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McCormick S.F. Multigrid Methods (Frontiers in Applied Mathematics)
McCormick S.F.  Multigrid Methods (Frontiers in Applied Mathematics)







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: Multigrid Methods (Frontiers in Applied Mathematics)

: McCormick S.F.

: en

: /

:

ed2k: ed2k stats

: 1987

: 300

: 26.10.2010

: | | ID
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A posteriori error estimates      114115
Accommodative scheme      27
Algebraic approximation property      143 156
Algebraic error reduction      5 30
Algebraic multigrid (AMG)      48 5253 7375
Algebraic multigrid (AMG) for scalar problems      97119
Algebraic multigrid (AMG) for systems problems      119127
Algebraic multigrid (AMG), coarse grid approximation in      8597
Algebraic multigrid (AMG), convergence results in      7882 8597
Algebraic multigrid (AMG), smoothing property of      8285
Algebraic multigrid (AMG), terminology and assumptions of      7578
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      4849 50 52 53
c-points      99100 101103 104 108 116117 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      3842 46 8587
Coarse grid approximation, correction      21 22 25 41 43 46 63 65 66 69 7681 104 107 109
Coarse grid approximation, finite difference approximations (CFA)      3941 49
Coarse grid approximation, Galerkin approximations (CGA)      4041 49
Coarse grid approximation, operators      76 7879 103104 124
Coarsening process      77 8788 99 100103 107 109 115-119
Coarsening process, strategy in AMG      96 101103 115119
Compressible flow      58
Condition number      11
Conjugate gradients      43 54 173
Conjugate residuals      43
Conservation laws      31
Conservative discretization      34
Convection-diffusion equation      5153
Convergence factor      9 11 14 24 25 108 114 124 132
Convergence factor, asymptotic      105 122123
Convergence factor, estimate of      150153 166167 169
Convergence factor, two-grid      173 176
Convergence factor, V-cycle      7981 121 127
Convergence theorems      76 7879
Convergence theory      142
Convergence theory in general case      153161
Convergence theory in symmetric, positive definite case      143150
Convergence theory, two-level      82 8889
Convex interpolation      122
Correction scheme (CS)      41 68
CS      (see Correction scheme)
Cycling      2123 2430
Cycling, accommodative      27
Cycling, computational costs of      23 26 104
Cycling, fixed      27
Cycling, full multigrid (FMG)      22 2530 69 161162 171 175
Cycling, sawtooth      43 44 47 50 64 67 68
Cycling, two-grid      43 44
Cycling, V-cycIe      7981 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 121122 142 143 167169 171
Discontinuous coefficients      3839 49 50 52 53 74 105 107 109
Discontinuous solutions      60 70 74
Discretization error      34 8 25
Discretization(s)      6163 119
Discretization(s) of elliptic variational problems      137143
Discretization(s), central      34
Discretization(s), conservative      3435
Elasticity problems      121123 141
Elliptic partial differential equations      7475
Elliptic systems      131 142
Elliptic variational problems      137143
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      8485 89 121
Error, discretization      3 34 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 5771
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 9point      164165
Euler time, finite difference      3233 35 37 40 49 50 62 112 131 172
Euler time, finite element      75 109 121 131 135
Euler time, finite volume      3435 37 3941 46 47 62
Euler time, flux splitting      3437 68
Euler time, Galerkin      4042 49 6971 77
Euler time, Lax Wendroff      61
Euler time, Runge Kutta-type      36
Euler time, uniform      119 127
Euler time, upwind difference      6263 68
F-points      99100 101104 106 126
F-variables      86 88 120 126
FAS-cycle      (see Full approximation scheme)
Finite difference discretization      3233 35 37 40 50 62 112 131 172
Finite element discretizations      75 109 121 131 135
Finite volume discretization      3435 37 3941 4647 62
Fixed scheme      27 (see also Cycling)
Flux splitting      34 3537 68
FMG      (see Cycling full
Fourier mode (smoothing) analysis      11 13 2425 44 45 131 176
Fourier mode (smoothing) analysis, estimates      162170
Full approximation scheme (FAS)      41 64
Full weighting      1718 38
Galerkin approximations      4041 42 49 6971 77
Gauss Seidel method (relaxation)      78 2729 42 63 70 77 82 83 84 105 118 120121 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      2729 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 109112
