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| Авторизация |
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| Wesseling P. — An introduction to multigrid methods |
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| Предметный указатель |
 turbulence model 234
Accelerating basic iterative methods 207
Accuracy 18 20 29 34 163 175 176 196 243 244
Accuracy condition 71
Accuracy of prolongation 190
Accuracy rule 252 254
Accurate 20 23
Adaptive 176
Adaptive, cycle 196 198
Adaptive, discretization 181 259
Adaptive, finite element 201
Adaptive, grid generation 209
Adaptive, grid refinement 208
Adaptive, local grid refinement 227
Adaptive, methods 181
Adaptive, schedule 173 175 196 197 256 258
Adaptive, strategy 175
Adjoint 9 64 242 259
Admissible states 33
Aircraft 1 208 209 210
Airfoil 217 218 219 220 221 222 223 231
Algebraic smoothing factor 93 95
Algorithm 3 44 45 52 53 56 58 81 82 95 145 146 170 175 182 183 194 196 203 204 208 246 248
Algorithmic efficiency 1
Aliasing 106 107 109 112
Alternating damped white-black Gauss — Seidel 167
Alternating damped zebra Gauss — Seidel 167
Alternating ILU 51 52 141
Alternating Jacobi 42 121 123
Alternating line Gauss — Seidel 126 127 131
Alternating modified incomplete point factorization 167
Alternating modified point ILU 144
Alternating nine-point ILU 144
Alternating seven-point ILU 51 143 144 145
Alternating symmetric line Gauss — Seidel 132 167
Alternating white-black 158 160
Alternating white-black Gauss — Seidel 44 157 230
Alternating zebra 152 155 156 157 224
Alternating zebra Gauss — Seidel 44 154
Amplification factor 6 105 112 114 120 124 125 128 130 134 138 142 143 144 146 162 223 224
Amplification matrix 148 149 154 155 157 158 159
Amplification polynomial 161 166
Anisotropic diffusion equation 115 118 120 123 124 125 135 136 138 142 154 155 230 231 251
antisymmetric 77
Approximate factorization 204
Approximation property 89 91 92 184 187 188
Artificial averaging term 244
Artificial compressibility 244
Artificial diffusion 234
Artificial dissipation 160 165 166 226
Artificial parameter 244
Artificial time-derivative 160
Artificial viscosity 35 57
Asymptotic expansion 190 219
Asymptotic rate of convergence 41
Autonomous code 204
Autonomous program 200
Autonomous subroutine 82 201
Average rate of converge 41
Average reduction factor 95
BACKWARD 42
Backward, difference operator 16 22
Backward, Euler 228
Backward, Gauss — Seidel 125 128
Backward, horizontal line Gauss — Seidel 44
Backward, ordering 43 44 51 129 234
Backward, vertical line Gauss — Seidel 223
Basic iterative method 6 7 36 37 41 42 46 47 53 56 96 97 160 201 202 203
Basic iterative type 245
Basic multigrid algorithm 168 172 194
Basic multigrid principle 169
Basic two-grid algorithm 168
Bifurcates 255
Bifurcation problem 170
Biharmonic equation 57
Bilinear interpolation 67 68 72 222 235 253
Black-box 2 82 200 204
Block Gauss — Seidel 42 44
Block Jacobi 42
Boundary condition 5 15 16 17 22 27 28 29 32 35 69 70 71 89 120 128 136 167 214 216 219 225 228 234 241 242 259
Boundary conforming 216
Boundary conforming, grid 213 214 215
Boundary fitted 214
Boundary fitted coordinate mapping 118
Boundary fitted coordinates 115
Boundary fitted grid 115
Boundary layer 210
Boussinesq 235 236 242 245 254 259
BOXMG 200 201
Buoyancy 236 241 255
Canonical form of the basic multigrid algorithm 194
