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| Ïîèñê ïî óêàçàòåëÿì |
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| McCormick S.F. — Multigrid Methods (Frontiers in Applied Mathematics) |
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| Ïðåäìåòíûé óêàçàòåëü |
A posteriori error estimates 114—115
Accommodative scheme 27
Algebraic approximation property 143 156
Algebraic error reduction 5 30
Algebraic multigrid (AMG) 48 52—53 73—75
Algebraic multigrid (AMG) for scalar problems 97—119
Algebraic multigrid (AMG) for systems problems 119—127
Algebraic multigrid (AMG), coarse grid approximation in 85—97
Algebraic multigrid (AMG), convergence results in 78—82 85—97
Algebraic multigrid (AMG), smoothing property of 82—85
Algebraic multigrid (AMG), terminology and assumptions of 75—78
Algebraic smoothness (see “Error algebraically
Aliasing 13
AMG (see “Algebraic multigrid”)
Anisotropic coefficients 51 105 107 109
Approximation assumption 81
Approximation property 138 145
Artificial viscosity method 34
Beam — Warming algorithm 71
Black box multigrid method 48 74 119 127
Boundary-fitted coordinate transformation 32 51
BOXMG 48—49 50 52 53
c-points 99—100 101—103 104 108 116—117 126
C-variables 86 88 126
C/F-relaxation 105 114
Cauchy — Riemann equations 120 128
CFA (see “Coarse grid finite
CGA (see “Coarse grid Galerkin
Chebyshev acceleration 43
Coarse grid approximation 38—42 46 85—87
Coarse grid approximation, correction 21 22 25 41 43 46 63 65 66 69 76—81 104 107 109
Coarse grid approximation, finite difference approximations (CFA) 39—41 49
Coarse grid approximation, Galerkin approximations (CGA) 40—41 49
Coarse grid approximation, operators 76 78—79 103—104 124
Coarsening process 77 87—88 99 100—103 107 109 115-119
Coarsening process, strategy in AMG 96 101—103 115—119
Compressible flow 58
Condition number 11
Conjugate gradients 43 54 173
Conjugate residuals 43
Conservation laws 31
Conservative discretization 34
Convection-diffusion equation 51—53
Convergence factor 9 11 14 24 25 108 114 124 132
Convergence factor, asymptotic 105 122—123
Convergence factor, estimate of 150—153 166—167 169
Convergence factor, two-grid 173 176
Convergence factor, V-cycle 79—81 121 127
Convergence theorems 76 78—79
Convergence theory 142
Convergence theory in general case 153—161
Convergence theory in symmetric, positive definite case 143—150
Convergence theory, two-level 82 88—89
Convex interpolation 122
Correction scheme (CS) 41 68
CS (see “Correction scheme”)
Cycling 21—23 24—30
Cycling, accommodative 27
Cycling, computational costs of 23 26 104
Cycling, fixed 27
Cycling, full multigrid (FMG) 22 25—30 69 161—162 171 175
Cycling, sawtooth 43 44 47 50 64 67 68
Cycling, two-grid 43 44
Cycling, V-cycIe 79—81 101 105 121 127
Cycling, W-cycle 21 22 64 160 173 174
Defect correction 34 49 54 58 71
Dirichlet boundary conditions 106 107 112 121—122 142 143 167—169 171
Discontinuous coefficients 38—39 49 50 52 53 74 105 107 109
Discontinuous solutions 60 70 74
Discretization error 3—4 8 25
Discretization(s) 61—63 119
Discretization(s) of elliptic variational problems 137—143
Discretization(s), central 34
Discretization(s), conservative 34—35
Elasticity problems 121—123 141
Elliptic partial differential equations 74—75
Elliptic systems 131 142
Elliptic variational problems 137—143
Energy inner product 2
Energy norm 4 79 131
Energy norm, convergence factors 150
Enthalpy damping 66
Entropy condition 60
Error, algebraic 5 30
Error, algebraically smooth 84—85 89 121
Error, discretization 3 3—4 25
Error, global 4 5 6 14 27
Error, oscillatory (high frequency) 11 16 17 19
Error, residual 27
