Numerical partial differential equations for environmental scientist and engineers: a first practical course
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2005
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [377] - 384 |
| Beschreibung: | XXIV, 388 S. graph. Darst. |
| ISBN: | 0387236198 |
Internformat
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| 245 | 1 | 0 | |a Numerical partial differential equations for environmental scientist and engineers |b a first practical course |
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
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| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Finite differences | |
| 650 | 4 | |a Finite element method | |
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| adam_text | NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS FOR ENVIRONMENTAL SCIENTISTS
AND ENGINEERS A FIRST PRACTICAL COURSE BY DANIEL R. LYNCH DARTMOUTH
COLLEGE DARTMOUTH, NEW HAMPSHIRE USA 4Y SPRINGER CONTENTS PREFACE XV
SYNOPSIS XIX I THE FINITE DIFFERENCE METHOD 1 1 INTRODUCTION 3 1.1 FROM
ALGEBRA TO CALCULUS AND BACK 3 1.2 DISTRIBUTED, LUMPED, DISCRETE SYSTEMS
4 1.3 PDE SOLUTIONS 6 1.4 IC S, BC S, CLASSIFICATION 7 A UNIQUENESS
PROOF: POISSON EQUATION 7 CLASSIFICATION OF BC S 8 CLASSIFICATION OF
EQUATIONS 9 2 FINITE DIFFERENCE CALCULUS 11 2.1 -1-D DIFFERENCES ON A
UNIFORM MESH 11 SUMMARY - UNIFORM MESH 13 2.2 USE OF THE ERROR TERM 15
2.3 1-D DIFFERENCES ON NONUNIFORM MESHES 16 2.4 POLYNOMIAL FIT 17 2.5
CROSS-DERIVATIVES 18 3 ELLIPTIC EQUATIONS 21 3.1 INTRODUCTION 21 3.2 1-D
EXAMPLE 21 3.3 2-D EXAMPLE 25 MOLECULES 25 MATRIX ASSEMBLY AND DIRECT
SOLUTION 28 ITERATIVE SOLUTION 29 3.4 OPERATION COUNTS 30 3.5
ADVECTIVE-DIFFUSIVE EQUATION 31 4 ELLIPTIC ITERATIONS 37 4.1 BARE
ESSENTIALS 37 4.2 POINT METHODS 39 4.3 BLOCK METHODS 43 ALTERNATING
DIRECTION METHODS 44 4.4 HELMHOLTZ EQUATION . . 46 VI CONTENTS 4.5
GRADIENT DESCENT METHODS ( 47 5 PARABOLIC EQUATIONS 51 5.1 INTRODUCTION
51 5.2 EXAMPLES: DISCRETE SYSTEMS 53 EULER 53 LEAPFROG 54 BACKWARD EULER
55 2-LEVEL IMPLICIT 55 5.3 BOUNDARY CONDITIONS 57 5.4 STABILITY,
CONSISTENCY, CONVERGENCE 58 CONVERGENCE - LUMPED SYSTEM 59 CONVERGENCE -
DISCRETE SYSTEM 60 CONSISTENCY 61 STABILITY 61 5.5 ACCURACY: FOURIER
ANALYSIS 64 CONTINUOUS SYSTEM 64 LUMPED SYSTEM 65 DISCRETE SYSTEM 67