Cartesian components 215
Cartesian tensor notation 14 33 211 224
Cell-centred 32 34 68 69 176 177 225 235
Cell-centred, coarsening 60 61 94 229 251
Cell-centred, discretization 13 27 60
Cell-centred, finite volume 28 30
Cell-centred, grid 27 64 68 69 94 100 101 103 104
Cell-centred, MG 83 94 103
Cell-centred, multigrid 73 76 84
Cell-centred, prolongation 69 71
Central approximation 239
Central difference 2 117 216 221 226 238
Central discretization 34 128 164 234
Central scheme 257
CFD 210
CFL 161 163
cgs 205 206 207
Checkerboard type fluctuations 236
Choleski 204
Cimmino 59
Circulation 219 221
Classical aerodynamics 213
Cluster 205
Coarse grid 7 8 10 60 68 106 107 110
Coarse grid, approximation 8 10 70 76 79 93 251
Coarse grid, correction 10 85 88 90 93 106 110 170 173 175 176 185 198 199
Coarse grid, equation 9 76 87 88
Coarse grid, matrix 9 90
Coarse grid, mode 107
Coarse grid, operator 80 81 82 230
Coarse grid, operator stencil 82
Coarse grid, problem 70 87 171 185
Coarse grid, solution 172 198 253
Code 200 207 222 225
Collective Gauss — Seidel 230 234
Colocated approach 244
Colocated formulation 259
Colocated grid 244
Complete factorization 47
Complete line LU factorization 53
Compressible 165 210 211 232 234 235 236 244
Computational complexity 1 179 204 209
Computational cost 179 204 210
Computational fluid dynamics 1 3 31 32 34 166 181 206 208 209 213 218 241 258 259
Computational Grid 5 16 21 27 60 62 213 214 220 225
Computational tomography 3
Computational work 177 183
Computing time 208 209 210 218 231 251 257 258 259
Computing work 178 181 200 210 211
Condition 201
Condition number 203 204
Conjugate gradient 202 203 204 205 206 207
Conjugate gradient, acceleration 202 204 205
Conjugate gradient, method 201
Conjugate gradient, squared 205
Conservation laws 33 211
Consistency 86 182 245
Consistent 37 70 88
Contact discontinuity 225
| Continuum mechanics 214
Contraction 215
Contraction number 38 200
Contravariant base vectors 215
Contravariant components 215
Control structure 194
Control theory 3
Control volume 220
Convection term 240 241 243 246
Convection-diffusion 8 181 206 240
Convection-diffusion equation 86 94 115 122 123 128 129 130 131 136 137 140 141 144 145 147 148 152 154 156 157 159 160 163 164 167 224 227 230 231 238 251
Convective flux 31
Convective term 26 27 238
Converge 53 59 95 182 201 204 222 230
Convergence 6 37 59 76 88 89 97 138 147 170 175 179 188 198 201 228 239 244
Convergence, analysis 89
Convergence, histories 181
Convergence, proofs 2
Convergence, theory 38
Convergent 37 39 58 91 96 98 119 186
Coordinate independent 124 218
Coordinate mapping 200 219
Coordinate transformation 215
Cost 188 256
Cost of nested iteration 183 188
Courant — Friedrichs — Lewy 161
Covariant base vectors 214
Covariant components 215
Covariant derivative 215
Crank — Nicolson 256
Crisp resolution 225 227
Cut 218 219 220
Damped 37
Damped point Gauss — Seidel 132
Damped point Jacobi 122 123
Damped vertical line Jacobi 120 121 123
Damped, alternating Jacobi 121 122 167
Damped, alternating line Jacobi 123
Damped, Euler 163
Damped, horizontal line Jacobi 121
Damped, Jacobi 8 94 119 162
Damping 39 96 97 98 130 131 134 150 151 152 154 155 156 157 159 160 167 170 224 230 249 250 258
Damping parameter 8 121 122
Data structure 214
DCA 79 82
Defect correction 57 58 201 227 231 234 239 256 257 258
