A Multigrid Tutorial: Second EditionThis second edition of the popular A Multigrid Tutorial preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements. This introductory book is ideally suited as a companion textbook for graduate numerical analysis courses. It is written for computational mathematicians, engineers, and other scientists interested in learning about multigrid. |
Contents
Chapter | 1 |
Chapter | 7 |
Chapter IV | 25 |
Chapter V | 39 |
Chapter VI | 57 |
Chapter VII | 71 |
Bibliography 93 | |
Contents | |
Implementation 45 | 45 |
Some Theory 73 | 73 |
Nonlinear Problems | 95 |
Selected Applications | 113 |
Algebraic Multigrid AMG | 137 |
Multilevel Adaptive Methods | 163 |
Finite Elements | 177 |
| 191 | |
Other editions - View all
A Multigrid Tutorial: Second Edition William L. Briggs,Van Emden Henson,Steve F. McCormick Limited preview - 2000 |
A Multigrid Tutorial: Second Edition William L. Briggs,Van Emden Henson,Steve F. McCormick Limited preview - 2000 |
Common terms and phrases
algebraic algorithm for computing applied approximation bilinear forms boundary conditions boundary value problem CF(P Chapter Chinese remainder theorem coarse coarse-grid coarse-grid correction coarsening complexity components composite grid computing the coefficients consider constant convergence factor cycle defined denote discrete Fourier transform discrete L2 norm discretization error eigenvalues eigenvectors elements exact solution example Exercise F-points f₁ fine-grid points full weighting grid points h₁ initial guess integer irreducible polynomial iteration matrix Jacobi method L2 norm level of discretization m/d steps m₁ mesh mod P(u mod u˛ modulo multigrid methods multiplications Newton-MG Newton's method nonlinear null space obtain an algorithm oscillatory modes polynomial rational numbers relaxation scheme relaxation sweeps residual equation shows smooth error solve solver stencil system of bilinear two-dimensional two-grid correction scheme updated V-cycle vector wavenumbers weighted Jacobi method Xoyo y-direction zero ω ω ω