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Wesseling P. — An introduction to multigrid methods
Wesseling P. — An introduction to multigrid methods



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Название: An introduction to multigrid methods

Автор: Wesseling P.

Аннотация:

Wesseling (Delft U. of Technology) presents an introduction to the application of multigrid methods to elliptic and hyperbolic partial differential equations for graduate level students in applied mathematics, engineers, and physicists. With frequent reference to the literature, he emphasizes the formulation of algorithms, choice of smoothing methods and analysis, problems with discontinuous coefficients, details of Galerkin coarse grid approximation, and applications in computational fluid dynamics.


Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 284

Добавлена в каталог: 20.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Richardson      94 162
Riemann      227
Robbins      17
Robust      96 98 110 115 120 122 124 125 127 128 129 130 131 132 136 139 141 142 144 154 157 159 166 167 201 230 251 258
Robustness      98 115 117 167 205 206 207
Rotated anisotropic diffusion equation      115 121 122 127 132 135 139 143 144 146 147 155 156 157
Rotated anisotropic diffusion problem      234
Rotation matrix      227
Rotational invariance      226
Rough      12 92 95 105 106 107
Rough, Fourier modes      149
Rough, grid function      92
Rough, modes      163
Rough, part      6 7 93 108
Rough, wavenumbers      7 107 108 109 112 119
Rounding errors      45
Route to chaos      209
Runge — Kutta      160 161 163 228 234
Sawtooth cycle      95 173 193
Scaling      70 86 87
Scaling factor      71 84
Scaling rule      71 229
SCGS      248 250 251 256 257 258
Self-adjoint      115 188
Semi-coarsening      109 110 123 124 125 177 180 181 231 251
Semi-iterative method      160 161 162
Separability      15
separable equations      183
Seven-point IBLU      57
Seven-point ILU      49 50 136 138 139 140 141 142
Seven-point incomplete factorization      137
Seven-point stencil      132 150 230 233 234
Seven-point structure      62
Shifted finite volume      237 252
Shock      35 221
Shock wave      225
Simple iterative method      179
SIMPLE method      247 248
SIMPLE smoothing      250
Simply connected      218
Single damping      155 156
Single grid work      180
singular      86 87 88 118 178 200
Singular perturbation      7 98 181
Singularities      181 204
Skewed      234
Small disturbance limit      222
Smooth      6 105 107
Smooth, grid function      92
Smooth, modes      163
Smooth, part      8 92 93 108
Smooth, wavenumber      107 108 109 148 149
Smoother      7 8 12 89 93 96 97 110 115 119 120 121 125 126 130 131
Smoothing      10 199
Smoothing algorithm      168 181
Smoothing analysis      3 96 101 111 116 136 223
Smoothing convergence      97
Smoothing efficiency      96 98
Smoothing factor      7 8 93 94 110 111 112 117 118 121 124 125 128 134 149 150 152 154 155 157 159 162 163 165 166 167 199 200
Smoothing iteration      105 181
Smoothing iteration matrix      89
Smoothing method      3 7 36 37 39 91 93 94 95 105 106 110 115 117 118 168 184 200
Smoothing number      94
Smoothing performance      85 120 130 132
Smoothing property      39 89 91 92 94 96 97 98 184 186 187 188
Sobolev      15
Software      200
Software tools      200
Solution branch      258
sparse      22 47 49 57
Sparsity      67 178
Sparsity pattern      80
Specific heat      212
Speed of sound      33 209 213 235
Split      36
Splitting      37 42 47 53 58 59 90 118 120 123 125 130 227 245 246 247 248
Stability      34 53 162 163 164 228 243
Stability domain      163 164
Stable      45 223 244
Staggered formulation      258
Staggered grid      236 237 243 244
Standard coarsening      109 112 124 176 178 180
Stencil      22 27 33 43 46 47 48 49 50 53 57 62 63 64 65 66 69 70 72 73 75 84 116 117 122 132 143 145 157 165 221
Stencil notation      62 63 65 66 80 112 118 132 133 137
Stochastic      209
Stokes      57 58 59 245 246 247 248 254 259
Storage      1 45 49 50 52 80 176 177 210