EXAMPLE: IMPLICIT LEAPFROG SYSTEM 71 5.6 CONSERVATION LAWS 76 5.7
TWO-DIMENSIONAL PROBLEMS 82 5.8 NONLINEAR PROBLEMS 85 6 HYPERBOLIC
EQUATIONS 89 6.1 INTRODUCTION 89 6.2 LUMPED SYSTEMS 93 6.3 HARMONIC
APPROACH 94 6.4 MORE LUMPED SYSTEMS 97 6.5 DISPERSION RELATIONSHIP 99
CONTINUOUS SYSTEM 99 LUMPED SYSTEM #1 100 LUMPED SYSTEM #2 101 LUMPED
SYSTEM # 3 . 102 LUMPED SYSTEM #4 103 6.6 DISCRETE SYSTEMS 104 DISCRETE
SYSTEM 1 (TELEGRAPH EQUATION) 106 DISCRETE SYSTEMS 3: COUPLED I S *
ORDER EQUATIONS 109 DISCRETE SYSTEM 4: IMPLICIT FOUR-POINT PRIMITIVE 115
6.7 LUMPED SYSTEMS IN HIGHER DIMENSIONS 116 II THE FINITE ELEMENT METHOD
121 7 GENERAL PRINCIPLES 123 7.1 THE METHOD OF WEIGHTED RESIDUALS 123
7.2 MWR EXAMPLES 125 7.3 WEAK FORMS 128 7.4 DISCRETE FORM 129 CONTENTS -
VII 7.5 BOUNDARY CONDITIONS 129 7.6 VARIATIONAL PRINCIPLES 130 7.7 WEAK
FORMS AND CONSERVATION PROPERTIES 133 8 A 1-D TUTORIAL 139 8.1
POLYNOMIAL BASES - THE LAGRANGE FAMILY 139 8.2 GLOBAL AND LOCAL
INTERPOLATION 140 8.3 LOCAL INTERPOLATION ON ELEMENTS 142 8.4 CONTINUITY
- HERMITE POLYNOMIALS . . . 143 8.5 EXAMPLE 146 8.6 BOUNDARY CONDITIONS
150 8.7 THE ELEMENT MATRIX 152 8.8 ASSEMBLY AND THE INCIDENCE LIST 157
8.9 MATRIX STRUCTURE 158 8.10 VARIABLE COEFFICIENTS 161 8.11 NUMERICAL
INTEGRATION 162 8.12 ASSEMBLY WITH QUADRATURE 164 9 MULTI-DIMENSIONAL
ELEMENTS 167 9.1 LINEAR TRIANGULAR ELEMENTS 167 LOCAL INTERPOLATION 167
DIFFERENTIATION 169 INTEGRATION 170 9.2 EXAMPLE: HELMHOLTZ EQUATION ON
LINEAR TRIANGLES 170 9.3 HIGHER ORDER TRIANGULAR ELEMENTS 172 LOCAL
COORDINATE SYSTEM 172 HIGHER-ORDER LOCAL INTERPOLATION ON TRIANGLES 173
DIFFERENTIATION 175 NUMERICAL INTEGRATION 177 9.4 ISOPARAMETRIC
TRANSFORMATION 179 9.5 QUADRILATERAL ELEMENTS 181 THE BILINEAR ELEMENT
181 HIGHER-ORDER QUADRILATERAL ELEMENTS 183 ISOPARAMETRIC QUADRILATERALS
183 10 TIME-DEPENDENT PROBLEMS 189 10.1 GENERAL APPROACH : . . . . 189
10.2 LUMPED AND DISCRETE SYSTEMS 189 10.3 EXAMPLE: DIFFUSION EQUATION
190 10.4 EXAMPLE: ADVECTION-DIFFUSION EQUATION 192 10.5 EXAMPLE: WAVE
EQUATION . 193 10.6 EXAMPLE: TELEGRAPH EQUATION 195 11 VECTOR PROBLEMS
197 11.1 INTRODUCTION 197 11.2 GRADIENT OF A SCALAR 197 GALERKIN FORM
198 NATURAL LOCAL COORDINATE SYSTEMS AND NEUMANN BOUNDARIES 199
DIRICHLET BOUNDARIES 201 VIII CONTENTS 11.3 ELASTICITY 202 WEAK FORM 202
CONSTITUTIVE RELATIONS 203 GAIERKIN APPROXIMATION 204 NATURAL LOCAL
