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Finite difference and finite volume discretization
Basic iterative methods
Prolongation and restriction
6 other sections not shown
amplification factor anisotropic diffusion equation application assumed basic iterative methods Brandt cell-centred cells choose coarse grid approximation coarse grid correction coefficients computational fluid dynamics computational grid conjugate gradient methods convection-diffusion equation damping defined dimensions Dirichlet boundary conditions discussed equation discretized according error example Exercise F-cycle Figure finest grid finite difference Finite volume discretization flow follows Fourier modes Fourier sine series Fourier smoothing analysis Fourier smoothing factors Gauss-Seidel method given gives grid G grid points Hackbusch 1985 Hence IBLU iteration matrix Lemma line Gauss-Seidel linear interpolation M-matrix mesh-size mixed derivative multigrid algorithm multigrid methods Navier-Stokes equations nested iteration non-linear multigrid obtained P,PD partial differential equations point Gauss-Seidel rate of convergence rotated anisotropic diffusion satisfied Section semi-coarsening seven-point ILU smoothing method smoothing property solution solved stencil notation structure diagram subroutine symmetric test problem Theorem transfer operators two-grid algorithm upwind discretization values vertex-centred Wittum zebra