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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Elements of Multigrid 31
Algebraic Multigrid AMG
Multilevel Adaptive Methods
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additions algebraic algorithm analysis applied approximation assume called Chapter coarse coarse-grid coarsening coefficients complexity components computing consider constant construction correction corresponding cost cycle defined denote depends derive determined developed dimensions direction discretization discretization error effective eigenvalues elements equation error example Exercise Figure fine-grid full weighting function Gauss-Seidel given gives grid grid points important indicates initial guess interpolation iteration linear m/d steps matrix means mesh method minimal model problem modes multigrid multiplications nonlinear norm Note observation obtain one-dimensional operator original oscillatory performance points polynomial reduce relaxation represented residual residual equation restriction satisfy scheme Show shown simple smooth solution solve space step strongly sweeps symmetric Table Theorem two-grid updated V-cycle vector weighted Jacobi write zero
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Finite Elemente: Theorie, schnelle Löser und Anwendungen in der ...
No preview available - 2007