COORDINATE SYSTEMS 204 REFERENCES - SOLID MECHANICS 205 11.4
ELECTROMAGNETICS 205 GOVERNING EQUATIONS 206 POTENTIALS AND GAUGE 206
HELMHOLTZ EQUATIONS IN THE POTENTIALS 207 WEAK FORM * * * * 208 BOUNDARY
CONDITIONS 209 RECONSTRUCTING E AND H 209 REFERENCES - E&M 209 11.5
FLUID MECHANICS WITH MIXED INTERPOLATION 210 GOVERNING EQUATIONS 210
BASES AND WEIGHTS 211 MIXED ELEMENTS 211 WEAK FORM 212 GAIERKIN
EQUATIONS 212 NUMBERING CONVENTION 213 COORDINATE ROTATION 214
REFERENCES: FLUID MECHANICS 214 11.6 OCEANIC TIDES 214 WEAK FORM AND
GAIERKIN HELMHOLTZ EQUATION 215 VELOCITY SOLUTION 216 REFERENCES -
OCEANIC TIDES 217 12 NUMERICAL ANALYSIS 219 12.1 1-D ELLIPTIC EQUATIONS
219 LAPLACE EQUATION ON 1-D LINEAR ELEMENTS 219 ADVECTIVE-DIFFUSIVE
EQUATION ON 1-D LINEAR ELEMENTS 219 HELMHOLTZ EQUATION ON 1-D LINEAR
ELEMENTS 221 POISSON EQUATION ON 1-D LINEAR ELEMENTS 223 INHOMOGENEOUS
HELMHOLTZ EQUATION ON 1-D LINEAR ELEMENTS . 226 12.2 FOURIER TRANSFORMS
FOR DIFFERENCE EXPRESSIONS 230 12.3 2-D ELLIPTIC EQUATIONS 236 LAPLACE
EQUATION ON BILINEAR RECTANGLES 236 HELMHOLTZ EQUATION ON BILINEAR
RECTANGLES 238 12.4 DIFFUSION EQUATION 240 STABILITY 241 MONOTONICITY
242 ACCURACY 243 LEAPFROG TIME-STEPPING 243 3-LEVEL IMPLICIT
TIME-STEPPING 245 12.5 EXPLICIT WAVE EQUATION 247 STABILITY 248 ACCURACY
248 CONTENTS , IX 12.6 IMPLICIT WAVE EQUATION 250 STABILITY 250 ACCURACY
251 12.7 ADVECTION EQUATION 251 EULER ADVECTION 252 TWO-LEVEL IMPLICIT
ADVECTION 253 LEAPFROG ADVECTION 253 12.8 ADVECTIVE-DIFFUSIVE EQUATION
255 EULER 256 2-LEVEL IMPLICIT 257 LEAPFROG 258 III INVERSE METHODS 263
13 INVERSE NOISE, SVD, AND LLS 265 13.1 MATRIX INVERSION AND INVERSE
NOISE 266 MEAN AND VARIABILITY. 266 COVARIANCE 266 VARIANCE 268 NOISE
MODELS 268 EIGENTHEORY 270 13.2 THE SINGULAR VALUE DECOMPOSITION 272 SVD
BASICS 273 THE SQUARE, NONSINGULAR CASE 274 THE SQUARE, SINGULAR CASE
275 THE SQUARE, NEARLY-SINGULAR CASE 277 THE OVER-DETERMINED CASE 277
THE UNDER-DETERMINED CASE 278 SVD COVARIANCE 278 SVD REFERENCES 279 13.3
LINEAR LEAST SQUARES AND THE NORMAL EQUATIONS 279 QUADRATIC FORMS AND
GRADIENT 279 ORDINARY LEAST SQUARES 280 WEIGHTED LEAST SQUARES 281
GENERAL LEAST SQUARES 282 14 FITTING MODELS TO DATA 285 14.1 INVERTING
DATA 285 MODEL-DATA MISFIT 285 DIRECT SOLUTION STRATEGIES AND INVERSE
NOISE 287 MORE ON THE MODEL-DATA MISFIT 288 14.2 CONSTRAINED
