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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
$k-\varepsilon$ 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
1 2 3
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