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Hackbusch W. — Multi-Grid Methods and Applications
Hackbusch W. — Multi-Grid Methods and Applications

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Название: Multi-Grid Methods and Applications

Автор: Hackbusch W.

Аннотация:

Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 773

Добавлена в каталог: 09.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\tau$-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, $\mathscr{V}$-coercive      15f
Form, adjoint, $\mathscr{V}$-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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