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| Hackbusch W. — Multi-Grid Methods and Applications |
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| Предметный указатель |
Alternating direction method (ADI) 55f 134 204
AMG 227
Anisotropic equation 201ff 207 226
Approximation property 113 135ff 140 142f 148 151 155f 202f 229 239ff
Associated operator 15 16 236
Asymptotic expansion 102 104 277f 293
Augmented system 248ff 257 271
Bifurcation 269f
Biharmonic equation 189f 233 236 245f 262
Boundary condition 42 177
Boundary condition, Dirichlet 41 43 95 175 291
Boundary condition, mixed 42 95
Boundary condition, natural 43 46
Boundary condition, Neumann 42 45 76 95f 173 253 291
Boundary condition, periodic 42 95 173ff 224 253
Boundary condition, separated discrete 69f 110
Buoyancy drivenflow 189f
Cauchy — Riemann equations 233 245
Coarse-grid correction 23 30 35 40 49 171 178 185 207 258f 292 297 309 340
Coarse-grid matrix 68f 182 214 327
Coarsening see "Mesh coarsening"
Computational work 86 103f 310f 314f 321f 328 334 337
Conjugate gradient method (CG) 38f 57 159
Consistency 44 46 224 240 282ff 308
Consistency, relative 69 100 110 284 308 327
Continuation problem 183 270ff
Contraction number 8 35f 49 88 98 100 115 161 166ff 172 179 193 221 224 285 311f 342
Convection diffusion equation 217ff 227 292
Convergence rate (rate of convergence) 6 49 90 173 179 224f 317f
Defect 19 21 35 116 132 185 331
Defect correction 226 282ff
Defect correction, local 293ff
Defect correction, mixed 292
Difference equations 18 43ff 145ff
Difference equations, backward 219ff
Difference star, stencil 18 44 79
Discontinuous coefficients see "Interface problems"
Distributive relaxation method 245ff
Domain decomposition 299ff
Double discretisation 292
Double layer potential 319f 325
Efficiency 1 88 93f 97 103
Eigenspace 252
Eigenvalue 210 252
Eigenvalue, multiple 256 260
Eigenvalue, problem 250 252f 255 260 347
Eigenvalue, problem, generalised 267f
Eigenvalue, problem, nonlinear 269 347 349
Eigenvalue, single 252 255 347
Eigenvector 252 267
Eigenvector, left 252f 260 267
Elliptic 42 43 147 202 228 234
Error, discretisation 48 98
Error, discretisation, (relative) truncation 275 278
Error, discretisation, expansion see "Asymptotic expansion"
Error, discretisation, iteration 98 115 277
Error, discretisation, relative discretisation 100 102 309 322
Extrapolation see "Richardson extrapolation"
Extrapolation,  -extrapolation 278ff
Fas 188 330
Finite element 47
Finite element, discretisation 46ff 66 71ff 135f 150 219 242 244 293
Finite element, isoparametric 156
Finite element, piecewise bilinear 60 78f 139
Finite element, piecewise linear 60 78
Five-point scheme 44 51 55f 63 79 89 100 126f 169 171f 176 180 202 218f
Form, adjoint 14
Form, adjoint,  -coercive 15f
Form, adjoint, -elliptic 14
Form, adjoint, bi-linear 14
Form, adjoint, bounded 14
Form, adjoint, continuous 14
Form, adjoint, sesqui-linear 14 16 46 47 235f
Fourier analysis 25 156 169ff 208 220
Fredholm integral equation of the first kind 325 349f
Fredholm integral equation of the second kind 305ff 328
Frozen coefficients 177f
Frozen truncation error technique 275
Full weighting 78
Galerkin approach, approximation 68 94 214 221f
