A Multigrid Tutorial: Second Edition
This 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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Some Theory 73
Algebraic Multigrid AMG
Multilevel Adaptive Methods
Elements of Multigrid 31
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additions algebraic algorithm algorithm for computing analysis applied approximation assume bilinear forms block boundary called Chapter coarse coarse-grid coarsening coefficients complexity components computing computing the coefficients condition consider constant construction convergence correction corresponding cost cycle defined denote depends derive described determined developed dimensions direction discretization effective eigenvalues elements equation equivalent error exact example Exercise factor field Figure filter fine-grid function Gauss-Seidel given gives grid grid points important indices initial guess interpolation iteration linear m/d steps matrix means method minimal model problem modes multigrid multiplications nonlinear norm Note obtain one-dimensional operator oscillatory performance points polynomial problem ratio reduce relaxation represented requires satisfy scheme shown shows simple smooth solution solve space sweeps symmetric Table Theorem V-cycle vector weighted Jacobi write zero
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