An Introduction to Multigrid MethodsWiley, 1992 - 284 pagine Multigrid methods have developed rapidly and are used as a powerful tool for the efficient solution of elliptic and hyperbolic equations. This text provides an introduction to multigrid methods for partial differential equations, with applications to practical flow problems. |
Sommario
6 | 2 |
The essential principle of multigrid methods for partial | 8 |
Finite difference and finite volume discretization | 14 |
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Introduction to Multigrid Methods Institute for Computer Applications in Science and Engineering,P. Wesseling Visualizzazione estratti - 1995 |
Parole e frasi comuni
amplification factor anisotropic diffusion equation application assumed basic iterative methods cell-centred cells coarse grid approximation coarse grid correction coefficients computational fluid dynamics conjugate gradient conjugate gradient methods convection-diffusion equation damping defined differential equation dimensions Dirichlet boundary conditions discussed e₁ equation discretized according error example F-cycle Figure finest grid finite difference follows Fourier modes Fourier sine series Fourier smoothing analysis Fourier smoothing factors Gauss-Seidel method given gives grid G grid points Hackbusch 1985 Hence Lemma line Gauss-Seidel linear interpolation M-matrix mesh-size multigrid algorithm multigrid methods Navier-Stokes equations nested iteration obtained P₁ P₂ point Gauss-Seidel rate of convergence robust rotated anisotropic diffusion satisfied Section semi-coarsening seven-point ILU smoother smoothing method smoothing property solution solved subroutine symmetric test problem Theorem two-grid algorithm upwind discretization values vector vertex-centred Wittum zebra μι