Galerkin method see "Finite element discretisation"
Gauss — Seidel iteration 40 49 58 63f 78 90 125ff 155 171f 184 202 209 220f 224 226 232f 246f
Gauss — Seidel iteration, 2-cyclic 125f 130
Gauss — Seidel iteration, accelerated symmetric 133f
Gauss — Seidel iteration, alternating 204
Gauss — Seidel iteration, blockwise (linewise) 54f 126 176 180 184 202 233
Gauss — Seidel iteration, lexicographical 51 128 176 180 229
Gauss — Seidel iteration, symmetric 52 129 133 151 176 180 221
Gauss — Seidel iteration, zebra-line 55 95
Grids 17 43 58f 89
Grids, infinite 43
Grids, non-uniform 71 75 227
Grids, staggered 76f 246f
h-ellipticity 228
Half-weighting 78 96
Hierarchy offinite elemtent subspaces 46 66 71ff 136 156
Hilbert scale 11f 15f 118 136
Hyperbolic equations 228f
ILLU 204 208 221ff 227 230
ILU 204 205ff 208 221ff 227
Incomplete (line) LU-decomposition see "ILU" "(ILLU)"
Indefinite equations 209ff 236
Injection, trivial 22 64 66 77f 174f 272 275 308
Integral equation see "Fredholm integral equation"
Integral equation, method 319f
Interface problems 212ff 295
Interpolation see "Prolongation"
Interpolation of Hilbert spaces 11f 114
Inverse assumption 136 142
Iteration, general 5
Iteration, general, Gauss — Seidel see "Gauss — Seidel iteration"
Iteration, Jacobi see "Jacobi iteration"
Iteration, Kaczmarz 58
Iteration, matrix 5 19 112 161 311ff 327
Iteration, Picard 309 311 323 324f 331
Iteration, Richardson 56 131
Iteration, Schwarz 300f 303
Jacobi iteration 18 52 57 184
Jacobi iteration, damped 19 20 52 122ff 151 158 184 266 282
Jacobi iteration, linewise 55 203
Level, level number 17 24 48
Limit point see "Turning point"
Local grid refinement 297ff
Local mode analysis 156 176ff 180 290
| Matrix, M 206 218 223f 227
Matrix, normal 8 128 253
Matrix, positive definite 8 16 69
Matrix, stiffness 47 67f 79 137 159
Matrix, symmetric 8 69 253
Matrix, unitary 8 25
Mehrstellenverfahren 44 282
Mesh coarsening 58f 71 77 226f
MGR 96
Model problem 169ff 173ff 201ff 217
Model problem, one-dimension 17 212 224
Multi-grid convergence for eigenvalue problems 261f 268
Multi-grid convergence for singular equations 266 269
Multi-grid convergence of the full (FMG) 98
Multi-grid convergence of the nonlinear 196ff
Multi-grid convergence of the second kind 303 305ff 310 313 315
Multi-grid convergence of the second kind, nonlinear 331f 339f
Multi-grid convergence with defect correction 284ff
Multi-grid iteration 30ff 80ff
Multi-grid iteration, algorithm of the linear 31 80f 82 90
Multi-grid iteration, algorithm of the nonlinear 183ff 187f 272f 299
Multi-grid iteration, convergence of the linear 85ff 92 161 163 165f 203
Natural convection 189f
Navier — Stokes equations 234 245
Nested iteration 98ff 321ff 333 340
Nested iteration for eigenvalue problems 261f 268
Nested iteration, modified 272ff
Nested iteration, nonlinear 188f 198
Newton-multi-grid iteration 182f 227
Nine-point scheme 44 51 69 79 126 171 173
Norm, dual 11 16 77 146
Norm, dual, energy 36 11 151 153f 165
Norm, dual, Euclidean 7 35 113 239 242
Norm, dual, matrix 7 118 157
Norm, dual, Sobolev 10
Norm, dual, spectral 7 25 27 35 52 118 239
Norm, dual, vector 6 118 145f
Nystroem's interpolation 322f 333 337
Optimal control 346 352f
Optimal error estimates 139 156