Error, smooth (low frequency) 11 16 18 19 20 22 73 76 85 96 97 121
Error, truncation 3 4 6 27 30
Euclidean inner product 77 138
Euclidean norm 4 9 77
Euler equations 36 57—71
Euler equations of inviscid gas dynamics 32
Euler equations, linearized isenthalpic 70
Euler equations, solver 66
Euler equations, steady state 61
Euler equations, time-dependent 60
Euler time 36
Euler time, 5-point and 9—point 164—165
Euler time, finite difference 32—33 35 37 40 49 50 62 112 131 172
Euler time, finite element 75 109 121 131 135
Euler time, finite volume 34—35 37 39—41 46 47 62
Euler time, flux splitting 34—37 68
Euler time, Galerkin 40—42 49 69—71 77
Euler time, Lax — Wendroff 61
Euler time, Runge — Kutta-type 36
Euler time, uniform 119 127
Euler time, upwind difference 62—63 68
F-points 99—100 101—104 106 126
F-variables 86 88 120 126
FAS-cycle (see “Full approximation scheme”)
Finite difference discretization 32—33 35 37 40 50 62 112 131 172
Finite element discretizations 75 109 121 131 135
Finite volume discretization 34—35 37 39—41 46—47 62
Fixed scheme 27 (see also “Cycling”)
Flux splitting 34 35—37 68
FMG (see “Cycling full
Fourier mode (smoothing) analysis 11 13 24—25 44 45 131 176
Fourier mode (smoothing) analysis, estimates 162—170
Full approximation scheme (FAS) 41 64
Full weighting 17—18 38
Galerkin approximations 40—41 42 49 69—71 77
Gauss — Seidel method (relaxation) 7—8 27—29 42 63 70 77 82 83 84 105 118 120—121 126 147 169
Gauss — Seidel method (relaxation) forward 42
Gauss — Seidel method (relaxation), alternating line 107
Gauss — Seidel method (relaxation), backward 42
Gauss — Seidel method (relaxation), block 45 49 50 52 128
Gauss — Seidel method (relaxation), line 70
Gauss — Seidel method (relaxation), point 49 50
Gauss — Seidel method (relaxation), red-black 27—29 42 149
Gauss — Seidel method (relaxation), symmetric 47 70
Gauss — Seidel method (relaxation), two-block 149
Grid complexity 103 108
GRIDPACK 48 49
Grids, nonrectangular 32 50 62 74 109—112
Grids, nonstaggered 63 124
Grids, nonuniform 36 39 74 109—112
Grids, size 54 73 74 110
h-Ellipticity measure 169—170
Half weighting 38
Helmholtz equations 50 94
Higher order systems 131
Hilbert scale of spaces 136—137
| Hyperbolic equations 32 53—54
Incomplete block LU-factorization (IBLU) 42 50
Incomplete factorization 42 43 45 49—50
Incomplete line LU-factorization (ILLU) 42
Incomplete LU-factorization (ILU) 42 50
Injection 17 137
Interpolation (see also “Prolongation”)
Interpolation formulas in AMG 90—91 93 102—105 117—119 120 126
Interpolation of eigenvectors 94 118—119
Interpolation, accuracy of 115
Interpolation, along direct connections 91—92
Interpolation, convex 116—117 122
Interpolation, general 92—93
Interpolation, linear 37 103 118
Interpolation, long-range 92 116
Interpolation, one-sided 95—96 101
Interpolation, piecewise multilinear 14
Interpolation, standard 87
Inviscid compressible flow 57
Irrotational flow 58
Isoparametric finite elements 171
Jacobi method (relaxation) 7—14 18 24 25 45 49 51 84
K-matrix 33—34 35 50
Kaczmarz method (relaxation) 42 50 128 174
Laplace equation 56 123 163 166
Laplace operator 106 107 108 109
Laplace operator, skewed 74
Lax — Wendroff time stepping 36 61 64—66
Lexicographic order 6
Linear interpolation 49
Lipschitz boundary 140 143
Local mode analysis 169—170
M-matrix 33 112 123
M-matrix, application of 90—91
M-matrix, symmetric 78 83—85 93 98 99 119
M-matrix, weakly diagonally dominant 91 92 94—95
MG00 48—49 50 52—53
MGAZ 52
MGD4 53
MGD5 50 52—53
MGDI 50 52—53
MGHZ 52
Navier — Stokes equations 57 58—60
Nested iteration 16—19 20 22
Neumann boundary conditions 112 143 171
