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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
Fourier, representation      153
Fourier, series      6 100 103 104 106 111 162
Fourier, sine series      8 100 101 108 109 110 111 114 119 120 123 124
Fourier, smoothing analysis      7 96 98 106 112 115 132 133 145 146 167 199 200 207 230 247 250
Fourier, smoothing factor      105 106 117 122 123 127 128 130 131 134 137 139 140 143 144 145 147 149 151 153 155 156 160 224 248
Fourier, two-grid analysis      254
Frechet derivative      201 222
Free convection      254 257
Freezing of the coefficients      118
Frequency-decomposition method      110
Frozen coefficient      8
Full approximation storage algorithm      171
Full multigrid      181
Full potential equation      213 218
Fundamental property      183
Galerkin coarse grid approximation      3 9 10 76 77 79 80 82 85 87 92 95
Gas dynamics      33 160 165 224
Gauss divergence theorem      15 16 24 34
Gauss — Seidel      5 6 7 8 10 12 43 44 59 94 132 234 247 248 249 250 251
Gauss — Seidel — Jacobi      46 130 132
gca      79 82
General coordinates      237 244
General ILU      52
Geometric complexity      213
Gerschgorin      97
Global discretization error      22 189
Global linearization      222
GOTO statement      168 196
Graph      47 48 49 50 51 52 57
Grashof      236 255
Gravity      236
Grid generation      15 208 213 234 259
Harmonic average      19
Heat conduction coefficient      212
Heat diffusion coefficient      236
Helmholtz      201
High mesh aspect ratio      166 231
Higher order prolongation      193
Historical development      2
Horizontal backward white-black Gauss — Seidel      44
Horizontal forward white-black      42
Horizontal forward white-black Gauss — Seidel      44
Horizontal line Gauss — Seidel      126 127 131 224
Horizontal line Jacobi      42
Horizontal symmetric white-black Gauss — Seidel      44
Horizontal zebra      42 152 154 159
Hybrid approximation      240
Hybrid scheme      238 239 240 241 243 255 257 258
Hyperbolic      1 33 115 157 160 166 212 213 223 224 225 230
Hyperbolic system      33 35
IBLU      53 56 147 148
IBLU factorization      55 56
IBLU preconditioning      206 207
IBLU variant      57
Ill conditioned      222
ILLU      53
ILU      47 51 52 53 94 167 224 234 247 248
ILU factorization      47 52 53
ILU preconditioning      206 207
IMPLICIT      34
Implicit stages      167
Incomplete block factorization      145 167
Incomplete block LU factorization      53
Incomplete factorization      47 48 49 51 98 167
Incomplete factorization, smoothing      132
Incomplete Gauss elimination      52
Incomplete line LU factorization      53
Incomplete LU      204
Incomplete LU, factorization      47 53
Incomplete point factorization      53 98
Incomplete point LU      47 132
Incompressible      167 235 236 243 244 258
Industrial flows      209
Inertial forces      209
Inflow boundary      32
Injection      71
Integral equation      3
INTERFACE      15 16 73 75
Interface problem      15 17 20 21 75 76 77 82
Interpolating transfer operator      74 76 85
Interpolation      66 253
Invariant form      214
Invariant formulation      218
Inviscid      210 211 234
Inviscid, flux      232
Irreducible      39 40
Irreversibility      221 225 227
Irreversible thermodynamic process      221
Isentropic      221
Iteration error      193
Iteration matrix      11 37 97 143 161 184 185 187
jacobi      6 39 43 46 59 132 247
Jacobi smoothing      118
Jacobian      201 215 227
JORDAN      38
Jump condition      16 17 19 20 24 25 26 73 74
K-matrix      39 40 46 78 85 86 96 116 117 133
Kaczmarz      59
Ker      86 87 88 89 92 93
Kinematic viscosity coefficient      209
Kutta condition      220 221
Laminar      255
Laplace      39 119 124 151 152 154 204
Large eddies      210
Large eddy simulation      210
Lax — Wendroff      34 225
Leonardo da Vinci      209
Lexicographic Gauss — Seidel      151
Lexicographic ordering      43 44
limiters      227
Line Gauss — Seidel      125 131 231
Line Jacobi      120 122 126
Line LU factorization      54
Linear interpolation      66 68 69 72 73 74 76 78 222 235
Linear multigrid      168
Linear multigrid, algorithm      173
Linear multigrid, code      217
Linear multigrid, method      187 222
Linear two-grid algorithm      10 169 170 171 173
Linearization      240
Local discretization error      22
Local linearization      222
Local mode      105
Local mode, smoothing factor      105 106
Local singularity      200
Local smoothing      118 200 204
Local time-stepping      163
Locally refined grid      208
Loss of diagonal dominance      85
LU factorization      45 47
Lumped operator      75
M-matrix      30 31 32 39 40 41 43 53 57 58 227
Maccormack      225
Mach number      209 213
Mapping      15 213 215 216 218
Mass balance      209
Mass conservation      211 235
Mass conservation equation      212 220 237
Matrix-dependent prolongation      74 75
Memory requirement      211
Mesh aspect ratio      115 251
Mesh Peclet number      30 40 86 117 128 152 154 157 165 251
Mesh Reynolds number      238 240
Mesh-size independent      71
Metric tensor      214 215
MG00      200 201
MGCS      201
MGD      200 201
Microchips      1
