# Practical Fourier Analysis for Multigrid Methods (Google eBook)

CRC Press, Oct 28, 2004 - Mathematics - 240 pages
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 detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.

This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the details of the subject.

The first chapter delivers an explanation of concepts, including Fourier components and multigrid principles. Chapter 2 highlights the basic elements of local Fourier analysis and the limits to this approach. Chapter 3 examines multigrid methods and components, supported by a user-friendly GUI. Chapter 4 provides case studies for two- and three-dimensional problems. Chapters 5 and 6 detail the mathematics embedded within the software system. Chapter 7 presents recent developments and further applications of local Fourier analysis for multigrid methods.

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### Contents

 INTRODUCTION 3 MAIN FEATURES OF LOCAL FOURIER ANALYSIS FOR MULTIGRID 29 MULTIGRID AND ITS COMPONENTS IN LFA 35 USING THE FOURIER ANALYSIS SOFTWARE 57 The Theory behind LFA 97 FOURIER ONEGRID OR SMOOTHING ANALYSIS 99
 FOURIER TWO AND THREEGRID ANALYSIS 147 FURTHER APPLICATIONS OF LOCAL FOURIER ANALYSIS 183 FOURIER REPRESENTATION OF RELAXATION 203 REFERENCES 207 Index 213 Copyright