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Lynch D.R. — Numerical Partial Differential Equations for Environmental Scientists and Engineers: A First Practical Course |
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Предметный указатель |
Accuracy 7 243 248 251 337
Acoustic waves 90
Adams 4
ADI 83
Adjoint, Direct Solution 309
Adjoint, Method 290
Adjoint, Model 291 302 308
Adjoint, Variables 289 290
Arakawa 118
assembly 164
Average 342
Backward Problem 265
Bandwidth 28 30 37 159 160
Basis functions 123
Bell 331
Bell, Interval 331
Best Prior Estimate 331
Bias 337 342
BiLinear Quadrilaterals 182
blue 342 343 345
Boundary Conditions, Electromagnetic Potentials 209
Boundary Conditions, FEM 129 150
Boundary value problem 7
Calculus of variations 130 131
Cauchy BC 8
cholesky 294
Classification 7
Classification of BC’s 8
Classification of PDE’s 9
Collocation 125
Complex Arrays 215
Condition number 271 283
Conjugate gradient method 49 293 311 319
Conservation 7
Conservation Analogies 77
Conservation, FDM 76
Conservation, FEM 133
Consistency 59 61
Constitutive relation 76 91 92
Constrained minimization 289
Constrained Minimization and GLS 289
Continuous system 4
Control variables 289
Convergence 7 58 60
Convolution 321
Courant number 94 96 105 107 248 250
Courant Number, Advective 252
Covariance 266 282
Covariance, Analytic Forms 348 359
Covariance, SDE 350 359
Crank — Nicolson 55 64 82
Critical damping 101
Cubic Quadrilaterals 186 187
Cubic Triangles 175
DATA 285 302
DATA ERROR 288
Data Product 336
Data, Active 336
Data, Passive 336
Delay, Assimilation 330
Delay, Observational 329
Delay, Publication 329
DFT 64
Diagonal dominance 40 41 82
Difference operators 232 233
Difference Operators, Backward 13
Difference Operators, Centered 13
dispersion relation 64 99
distributed system 4
Divergence theorem 77
Downstream Weighting 35
DuFort — Frankel 63
Eigenvalue problem 270
Elastic waves 91
Electric waves 92
Electromagnetism 118
Element matrix 152
Elliptic 9
Ensemble 293
EOFs 321
Estimate 335
Estimation 265
Estimation error 341
FD case 233
FD case, Backward 55 64
Feature Model 321
Fluid mechanics 116
Forecast 330 336
Forward 13
Forward Model 335
Forward Problem 265 290 302
Forward, Dirichlet BC 8 129
Forward, Discrete Form 129
Forward, Discrete System 4 189
Forward, Discretization Factor 101 102
Forward, Discretization Factors 232 233
Forward, Extrapolation 336
Four — Point Implicit 115
Fourier (von Neumann) Analysis 64
Fourier series 321
Fourier Transforms of Difference Operators, 230
Gage Relation 206
Galerkin 124
Galerkin, Boundary Flux 202
Gauss — Markov, Covariance 347
Gauss — Markov, Estimate 344 347 359
Gauss — Markov, Theorem 341 344
Gauss — Seidel 30 41 43 82
Geophysical fluid dynamics 118
GLS — OA Equivalence 356
Gradient descent 47 289 291 302 310 318
Gradient Descent, Optimal Step Size 48 292 311 318
Gradient — Flux Relation 199
Harmonic 321
Harmonic Systems 94
Hermite polynomials 143
Hindcast 330 336
Hyperbolic 9
Incidence List 157
Increment 38
Increment, Matrix 37
Increment, Residual 38
Initial value problem 7
Initialization Period 331
Inner product 123
Interpolation 336
Interpolation, Hermitian 145
Interpolation, Lagrange 142
Interpolation, local 141 142
Inverse Model 335
Inverse problem 265
Inverse Truth 338
Irreducibility 40
Isoparametric mapping 179 181 183
Iteration, convergence 39
Iteration, Error 38
Iterative methods 29
Iterative Methods, Alternating Direction 44 83