Mixed derivative      27 32 84 115 116 121 127 132 142 143 144 147 155 156 157 167 234
Mixed type      213
Model problem      4 7 8
Modification      48 49 50 52 145
Modified ILU factorization      47
Modified incomplete $LL^T$      204
Modified incomplete factorization      134
Modified incomplete point factorization      47
Momentum balance      209 236
Momentum conservation      211
Momentum equation      212 237 251
Monotone scheme      225
Monotonicity      225 227
MUDPACK      200
Multi-coloured Gauss — Seidel      150
Multigrid      3 15
Multigrid, algorithm      2 36 96 115 168 184 189 196 199 200 204
Multigrid, analysis      11
Multigrid, bibliography      2 218
Multigrid, code      93 115 181 201 204
Multigrid, contraction number      199
Multigrid, convergence      88 115 167 184 188 204
Multigrid, cycle      173
Multigrid, iteration matrix      184
Multigrid, literature      2
Multigrid, method      1 2 6 33 47 92 95
Multigrid, principles      3 201
Multigrid, program      2 13
Multigrid, schedule      95 168 173
Multigrid, software      199 200
Multigrid, work      178 180
Multistage method      161 162 163
Multistage smoother      164
Multistage smoothing      160 166
NAG      200
Navier-Stokes      2 53 57 58 59 165 167 211 212 232 234 235 243 244 245 247 248 258
Nested iteration      171 181 182 188 190 191 192 193 217 256
Nested iteration algorithm      183 189
Neumann      13 17 22 23 27 28 29 63 86 101 102 104 111 178 241
Neutron diffusion      206
Newton      201 211 222 230
Nine-point IBLU      54 55
Nine-point ILU      50 141 142 143
Nine-point stencil      150 233
No-slip condition      232
Non-consistent      88
Non-dimensional      236
Non-linear multigrid      217 231
Non-linear multigrid algorithm      171 174 188 222 229 230 240 256 258
Non-linear multigrid methods      70 201 228 258
Non-linear smoother      217
Non-linear theory      188
Non-linear two-grid algorithm      169 253
Non-orthogonal coordinates      234
Non-recursive      196
Non-recursive formulation      168 194
Non-recursive multigrid algorithm      195 197
Non-robustness      205
Non-self-adjoint      57
Non-smooth      6 7 13 107
Non-smooth, part      92 93
Non-symmetric      13 98 205
Non-uniform grid      235
Non-zero pattern      5
Numerical experiments      206
Numerical software      201
Numerical viscosity      239 258
One-sided difference      244
One-stage method      162 163
Operator-dependent,      80
Operator-dependent, prolongation      73 74 78 86
Operator-dependent, transfer operator      73 76 85 201 207
Operator-dependent, vertex-centred prolongation operator      77
Optimization      3
Order of the discretization error      189
Orthogonal decomposition      92
Orthogonal projection      92
Orthogonality      6 99 100 102 103
Outflow boundary      32
Packages      201
Parabolic      3 212
Parabolic boundary conditions      5 6
Parabolic initial value problem      256
Parallel computers      53
Parallel computing      43 44 46 118 132 152 214 251
Parallel machines      46 81
Parallelization      57 121 157 166 167
Parallelize      123 230
Particle Physics      3
Pattern ordering      132
Pattern recognition      3
Peclet      30 152
Perfect gas      212
Perfectly conducting      254
Periodic boundary conditions      5 6 7 100 103 104 108 111 112 113 118 154 162
Periodic grid function      6
Periodic oscillation      258
Piecewise constant interpolation      68
Plane Gauss — Seidel      167
PLTMG      200 201
Point Gauss — Seidel      42 43 46 95 128
Point Gauss — Seidel — Jacobi      44 125
Point Jacobi      42 118 119 122
Point-factorization      134
Point-wise smoothing      166
poisson      2 95 201 216
Poisson solver      152 201
Porous media      259
Post conditioned      245
Post-conditioning      58 246 247
Post-smoothing      11 12 95 170 177 185 256
Post-work      179
Potential      210 211 212 213 219 220 221
Potential equation      210
Power method      95
Prandtl      236
Pre-smoothing      11 93 95 170 173 176 177 185 256
Pre-work      179
Preconditioned CGS algorithm      205
Preconditioned conjugate gradient      183 203 204
Preconditioned system      202 203 204
Preconditioner      205
Preconditioning      58 204 207
Pressure      211 219 237 247 250 251
Pressure term      241
PROGRAM      169 172 175 176 182 194 200 201
Projection      88 93 94 149 182
Prolongation      8 9 10 60 62 64 65 66 70 76 77 95 168 192 229 235 252 253
Prolongation operator      182
QR factorization      88
Quasi-periodic flow      255
Quasi-periodic oscillation      258
RANGE      86 88 92 93
Rate of convergence      2 6 11 12 41 89 91 116 171 181 184 185 187 203 204 205 207 256
Recursion      194
RECURSIVE      178
Recursive algorithm      172 173 174 175
Recursive formulation      168
Reduction factor      95
Reentrant corner      200
Regular splitting      39 40 41 43
Relaxation parameter      248
Reservoir engineering      206 259
Residual averaging      167
Rest matrix      48
Restriction      8 9 60 62 63 64 70 76 95 168 171 229 235 252 253
Retarded density      221 223
Retarding the density      222 225
Reversible      221
Reynolds      209 236 250
Reynolds-averaged      210
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