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. |
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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
Ahuh algebraic algorithm amplification factor applied boundary conditions boundary value problem Chapter coarse coarse-grid correction coarse-grid operator coarse-grid points coarsening coarsest grid coefficients composite grid computed Consider convergence factor defined dimensions discrete L2 norm discretization error eigenvalues eigenvectors error norm exact solution example Exercise F-points Figure fine-grid points finite difference Fourier modes function Galerkin Gauss-Seidel method geometric grid points grid spacing h 2h intergrid transfer interpolation operator iteration matrix level of discretization linear interpolation M-matrix mesh multigrid methods Neumann boundary conditions Newton-MG Newton's method nonzero null space one-dimensional model problem oscillatory modes Poisson equation R(In relaxation scheme relaxation sweeps residual equation residual norm semicoarsening Show smooth error smooth modes solve solver stencil symmetric two-dimensional two-grid correction scheme uniform grid updated V-cycle v₁ variational properties vector wavenumbers weighted Jacobi method y-direction zero