MINIMIZATION AND GRADIENT DESCENT 289 GENERALIZED LEAST SQUARES AS
CONSTRAINED MINIMIZATION 289 THE ADJOINT METHOD 290 GRADIENT DESCENT 291
SUMMARY - ADJOINT METHOD WITH GRADIENT DESCENT 293 MONTE CARLO VARIANCE
ESTIMATION - INVERSE NOISE 293 14.3 INVERTING DATA WITH REPRESENTERS 294
X CONTENTS THE PROCEDURE 295 INVERSE NOISE 296 14.4 INVERTING DATA WITH
UNIT RESPONSES 296 PROCEDURE 296 14.5 SUMMARY: GLS DATA INVERSION 297
14.6 PARAMETER ESTIMATION 298 GLS OBJECTIVE 299 FIRST-ORDER CONDITIONS
FOR GLS EXTREMUM 299 THE GRADIENT IN PARAMETER SPACE 300 AN ADJOINT
METHOD FOR PARAMETER ESTIMATION 302 14.7 SUMMARY - TERMINOLOGY 302 15
DYNAMIC INVERSION 305 15.1 PARABOLIC MODEL: ADVECTIVE-DIFFUSIVE
TRANSPORT 305 FORWARD MODEL IN DISCRETE FORM 306 OBJECTIVE AND
FIRST-ORDER CONDITIONS 307 ADJOINT MODEL 308 DIRECT SOLUTION - AN
ELLIPTIC PROBLEM IN TIME 309 ITERATIVE SOLUTION BY GRADIENT DESCENT 310
SPECIAL CASE #1: SHOOTING 312 SPECIAL CASE #2: AGNOSTIC P 313
PARAMETER ESTIMATION 313 15.2 HYPERBOLIC MODEL: TELEGRAPH EQUATION 315
PROBLEM STATEMENT 315 OPTIMAL FIT: GLS OBJECTIVE AND FIRST-ORDER
CONDITIONS 316 GRADIENT DESCENT ALGORITHMS 318 CONJUGATE GRADIENT
DESCENT 319 SOLUTION BY REPRESENTERS 319 15.3 REGULARIZATION 321
REDUCTION OF THE DOF S 321 THE WEIGHT MATRIX 322 HEURISTIC SPECIFICATION
OF [W] USING FEM 322 15.4 EXAMPLE: NONLINEAR INVERSION 323 16 TIME
CONVENTIONS FOR REAL-TIME ASSIMILATION 329 16.1 TIME 329 16.2
OBSERVATIONAL DATA 329 16.3 SIMULATION DATA PRODUCTS 330 16.4 SEQUENTIAL
SIMULATION 331 16.5 WHAT TIME IS IT? 332 16.6 EXAMPLE: R-T OPERATIONS,
CRUISE EL 9904 332 17 SKILL ASSESSMENT FOR DATA ASSIMILATIVE MODELS 335
17.1 VOCABULARY 335 FORWARD AND INVERSE MODELS 335 TRUTH, DATA,
PREDICTION 335 SKILL 336 ACCURACY/BIAS, PRECISION/NOISE 336 17.2
OBSERVATIONAL SYSTEM SIMULATION EXPERIMENTS: EXAMPLE 337 CONTENTS , XI
18 STATISTICAL INTERPOLATION 341 18.1 INTRODUCTION: POINT ESTIMATION 341
18.2 INTERPOLATION AND THE GAUSS-MARKOV THEOREM 343 18.3 INTERPOLATING
AND SAMPLING FINITE FIELDS 345 18.4 ANALYTIC COVARIANCE FUNCTIONS 348
18.5 STOCHASTICALLY-FORCED DIFFERENTIAL EQUATION (SDE) 350 EXAMPLE 1 351
EXAMPLE 2 356 18.6 OA-GLS EQUIVALENCE 356 18.7 KRIGING 358 18.8
CONCLUDING REMARKS 359 APPENDICES 361 AL. VECTOR IDENTITIES 363 A2.
COORDINATE SYSTEMS 365 A3. STABILITY OF QUADRATIC ROOTS 367 A4.