Ordering of the grid points 50 232
Ordering of the grid points, chequer-board 50f 78 126 171
Ordering of the grid points, four-colour 51 78
Ordering of the grid points, lexicographical 50f 126
Ordering of the grid points, red-black see "Chequer-board"
Ordering of the grid points, zebra-line 51 126
Panel method 307 320
Parabolic problems 276 351ff
Parallel processing 303
Peaceman — Rachford method 56
Petrov — Galerkin method 219 222
Poisson equation 14 38 41 44f 49 56 89f 97 139 146 157 180 236 295 301 319f 349
potential flow 320
Projection, orthogonal 13 67 142 151 154 178f
Prolongation 22 58ff 232 308
Prolongation, canonical 66f 78f 136
Prolongation, matrix-dependent 214ff 222
Prolongation, nine-point 60 78f 90 170 172
Prolongation, piecewise constant 77 222 309
Prolongation, piecewise cubic 61f 66 107 110 190 317
Prolongation, piecewise linear 22 59ff 66 77 308 317
Prolongation, piecewise quadratic 61ff 66 110
Prolongation, seven-point 60f 78f 222
Rayleigh quotient 253 265 268f
Re-entrant corner 75 95 140 293 295
Reduction factor, averaged 95
Regularity 95 137 140 154 156
Regularity, discrete 145ff 156 284 307
Relaxation see "Gauss — Seidel iteration"
Restriction 21f 64ff 174f 308
Restriction, canonical 66f 78 136
Restriction, nine-point 65 78f 90 171f
Restriction, seven-point 65 78f
Restriction, weighted 22 65 77
Restriction,five-point 78
Richardson extrapolation 104f 277f 338
Ritz projection 264 267 269
Saddle point problem 236 238ff
Sawtooth cycle 222
Scalar product 6f 10f 40 64 66
SCALE see "Hilbert scale"
Semi-iterative methods 56f 76 131ff 152 185 243f
Seven-point scheme 44 204
Shortley — Weller scheme 45 94 146
Singular equation 253f 256f 265ff
Singular perturbation 201ff 234 245
Smoothing iteration 20 49ff 16 207 242ff 302 309 324
Smoothing iteration, nonlinear 184f
Smoothing iteration, post- 25 34 36 49 63f 76 81 84 115f 163
Smoothing iteration, pre- 24 36 48 63f 76 84 161
Smoothing number 37 49 53 56 115 124 127 132 180
Smoothing property 113f 116ff 120 122ff 125ff 131ff 144 155 158 203 243
Smoothing rate 37 53 56 177 179f 202f 208 225
Sobolev space 10f
Space, dual 10 46
Space, dual, intermediate 11
Spectral radius 6f 25 27 112 172 292
Spectrum 6
Steklov eigenvalue problem 267 348
Stiffness matrix see "Matrix"
Stokes equations 233 235 238 242ff 246 253
Storage 89 346
Successive overrelaxation (SOR) 37f 52 94
Successive overrelaxation (SOR), symmetric 37 52
Symmetric case 150f 164f
Systems of elliptic equations 231ff 345f
Time-dependent problems see "Parabolic problems"
Transonic potential equation 229
Trivial injection see "Injection"
Turning point 270ff
Two-grid iteration 21ff 23 48f 74f 112ff 179
Two-grid iteration for eigenvalue problems 257ff
Two-grid iteration of the second kind 309f
Two-grid iteration, convergence of the linear 25ff 112 114 116 172
Two-grid iteration, convergence of the nonlinear 192ff
Two-grid iteration, nonlinear 185ff
Upwind differencing see "Backward difference"
V-cycle 33 81 83 86f 94 104 165f
Variational problem 14 43 135 209 235
viscosity 234
Viscosity, artificial 219f 223ff
Viscosity, numerical 219
Von Karman equations 231
W-cycle 33 81 86f 163 165 168 310
Weak formulation see "Variational problem"
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