Download or read book Extended Local Fourier Analysis for Multigrid written by Roman Wienands and published by . This book was released on 2001 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book Extending and Automating Fourier Analysis for Multigrid Methods written by Hannah Rittich and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Local Fourier Analysis for Saddle point Problems written by Yunhui He and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution of saddle-point problems has attracted considerable interest in recent years, due to their indefiniteness and often poor spectral properties that make efficient solution difficult. While much research already exists, developing efficient algorithms remains challenging. Researchers have applied finite-difference, finite element, and finite-volume approaches successfully to discretize saddle-point problems, and block preconditioners and monolithic multigrid methods have been proposed for the resulting systems. However, there is still much to understand. Magnetohydrodynamics (MHD) models the flow of a charged fluid, or plasma, in the presence of electromagnetic fields. Often, the discretization and linearization of MHD leads to a saddle-point system. We present vector-potential formulations of MHD and a theoretical analysis of the existence and uniqueness of solutions of both the continuum two-dimensional resistive MHD model and its discretization. Local Fourier analysis (LFA) is a commonly used tool for the analysis of multigrid and other multilevel algorithms. We first adapt LFA to analyse the properties of multigrid methods for both finite-difference and finite-element discretizations of the Stokes equations, leading to saddle-point systems. Monolithic multigrid methods, based on distributive, Braess-Sarazin, and Uzawa relaxation are discussed. From this LFA, optimal parameters are proposed for these multigrid solvers. Numerical experiments are presented to validate our theoretical results. A modified two-level LFA is proposed for high-order finite-element methods for the Lapalce problem, curing the failure of classical LFA smoothing analysis in this setting and providing a reliable way to estimate actual multigrid performance. Finally, we extend LFA to analyze the balancing domain decomposition by constraints (BDDC) algorithm, using a new choice of basis for the space of Fourier harmonics that greatly simplifies the application of LFA. Improved performance is obtained for some two- and three-level variants.

Download or read book Automated Local Fourier Analysis aLFA and Geometric Multigrid for Graphene written by Nils Kintscher and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Fourier Analysis of Multigrid type Iterative Methods written by Naomi H. Decker and published by . This book was released on 1987 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Local Fourier Mode Analysis in the Multigrid Solution of Coupled Systems written by David Michael Alber and published by . This book was released on 2004 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fourier Analysis of Multigrid Methods for General Systems of PDE written by Per Lötstedt and published by . This book was released on 1990 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multigrid Techniques written by Achi Brandt and published by SIAM. This book was released on 2011-07-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition of a classic text presents the best practices of developing multigrid solvers for large-scale computational problems. This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics and numerical analysis.

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.

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.

Download or read book Multigrid Methods written by W. Hackbusch and published by Springer. This book was released on 2006-11-15 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Multilevel Optimization in VLSICAD written by Jingsheng Jason Cong and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades, multiscale algorithms have become a dominant trend in large-scale scientific computation. Researchers have successfully applied these methods to a wide range of simulation and optimization problems. This book gives a general overview of multiscale algorithms; applications to general combinatorial optimization problems such as graph partitioning and the traveling salesman problem; and VLSICAD applications, including circuit partitioning, placement, and VLSI routing. Additional chapters discuss optimization in reconfigurable computing, convergence in multilevel optimization, and model problems with PDE constraints. Audience: Written at the graduate level, the book is intended for engineers and mathematical and computational scientists studying large-scale optimization in electronic design automation.

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.

Download or read book Fourier Analysis of a Robust Multigrid Method for Convection diffusion Equations written by Arnold Reusken and published by . This book was released on 1994 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fourier Analysis written by William O. Bray and published by CRC Press. This book was released on 2020-12-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.