INVERSION NOTES 369 A5. TIME CONVENTIONS 371 BIBLIOGRAPHY 377 INDEX 385
|
| adam_txt |
NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS FOR ENVIRONMENTAL SCIENTISTS
AND ENGINEERS A FIRST PRACTICAL COURSE BY DANIEL R. LYNCH DARTMOUTH
COLLEGE DARTMOUTH, NEW HAMPSHIRE USA 4Y SPRINGER CONTENTS PREFACE XV
SYNOPSIS XIX I THE FINITE DIFFERENCE METHOD 1 1 INTRODUCTION 3 1.1 FROM
ALGEBRA TO CALCULUS AND BACK 3 1.2 DISTRIBUTED, LUMPED, DISCRETE SYSTEMS
4 1.3 PDE SOLUTIONS 6 1.4 IC'S, BC'S, CLASSIFICATION 7 A UNIQUENESS
PROOF: POISSON EQUATION 7 CLASSIFICATION OF BC'S 8 CLASSIFICATION OF
EQUATIONS 9 2 FINITE DIFFERENCE CALCULUS 11 2.1 -1-D DIFFERENCES ON A
UNIFORM MESH 11 SUMMARY - UNIFORM MESH 13 2.2 USE OF THE ERROR TERM 15
2.3 1-D DIFFERENCES ON NONUNIFORM MESHES 16 2.4 POLYNOMIAL FIT 17 2.5
CROSS-DERIVATIVES 18 3 ELLIPTIC EQUATIONS 21 3.1 INTRODUCTION 21 3.2 1-D
EXAMPLE 21 3.3 2-D EXAMPLE 25 MOLECULES 25 MATRIX ASSEMBLY AND DIRECT
SOLUTION 28 ITERATIVE SOLUTION 29 3.4 OPERATION COUNTS 30 3.5
ADVECTIVE-DIFFUSIVE EQUATION 31 4 ELLIPTIC ITERATIONS 37 4.1 BARE
ESSENTIALS 37 4.2 POINT METHODS 39 4.3 BLOCK METHODS 43 ALTERNATING
DIRECTION METHODS 44 4.4 HELMHOLTZ EQUATION . . 46 VI CONTENTS 4.5
GRADIENT DESCENT METHODS ( 47 5 PARABOLIC EQUATIONS 51 5.1 INTRODUCTION
51 5.2 EXAMPLES: DISCRETE SYSTEMS 53 EULER 53 LEAPFROG 54 BACKWARD EULER
55 2-LEVEL IMPLICIT 55 5.3 BOUNDARY CONDITIONS 57 5.4 STABILITY,
CONSISTENCY, CONVERGENCE 58 CONVERGENCE - LUMPED SYSTEM 59 CONVERGENCE -
DISCRETE SYSTEM 60 CONSISTENCY 61 STABILITY 61 5.5 ACCURACY: FOURIER
ANALYSIS 64 CONTINUOUS SYSTEM 64 LUMPED SYSTEM 65 DISCRETE SYSTEM 67
EXAMPLE: IMPLICIT LEAPFROG SYSTEM 71 5.6 CONSERVATION LAWS 76 5.7
TWO-DIMENSIONAL PROBLEMS 82 5.8 NONLINEAR PROBLEMS 85 6 HYPERBOLIC
EQUATIONS 89 6.1 INTRODUCTION 89 6.2 LUMPED SYSTEMS 93 6.3 HARMONIC
APPROACH 94 6.4 MORE LUMPED SYSTEMS 97 6.5 DISPERSION RELATIONSHIP 99
CONTINUOUS SYSTEM 99 LUMPED SYSTEM #1 100 LUMPED SYSTEM #2 101 LUMPED
SYSTEM # 3 . 102 LUMPED SYSTEM #4 103 6.6 DISCRETE SYSTEMS 104 DISCRETE
SYSTEM 1 (TELEGRAPH EQUATION) 106 DISCRETE SYSTEMS 3: COUPLED I S *
ORDER EQUATIONS 109 DISCRETE SYSTEM 4: IMPLICIT FOUR-POINT PRIMITIVE 115
6.7 LUMPED SYSTEMS IN HIGHER DIMENSIONS 116 II THE FINITE ELEMENT METHOD
121 7 GENERAL PRINCIPLES 123 7.1 THE METHOD OF WEIGHTED RESIDUALS 123
7.2 MWR EXAMPLES 125 7.3 WEAK FORMS 128 7.4 DISCRETE FORM 129 CONTENTS -
VII 7.5 BOUNDARY CONDITIONS 129 7.6 VARIATIONAL PRINCIPLES 130 7.7 WEAK
FORMS AND CONSERVATION PROPERTIES 133 8 A 1-D TUTORIAL 139 8.1
POLYNOMIAL BASES - THE LAGRANGE FAMILY 139 8.2 GLOBAL AND LOCAL
INTERPOLATION 140 8.3 LOCAL INTERPOLATION ON ELEMENTS 142 8.4 CONTINUITY