Strong coupling      136 154
Strongly coupled      125 166
Structure      48 49 50 62 80 82 83 84
Structure, diagram      168 194 195 196 199 256
Structured grid      213 214 215
Structured non-recursive algorithm      168
Structured program      194
SUBROUTINE      95 159 169 170 171 172 173 174 175 176 178 179 182 184 194 196 199 200
Subsonic      213 219 222 224
Successive over-relaxation      6
Supercritical flow      231
Superlinear      178
Supersonic      213 221 222 224
Switching function      222 239
symmetric      22 47 53 77 84 96 97 116 131 204
Symmetric, collective Gauss — Seidel      231
Symmetric, coupled Gauss — Seidel      248
Symmetric, Gauss — Seidel      125
Symmetric, horizontal line Gauss — Seidel      44
Symmetric, IBLU factorization      57
Symmetric, ILU factorization      53
Symmetric, point Gauss — Seidel      46 53 128 129
Symmetric, positive definite      59 94 97 202 205 206
Symmetric, vertical line Gauss — Seidel      131
Symmetry      67 68 69
Taylor      23
Temperature      211 235 236 241 246 254
Temperature equation      243 250
Tensor analysis      214
Tensor notation      224
Test problems      115 116 117 128 129 132 160 167 205 206 207 223 230 251
Thermal expansion coefficient      235 236
Thermally insulated      241
Thermodynamic irreversibility      35
Three dimensions      167
Three-dimensional smoothers      167
Time discretization      34 228 234 242
Time-stepping      160
Tolerance      176 198
Topological structure      214
Total energy      211
Trailing edge      220 221
Transfer operator      15 60 62 66 71 76 89 94 168 222 252 254
Transient waves      228
Transonic      213 218 222 223
Transonic potential equation      224
TRANSPOSE      9 64 242
Tridiagonal matrix      46
Tridiagonal systems      44
Trilinear interpolation      67 69 72
Trivial restriction      189
Truncation error      67 182 183 192
Turbulence      209 234
Turbulence modelling      210
Turbulent eddies      209 210
Turbulent flow      210
Two-grid algorithm      8 10 13 79 87 89 90 172
Two-grid analysis      11 89
Two-grid convergence      79 92 184
Two-grid iteration      10
Two-grid iteration matrix      90
Two-grid method      5 8 10 89 91
Two-grid rate of convergence      90 91
Under-relaxation      127
Under-relaxation factor      250
Uniform ellipticity      14
unique      88
Uniqueness      15
Unstable      164 165
Upwind      29 35 157 222
Upwind, approximation      239
Upwind, difference      117
Upwind, discretization      30 31 32 57 85 86 94 128 160 164 227 232 238 239 240
V-cycie      95 173 174 175 178 179 180 181 188 194 195 196 231 258
Variational      3
Vector computers      53
Vector field      215
Vector length      46
Vector machines      46 81
Vectorization      57 121 157 166 167
Vectorize      82 123 230 234
Vectorized computing      43 44 46 118 132 152 214 239 251
Velocity potential      212
Vertex      5 6 8 21 61 229
Vertex-centred      29 32 66 68 69 71 102 176 177
Vertex-centred, coarsening      8 60 61
Vertex-centred, discretization      5 21 28 60 75 220
Vertex-centred, grid      21 75 100 101 103 104 106
Vertex-centred, multigrid      73 76 83
Vertex-centred, prolongation      66 71 72 193
Vertical backward white-black      42 44
Vertical line Gauss — Seidel      127 131
Vertical line Jacobi      42
Vertical zebra      42 154 159
Virtual points      23
Virtual values      23 28 32 101
Viscous      209 212 232 233 234 240 241
Vorticity-stream function formulation      2 53
W-cycle      95 173 174 175 178 179 180 181 194 195 196 258
Wake      210
Wavenumber      7
Weak formulation      15 16 19 23 24
Weak solution      35
While clause      194 196
White -black ordering      43 44
White-black      42 132 157
White-black Gauss — Seidel      46 148 150 152 251
White-black line Gauss — Seidel      44 46
Wiggles      41 225 238
Work      1 2 45 179 203 256
Work unit      181 183 188 192 211 256 258
Wu      181 211 256 258
Zebra      132 157 224
Zebra Gauss — Seidel      46 148 152
Zeroth-order interpolation      76
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