Extending and Automating Fourier Analysis for Multigrid Methods PDF Download
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Author: Hannah Rittich
Publisher:
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Category :
Languages : en
Pages :
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Author: Hannah Rittich
Publisher:
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Category :
Languages : en
Pages :
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Author: Roman Wienands
Publisher: CRC Press
ISBN: 1420034995
Category : Mathematics
Languages : en
Pages : 235
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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: Roman Wienands
Publisher:
ISBN: 9783884574034
Category :
Languages : en
Pages : 176
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Author: Per Lötstedt
Publisher:
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Category :
Languages : en
Pages : 35
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Author: Naomi H. Decker
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Category :
Languages : en
Pages : 264
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Author: Nils Kintscher
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Category :
Languages : en
Pages :
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Author: Hans-Joachim Bungartz
Publisher: Springer Nature
ISBN: 3030479560
Category : Computers
Languages : en
Pages : 624
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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: Yunhui He
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Category :
Languages : en
Pages :
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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.
Author: Arnold Reusken
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Author: Guohua Zhou
Publisher:
ISBN:
Category : Fourier analysis
Languages : en
Pages : 186
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