Analysis of the SOR Iteration for the 9-point LaplacianNational Aeronautics and Space Administration, Langley Research Center, 1986 - Numerical analysis |
Common terms and phrases
9-pt line 9-pt point methods 9-pt stencil Adams and Jordan[1986 analyzed asymptotic c₁ change of variables complex conjugate converge slightly faster convergence behavior convergence rate cosnh data flow determine the optimal eigen eigenmodes eigenvalue eigenvector corresponding equivalence classes Figure 3.6b five-point model problem four colors Fourier analysis given in Figure gives grid is colored grid points hence iteration matrix iteration number Jacobi method k₁ line methods line SOR methods multicolor orderings natural rowwise ordering nine-point stencil nodes Numerical Analysis optimal w overrelaxation parallel computers Point and Line point SOR methods Popt pseudo SOR method quartic equation rate of convergence real root Red/Black ordering separation of variables SIAM Journal sinny sinx small h smooth initial data SOR iteration spectral radius Stencil in Variable true SOR methods update formula v+1 v+1 v+2 v+2 v+3 v+3 values w²cos²nh Wopt α³