraic Multigrid and Adaptive Strategies written by R. D. Falgout and published by . This book was released on 2006 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving linear systems arising from systems of partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. The method is used in an adaptive, self-correcting framework and tested numerically.
Author : Erik Dick
Publisher : Springer Science & Business Media
ISBN 13 : 3642583121
Total Pages : 306 pages
Book Rating : 4.6/5 (425 download)
Download or read book Multigrid Methods VI written by Erik Dick and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Ulrich Trottenberg
Publisher : Academic Press
ISBN 13 : 9780127010700
Total Pages : 652 pages
Book Rating : 4.0/5 (17 download)
Download or read book Multigrid Methods written by Ulrich Trottenberg and published by Academic Press. This book was released on 2001 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Stephen F. Mccormick
Publisher : CRC Press
ISBN 13 : 1000147223
Total Pages : 668 pages
Book Rating : 4.0/5 (1 download)
Download or read book multigrid methods written by Stephen F. Mccormick and published by CRC Press. This book was released on 2020-08-12 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
ISBN 13 : 3662024276
Total Pages : 391 pages
Book Rating : 4.6/5 (62 download)
Download or read book Multi-Grid Methods and Applications written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Stephen McCormick
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (227 download)
Download or read book Algebraic Multigrid and the Fast Adaptive Composite Grid Method in Large Scale Computation written by Stephen McCormick and published by . This book was released on 1986 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report describes research undertaken at the Research Institute of Colorado on two computational mathematics topics: algebraic multigrid (AMG), and the fast adaptive composite grid method (FAC). Conventional or geometric multigrid algorithms depend on knowledge of the underlying geometry for a given problem (e.g., a partial differential equation). This knowledge is used to predetermine coarser grids and the attendant operators and intergrid transfers. Although very efficient solvers can be developed in this way, the dissemination and use of geometric multigrid have been impeded by the need to tailor the algorithm to each application. A fairly general black box solver based on multigrid principles would be useful in overcoming these difficulties. The second project area was the study of FAC in the context of multiprocessor computer systems. FAC is developed for elliptic equations.
Author :
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (16 download)
Download or read book Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients written by and published by . This book was released on 2012 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-?AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.
Author : Ralf Kornhuber
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.3/5 (91 download)
Download or read book Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems written by Ralf Kornhuber and published by . This book was released on 1997 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
![Download Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients [Adaptive Algebraic Multigrid for Sequence of Problems with Slowly Varying Random Coefficients]. PDF Online Free](https://books.google.com/books/content/images/frontcover/38v8vgEACAAJ?fife=w200-h370)
Author :
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (16 download)
Download or read book Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients [Adaptive Algebraic Multigrid for Sequence of Problems with Slowly Varying Random Coefficients]. written by and published by . This book was released on 2013 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our paper proposes an adaptive strategy for reusing a previously constructed coarse space by algebraic multigrid to construct a two-level solver for a problem with nearby characteristics. Furthermore, a main target application is the solution of the linear problems that appear throughout a sequence of Markov chain Monte Carlo simulations of subsurface flow with uncertain permeability field. We demonstrate the efficacy of the method with extensive set of numerical experiments.
Author : Panayot S. Vassilevski
Publisher : Springer Science & Business Media
ISBN 13 : 0387715649
Total Pages : 527 pages
Book Rating : 4.3/5 (877 download)
Download or read book Multilevel Block Factorization Preconditioners written by Panayot S. Vassilevski and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Author :
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (227 download)
Download or read book The Fast Adaptive Composite Grid Method and Algebraic Multigrid in Large Scale Computation written by and published by . This book was released on 1991 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report documents the progress of the project over the last four years.
