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Author : Mohamed Othman
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (969 download)
Download or read book Multigrid Solution with Rotated High-order Discretizations for Solving Poisson Equation written by Mohamed Othman and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yair Shapira
Publisher : Springer Science & Business Media
ISBN 13 : 0387497641
Total Pages : 315 pages
Book Rating : 4.3/5 (874 download)
Download or read book Matrix-Based Multigrid written by Yair Shapira and published by Springer Science & Business Media. This book was released on 2008-07-02 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.
Author : Todd A. Oliver
Publisher :
ISBN 13 :
Total Pages : 74 pages
Book Rating : 4.:/5 (318 download)
Download or read book Multigrid Solution for High-order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations written by Todd A. Oliver and published by . This book was released on 2004 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the p-multigrid solver, which relies on an element-line Jacobi smoother. The element-line Jacobi smoother solves implicitly on lines of elements formed based on the coupling between elements in a p = 0 discretization of the scalar transport equation. Fourier analysis of 2-D scalar convection-diffusion shows that the element-line Jacobi smoother as well as the simpler element Jacobi smoother are stable independent of p and flow condition. Mesh refinement studies for simple problems with analytic solutions demonstrate that the discretization achieves optimal order of accuracy of O(h(̂p+l)). A subsonic, airfoil test case shows that the multigrid convergence rate is independent of p but weakly dependent on h. Finally, higher-order is shown to outperform grid refinement in terms of the time required to reach a desired accuracy level.
Author : Wolfgang Joppich
Publisher : Springer Science & Business Media
ISBN 13 : 3709192536
Total Pages : 327 pages
Book Rating : 4.7/5 (91 download)
Download or read book Multigrid Methods for Process Simulation written by Wolfgang Joppich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Stephen F. McCormick
Publisher : SIAM
ISBN 13 : 1611971055
Total Pages : 292 pages
Book Rating : 4.6/5 (119 download)
Download or read book Multigrid Methods written by Stephen F. McCormick and published by SIAM. This book was released on 1987-12-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
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 : Michael Holst
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (31 download)
Download or read book Multigrid Solution of the Poisson-Boltzmann Equation written by Michael Holst and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems occurring in reactor physics. A detailed analysis of the resulting method is presented for several computer architectures, including comparisons to diagonally scaled CG, ICCG, vectorized ICCG and MICCG, and to SOR provided with an optimal relaxation parameter. Our results indicate that the multigrid method is superior to the preconditioned CG methods and SOR, and that the advantage of multigrid grows with the problem size."
Author : Krishna Prasad M. Varadarajan
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (291 download)
Download or read book Solution of Poisson Equation Using Multigrid Methods written by Krishna Prasad M. Varadarajan and published by . This book was released on 1992 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Breitsamter
Publisher : Springer Science & Business Media
ISBN 13 : 3540444378
Total Pages : 428 pages
Book Rating : 4.5/5 (44 download)
Download or read book Numerical Flow Simulation I written by Christian Breitsamter and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 836 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans-Joachim Bungartz
Publisher : Springer Nature
ISBN 13 : 3030479560
Total Pages : 624 pages
Book Rating : 4.0/5 (34 download)
Download or read book Software for Exascale Computing - SPPEXA 2016-2019 written by Hans-Joachim Bungartz and published by Springer Nature. This book was released on 2020-07-30 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
Author :
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (243 download)
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bertus Johann Steyn
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.:/5 (794 download)
Download or read book A Multigrid Algorithm for the Solution of the Poisson Equation written by Bertus Johann Steyn and published by . This book was released on 1999 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Philippe G. Ciarlet
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444512246
Total Pages : 1187 pages
Book Rating : 4.5/5 (122 download)
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications
Author : Roman Wienands
Publisher : CRC Press
ISBN 13 : 1420034995
Total Pages : 235 pages
Book Rating : 4.4/5 (2 download)
Download or read book Practical Fourier Analysis for Multigrid Methods written by Roman Wienands and published by CRC Press. This book was released on 2004-10-28 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile
Author : Achi Brandt
Publisher : SIAM
ISBN 13 : 9781611970753
Total Pages : 239 pages
Book Rating : 4.9/5 (77 download)
Download or read book Multigrid Techniques written by Achi Brandt and published by SIAM. This book was released on 2011-01-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
