## An Introduction to Multigrid MethodsInspired by a series of lectures given in Delft, Bristol, Lyons, Zurich, and Beijing, this book is a corrected reprint of the 1992 classic. Provides a complete introduction to multigrid methods for partial differential equations, without requiring an advanced knowledge of mathematics. Topics such as the basic multigrid principle, smoothing methods and their Fourier analysis, course grid approximation, multigrid cycles and results of multigrid theory are treated. Applications in computational fluid dynamics are discussed extensively. |

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### Contents

Finite difference and finite volume discretization | 14 |

Basic iterative methods | 36 |

Prolongation and restriction | 60 |

Copyright | |

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amplification factor anisotropic diffusion equation application assumed basic iterative methods Brandt cell-centred cells choose coarse grid approximation coarse grid correction coefficients computational fluid dynamics computational grid conjugate gradient methods convection-diffusion equation damping defined dimensions Dirichlet boundary conditions discussed equation discretized according error example Exercise F-cycle Figure finest grid finite difference finite volume discretization flow follows Fourier modes Fourier sine series Fourier smoothing analysis Fourier smoothing factors Gauss-Seidel method given gives grid G grid points Hackbusch 1985 Hence IBLU iteration matrix Lemma line Gauss-Seidel linear interpolation M-matrix mesh-size mixed derivative multigrid algorithm multigrid methods Navier-Stokes equations nested iteration non-linear multigrid obtained point Gauss-Seidel rate of convergence rotated anisotropic diffusion satisfied Section semi-coarsening seven-point ILU smoothing method smoothing property solution solved stencil notation structure diagram subroutine symmetric Table test problem Theorem transfer operators two-grid algorithm upwind discretization values vertex-centred Wesseling Wittum zebra