Newton method 36—37 49 53 68—69 123 129
Nonconforming finite element method 171
Nonlinear basis functions 171
Nonlinear problems 32 53—54 64 123—124
Nonsymmetric operators 105 112—114
Nonuniform grids 36 39
Norm 2 3—5 9 “Euclidean
Norm of residual and global errors 27—28
Norm, discrete 132—134
Operator complexity 103 123
P-smoothing factor 45
padding 32 50
Parallelization 65—66 84
Periodic boundary conditions 163—164 166
Plane-stress problem 121
PLTMG 48 49
Poisson equations 24 26 50 54
Poisson solver 48
Poisson’s ratio 121
Prandtl numbers 59
Prolongation 37—39 47—48 49 54
Prolongation, designing 171—172
Prolongation, matrix-dependent 49 50 53
R-smoothing factors 45 47
Rayleigh quotient 118—119
Re-entrant comer 110 142
Red-black relaxation 27—29 42 149
Regularity 140—142
Relaxation 7—19 70
Relaxation, acceleration of 43
Relaxation, block 149—150
Relaxation, C/F 105 114
Relaxation, choosing 107
Relaxation, Jacobi (see “Jacobi method (relaxation)”)
Relaxation, Kaczmarz (see Kaczmarz method (relaxation)”)
Relaxation, local 129
Relaxation, red-black 27—29 42 149
Relaxation, Richardson (see “Richardson method (relaxation)”)
Relaxation, switched evolution (SER) 69
Relaxation, ZEBRA 42 52 176
Residual equation 19 20
Residual transfer (see “Restriction”)
Restriction 17—18 37—39 47—48 54 76 105 “Injection” “Full
Reynolds numbers 59—60
Richardson method (relaxation) 146 166—167 174
Runge — Kutta time stepping method 67
Runge — Kutta-type discretization 36
Semidiscretization 66—68
Shallow water equations 32
Smooth boundaries 142
Smooth coefficients 52
Smooth error 11 16 18 19 20 45 73 85 96 97 121
Smooth error, reduction of 22
Smooth error, vectors 76
Smoothers (see “Relaxation”)
Smoothing analysis (see “Fourier mode (smoothing) analysis”)
Smoothing assumption 81—85
Smoothing factors 24 70 143 146—148 149 156
Smoothing factors for block Jacobi and block Gauss — Seidel system 172
Smoothing factors, optimal 166
Smoothing methods (see “Relaxation”)
Smoothing property 14 81—85
Smoothness, algebraic 84—85 99
Sobolev spaces 3 141 142
Software 48—50 (see also “BOXMG” “BOXMG” “BOXMG” “GRIDPACK” “MGAZ” “MGD1” “BOXMG” “MGD4” “BOXMG” “MGD5” “BOXMG” “MGHZ” “MG00” “BOXMG” “PLTMG”)
Spectral analysis (see Fourier mode (smoothing) analysis)
Spectral radius 4
Stationary linear iterative methods 8 18 144
Steepest descent method 173
Steger — Warming scheme 68
Stencils 15 106 107
Stencils for restriction operators 17—18
Stencils, 5-point 6
Stencils, 9-point symmetric 163—164
Stencils, finite difference 33
Stencils, symmetric 176
Stokes equations 57 58 128
Strong connections 114 116—117
Subsonic flow 53 70
Supersonic flow 65 70
Switched evolution relaxation (SER) 69
Symmetric operators 3—4 38 77—78 83—85 93 98—99 114 119—120 132—133 143-150 159
Time-dependent problems 36 57—60 64—69
Transonic flow 53 58 65
Truncation, error 3 4 6 27 30
Truncation, level of 26
Upwind differencing 37
V-cycle (see “Cycling” “W-cycle”)
Variational multigrid theory 131 170
Variational multigrid theory, algebraic assumption motivation and verification in 136—143
Variational multigrid theory, convergence theory and 143—150 153—161
Variational multigrid theory, estimate of convergence factors in 150—153
Variational multigrid theory, Fourier analysis estimates and 162—170
Variational multigrid theory, full multigrid and 161—162
Variational multigrid theory, notation assumptions in 132—135
Variational multigrid theory, problems in 171—177
Vectorization 42 43 48 50 71 84
viscosity 58 59
VLSI design problem 123—124
W-cycle (see “Cycling” “W-cycle”)
Work units (WU) 23 29
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