Grids, nonstaggered      63 124
Grids, nonuniform      36 39 74 109112
Grids, size      54 73 74 110
h-Ellipticity measure      169170
Half weighting      38
Helmholtz equations      50 94
Higher order systems      131
Hilbert scale of spaces      136137
Hyperbolic equations      32 5354
Incomplete block LU-factorization (IBLU)      42 50
Incomplete factorization      42 43 45 4950
Incomplete line LU-factorization (ILLU)      42
Incomplete LU-factorization (ILU)      42 50
Injection      17 137
Interpolation      (see also Prolongation)
Interpolation formulas in AMG      9091 93 102105 117119 120 126
Interpolation of eigenvectors      94 118119
Interpolation, accuracy of      115
Interpolation, along direct connections      9192
Interpolation, convex      116117 122
Interpolation, general      9293
Interpolation, linear      37 103 118
Interpolation, long-range      92 116
Interpolation, one-sided      9596 101
Interpolation, piecewise multilinear      14
Interpolation, standard      87
Inviscid compressible flow      57
Irrotational flow      58
Isoparametric finite elements      171
Jacobi method (relaxation)      714 18 24 25 45 49 51 84
K-matrix      3334 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 6466
Lexicographic order      6
Linear interpolation      49
Lipschitz boundary      140 143
Local mode analysis      169170
M-matrix      33 112 123
M-matrix, application of      9091
M-matrix, symmetric      78 8385 93 98 99 119
M-matrix, weakly diagonally dominant      91 92 9495
MG00      4849 50 5253
MGAZ      52
MGD4      53
MGD5      50 5253
MGDI      50 5253
MGHZ      52
Navier Stokes equations      57 5860
Nested iteration      1619 20 22
Neumann boundary conditions      112 143 171
Newton method      3637 49 53 6869 123 129
Nonconforming finite element method      171
Nonlinear basis functions      171
Nonlinear problems      32 5354 64 123124
Nonsymmetric operators      105 112114
Nonuniform grids      36 39
Norm      2 35 9 Euclidean
Norm of residual and global errors      2728
Norm, discrete      132134
Operator complexity      103 123
P-smoothing factor      45
padding      32 50
Parallelization      6566 84
Periodic boundary conditions      163164 166
Plane-stress problem      121
PLTMG      48 49
Poisson equations      24 26 50 54
Poisson solver      48
Poissons ratio      121
Prandtl numbers      59
Prolongation      3739 4748 49 54
Prolongation, designing      171172
Prolongation, matrix-dependent      49 50 53
R-smoothing factors      45 47
Rayleigh quotient      118119
Re-entrant comer      110 142
Red-black relaxation      2729 42 149
Regularity      140142
Relaxation      719 70
Relaxation, acceleration of      43
Relaxation, block      149150
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      2729 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      1718 3739 4748 54 76 105 Injection Full
Reynolds numbers      5960
Richardson method (relaxation)      146 166167 174
Runge Kutta time stepping method      67
Runge Kutta-type discretization      36
Semidiscretization      6668
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      8185
Smoothing factors      24 70 143 146148 149 156
Smoothing factors for block Jacobi and block Gauss Seidel system      172
Smoothing factors, optimal      166
Smoothing methods      (see Relaxation)
Smoothing property      14 8185
Smoothness, algebraic      8485 99
Sobolev spaces      3 141 142
Software      4850 (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      1718
Stencils, 5-point      6
Stencils, 9-point symmetric      163164
Stencils, finite difference      33
Stencils, symmetric      176
Stokes equations      57 58 128
Strong connections      114 116117
Subsonic flow      53 70
Supersonic flow      65 70
Switched evolution relaxation (SER)      69
Symmetric operators      34 38 7778 8385 93 9899 114 119120 132133 143-150 159
Time-dependent problems      36 5760 6469
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      136143
Variational multigrid theory, convergence theory and      143150 153161
Variational multigrid theory, estimate of convergence factors in      150153
Variational multigrid theory, Fourier analysis estimates and      162170
Variational multigrid theory, full multigrid and      161162
Variational multigrid theory, notation assumptions in      132135
Variational multigrid theory, problems in      171177
Vectorization      42 43 48 50 71 84
viscosity      58 59
VLSI design problem      123124
W-cycle      (see Cycling W-cycle)
Work units (WU)      23 29
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