density 33 211 213 218 221 222 235 236
Diagonal 42
Diagonal, dominance 40
Diagonal, Gauss — Seidel 46
Diagonal, ordering 43 230 234
Diffusion 14 164 243
Dimensionless equation 255
Dimensionless form 236
Dimensionless parameter 209
Direct simulation 210
Dirichlet 8 13 17 22 27 28 29 32 63 69 94 100 101 102 103 104 111 113 114 119 123 126 136 149 162 241 254
Discontinuity 225 227
Discontinuous coefficient 3 14 25 82 201 206
Discrete approximation 189
Discrete Fourier sine transform 100 104
Discrete Fourier Transform 98 103
Discretization 116 117 201 213
Discretization, accuracy 256
Discretization, coarse grid approximation 9 10 79 82
Discretization, error 190 192 193 239
Dissipation 221 225
Dissipative 160
Distribution step 248
Distributive Gauss — Seidel 246 247
Distributive ILU 247 248 250 251
Distributive iteration 58 59 244 248
Distributive method 249
Distributive smoothers 245
Distributive type 245
diverge 182
Divergence 215
Divergent 37 91 92
Double damping 155 157
Doubly connected 218
Driven cavity 258
Dynamic viscosity 212
Efficiency 157 167 177 201 206 207 211
Efficient 2 53 130 136 139 141 148 157 159 167 217 244 250 258
Eigenfunction 105 106 111 113
Eigenstructure 38 84
Eigenvalue 3 37 39 85 89 97 98 105 112 153 159 203 204 227
Eigenvector 39 146
Elliptic 1 2 6 14 183 212 213 223
Elliptic grid generation 215
Elliptic-hyperbolic 218
ELLPACK 200
Energy conservation 211
energy equation 212 235 236
entropy 221
Entropy condition 225 227
Equation of state 212
Equations of motion 209
Error after nested iteration 191 192 193
Error amplification matrix 11
Error matrix 49 50 52
Error of nested iteration 189
Essential multigrid principle 4 6 12
Euler 33 160 165 208 210 211 212 224 227 230 231 232 234 235
Existence 15 57
Expansion shocks 221 225
Explicit 34
Exponential Fourier series 8 111 114 123
F-cycle 173 174 175 179 180 181 188 194 195 196
Fine grid 8 10 60 68 106 107
Fine grid problem 9 70
Fine grid, Fourier mode 107
Fine grid, mode 107
Finite difference 2 3 5 14 15 16 17 20 21 22 23 28 31 32 116 117 201 245
Finite difference method 5 225
Finite element 3 14 225
Finite grid matrix 9 88
Finite volume 3 14 15 16 18 19 20 21 23 24 26 29 31 32 34 70 78 94 220 221 225 226 229 230 231 232 237 238 241 242 252
Five-point IBLU 57
Five-point ILU 48 50 132 134 135 136 137
Five-point stencil 132 230 248
Five-stage method 165 166
Fixed cycle 196
Fixed schedule 173 194 195 196
Floating point operations 45
FLOP 210
Flow diagram 168 194 196
Fluid dynamics 57 115 117 160 211 213 251
Fluid mechanics 33 128 163 211
Flux splitting 31 35 226 227 231 232 234 244
FORTRAN 168 194 196
Forward 42
Forward, difference operator 16 22
Forward, Euler 162 163
Forward, Gauss — Seidel 43
Forward, horizontal line Gauss — Seidel 44
Forward, ordering 42 43 44 129 234
Forward, point Gauss — Seidel 123 124 125 128
Forward, vertical line 42
Forward, vertical line Gauss — Seidel 125 131 224
Forward, vertical line ordering 44 129
Four-direction damped point, Gauss — Seidel — Jacobi 167
Four-direction point Gauss — Seidel 129 230
Four-direction point, Gauss — Seidel — Jacobi 44 130 131 230
Four-stage method 164 165
FOURIER 89
Fourier, analysis 5 98 110 148
Fourier, component 99
Fourier, cosine series 104
Fourier, mode 6 7 99 104 106 107 108 109 113 148
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