Practical Fourier Analysis for Multigrid Methods
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A01=Roman Wienands
A01=Wolfgang Joppich
advanced mathematics
Author_Roman Wienands
Author_Wolfgang Joppich
Bilinear Interpolation
boundary
boundary value problems
Category=PBK
coarse
Coarse Grid Approximation
Coarse Grid Correction
Coarsening Strategy
components
condition
correction
dirichlet
Driven Cavity Problem
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equation
FMG
Fourier Components
Fourier Frequencies
FOURIER REPRESENTATION
Fourier Symbols
Gauss Seidel Relaxation
Grid Points
iterative solvers
Jacobi Relaxation
local Fourier analysis for multigrid systems
Low Frequency Order
Multigrid Algorithms
Multigrid Method
numerical analysis
Odd
operator
Operator Lh
partial differential equations
Point Relaxation
Point Smoother
poisson
Poisson Type Equations
scientific computing
Smoothing Properties
Standard Coarsening
transfer
Transfer Operators
Upwind Discretization
Product details
- ISBN 9781584884927
- Weight: 494g
- Dimensions: 152 x 229mm
- Publication Date: 28 Oct 2004
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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 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.
Roman Wienands, Wolfgang Joppich
