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Lynch D.R. — Numerical Partial Differential Equations for Environmental Scientists and Engineers: A First Practical Course
Lynch D.R. — Numerical Partial Differential Equations for Environmental Scientists and Engineers: A First Practical Course

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Название: Numerical Partial Differential Equations for Environmental Scientists and Engineers: A First Practical Course

Автор: Lynch D.R.

Аннотация:

This book concerns the practical solution of Partial Differential Equations (PDEs). It reflects an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It assumes the reader has gained some intuitive knowledge of PDE solution properties and now wants to solve some for real, in the context of practical problems arising in real situations. The practical aspect of this book is the infused focus on computation. It presents two major discretization methods — Finite Difference and Finite Element. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems. It is divided into three parts. Part I is an overview of Finite Difference Methods. Part II focuses on Finite Element Methods, including an FEM tutorial. Part III deals with Inverse Methods, introducing formal approaches to practical problems which are ill-posed.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 388

Добавлена в каталог: 14.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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