Iterative Methods, Block or Line 29 43
Iterative Methods, Optimal 46
Iterative Methods, Point 29 39
jacobi 29 41 43 82
Jacobi matrix 176 180 182
Jacobian 86
| Just-in — Time 331
Kriging 341 358
Kriging and Mining 359
Lagrange multipliers 289
Lagrange Polonomials 139 142
Leapfrog 54
Least — Squares, as a WRM 124
Leendertse 118
Linear 147
Linear estimator 341
Linear Quadrilaterals 186
Linear Triangles 171
LLS 279
Local coordinate system 200 204
Lorentz Gage 206
LU decomposition 23 28 82 161 192 291
Lumped system 4 189
Mass matrix 190 194
Maxwell 116 205
Measurement error 288 346
Measurement Noise 288
Misfit 285 288 290 302 336
Mixed BC 8 129
Mixed Interpolation 210 211
Model Identification 335
Molecule 25
Monotonicity 242
Monte Carlo 293
Neumann BC 8 129
Newton — Raphson 85
Noise 266 283
Noise, Filter 267
Noise, Inverse Noise 266 287 293 337 338
Noise, models 268
Noise, Representers 296
Observational 359
Parabolic 9
Parameter estimation 298 313
Parameter Estimation, Gradient 299 300
Parasite 74 76
Peclet number 32 256
Periodic solutions 94
Plane strain 203
Plane stress 203
Platzman 118
Positive definite 41
Posterior 336
Potential 76
Potential, electromagnetic 206
PRECISION 337
Prediction, error 336
Primitive Pair 89
Prior 336
Prior Estimate 290 302
Process 350 359
Process and Meteorology 359
Process, GLS 282 283
Process, GLS Equivalence 356
Process, Normal Equations 279
Process, Nugget Effect 358
Process, Nyquist Point 62 65 66 101 109
Process, Obective Analysis 324 328
Process, Objective Analysis 341 344
Process, Odd — Even Decoupling 72 97
Process, OLS 280
Process, Operations Count 30 161
Process, Optimal Interpolation 341 344
Process, OSSE 336 337
Process, Overfitting 336
Process, WLS 281
Propagation factor 70 105 243 253 257
Propagation Factor, Characteristic Time 71 105
Quadratic Forms, Gradient 279
Quadratic Quadrilaterals 186
Quadratic triangles 174
Quadrature, Gauss — Legendre 163 164 183 185
Quadrature, Triangles 178 179
Radiation BC 8
Regularization 282 321 322
Representers 294 319
Residual, PDE 123
Richardson number 53
Robbins BC 8
Rotation matrix 200 204 214
Runge — Kutta 4
Sample 285
Sampling error 346
Sampling matrix 285 286 288 346
Semivariogram 358
Shadow Node 24 25
Shallow water waves 91
shooting 312
Singular values 273
Singular vectors 273
Skill 336
SOR 30 41 82
SOR, Optimal 41 43
Source 77
Sparseness 29 37 159
Spectral radius 39 43
Split — Time 112
Stability 7 59 61 241 248 250
Staggered mesh 97
Statistical Interpolation 341
Steepest descent 48 292 318
Stiffness matrix 190 194
Stochastic differential equation 341 350
Stochastic Differential Equation and OA 359
storage requirements 30 161 192
Stress tensor 202
Subdomain 125
Subgrid Variability 345
SVD 273 283
Taylor series 11
Telegraph equation 89 92
Terminal Condition 305 307 308 312 317
Terminology, Data Inversion 302
Terminology, Skill Assessment 335
Thomas algorithm 23
Tidal 332
Time of Availability 329
Time of Occurrence 329
Time, Greenwich 332
Time, Gregorian 332
Trace 268
Tridiagonal 23 94
Truth 288 335
Unit Response 295 296
Unresolvable 345
Upstream Weighting 33
Variance 268
Variational calculus 130 131
Variogram 358
Vector Bases 197 206 209
Vector Bases, von Neumann (Fourier) Analysis 64
Washboard Mode 62
Wavelength 64 232
Wavenumber 64 232
Weak form 128
Weight matrix 282 283 322
Weight Matrix, Covariance 322
Weight Matrix, FEM 322
Weight Matrix, Regularization 322
Weighted residual 123
Yee 118
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