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Practical Fourier Analysis for Multigrid Methods

Practical Fourier Analysis for Multigrid Methods by Roman Wienands
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PRACTICAL APPLICATION OF LFA AND xlfa
Introduction
Some Notation
Basic Iterative Schemes
A First Discussion of Fourier Components
From Residual Correction to Coarse-Grid Correction
Multigrid Principle and Components
A First Look at the Graphical User Interface

Main Features of Local Fourier Analysis for Multigrid
The Power of Local Fourier Analysis
Basic Ideas
Applicability of the Analysis

Multigrid and Its Components in LFA
Multigrid Cycling
Full Multigrid
xlfa Functionality-An Overview
Implemented Coarse-Grid Correction Components
Implemented Relaxations

Using the Fourier Analysis Software
Case Studies for 2D Scalar Problems
Case Studies for 3D Scalar Problems
Case Studies for 2D SYSTEMS of Equations
Creating New Applications

THE THEORY BEHIND LFA
Fourier One-Grid or Smoothing Analysis
Elements of Local Fourier Analysis
High and Low Fourier Frequencies
Simple Relaxation Methods
Pattern Relaxations
Smoothing Analysis for Systems
Multistage (MS) Relaxations
Further Relaxation Methods
The Measure of h-Ellipticity

Fourier Two- and Three-Grid Analysis
Basic Assumptions
Two-Grid Analysis for 2D Scalar Problems
Two-Grid Analysis for 3D Scalar Problems
Two-Grid Analysis for Systems
Three-Grid Analysis

Further Applications of Local Fourier Analysis
Orders of Transfer Operators
Simplified Fourier k-Grid Analysis
Cell-Centered Multigrid
Fourier Analysis for Multigrid Preconditioned by GMRES

APPENDIX
Fourier Representation of Relaxation
Two-Dimensional Case
Three-Dimensional Case
CRC Press; October 2004
235 pages; ISBN 9781420034998
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Title: Practical Fourier Analysis for Multigrid Methods
Author: Roman Wienands; Wolfgang Joppich
 
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