- HERMITE POLYNOMIALS . . . 143 8.5 EXAMPLE 146 8.6 BOUNDARY CONDITIONS
150 8.7 THE ELEMENT MATRIX 152 8.8 ASSEMBLY AND THE INCIDENCE LIST 157
8.9 MATRIX STRUCTURE 158 8.10 VARIABLE COEFFICIENTS 161 8.11 NUMERICAL
INTEGRATION 162 8.12 ASSEMBLY WITH QUADRATURE 164 9 MULTI-DIMENSIONAL
ELEMENTS 167 9.1 LINEAR TRIANGULAR ELEMENTS 167 LOCAL INTERPOLATION 167
DIFFERENTIATION 169 INTEGRATION 170 9.2 EXAMPLE: HELMHOLTZ EQUATION ON
LINEAR TRIANGLES 170 9.3 HIGHER ORDER TRIANGULAR ELEMENTS 172 LOCAL
COORDINATE SYSTEM 172 HIGHER-ORDER LOCAL INTERPOLATION ON TRIANGLES 173
DIFFERENTIATION 175 NUMERICAL INTEGRATION 177 9.4 ISOPARAMETRIC
TRANSFORMATION 179 9.5 QUADRILATERAL ELEMENTS 181 THE BILINEAR ELEMENT
181 HIGHER-ORDER QUADRILATERAL ELEMENTS 183 ISOPARAMETRIC QUADRILATERALS
183 10 TIME-DEPENDENT PROBLEMS 189 10.1 GENERAL APPROACH : . . . . 189
10.2 LUMPED AND DISCRETE SYSTEMS 189 10.3 EXAMPLE: DIFFUSION EQUATION
190 10.4 EXAMPLE: ADVECTION-DIFFUSION EQUATION 192 10.5 EXAMPLE: WAVE
EQUATION '. 193 10.6 EXAMPLE: TELEGRAPH EQUATION 195 11 VECTOR PROBLEMS
197 11.1 INTRODUCTION 197 11.2 GRADIENT OF A SCALAR 197 GALERKIN FORM
198 NATURAL LOCAL COORDINATE SYSTEMS AND NEUMANN BOUNDARIES 199
DIRICHLET BOUNDARIES 201 VIII CONTENTS 11.3 ELASTICITY 202 WEAK FORM 202
CONSTITUTIVE RELATIONS 203 GAIERKIN APPROXIMATION 204 NATURAL LOCAL
COORDINATE SYSTEMS 204 REFERENCES - SOLID MECHANICS 205 11.4
ELECTROMAGNETICS 205 GOVERNING EQUATIONS 206 POTENTIALS AND GAUGE 206
HELMHOLTZ EQUATIONS IN THE POTENTIALS 207 WEAK FORM * * * * 208 BOUNDARY
CONDITIONS 209 RECONSTRUCTING E AND H 209 REFERENCES - E&M 209 11.5
FLUID MECHANICS WITH MIXED INTERPOLATION 210 GOVERNING EQUATIONS 210
BASES AND WEIGHTS 211 MIXED ELEMENTS 211 WEAK FORM 212 GAIERKIN
EQUATIONS 212 NUMBERING CONVENTION 213 COORDINATE ROTATION 214
REFERENCES: FLUID MECHANICS 214 11.6 OCEANIC TIDES 214 WEAK FORM AND
GAIERKIN HELMHOLTZ EQUATION 215 VELOCITY SOLUTION 216 REFERENCES -
OCEANIC TIDES 217 12 NUMERICAL ANALYSIS 219 12.1 1-D ELLIPTIC EQUATIONS
219 LAPLACE EQUATION ON 1-D LINEAR ELEMENTS 219 ADVECTIVE-DIFFUSIVE
EQUATION ON 1-D LINEAR ELEMENTS 219 HELMHOLTZ EQUATION ON 1-D LINEAR
ELEMENTS 221 POISSON EQUATION ON 1-D LINEAR ELEMENTS 223 INHOMOGENEOUS
HELMHOLTZ EQUATION ON 1-D LINEAR ELEMENTS . 226 12.2 FOURIER TRANSFORMS
FOR DIFFERENCE EXPRESSIONS 230 12.3 2-D ELLIPTIC EQUATIONS 236 LAPLACE
EQUATION ON BILINEAR RECTANGLES 236 HELMHOLTZ EQUATION ON BILINEAR
RECTANGLES 238 12.4 DIFFUSION EQUATION 240 STABILITY 241 MONOTONICITY
242 ACCURACY 243 LEAPFROG TIME-STEPPING 243 3-LEVEL IMPLICIT
TIME-STEPPING 245 12.5 EXPLICIT WAVE EQUATION 247 STABILITY 248 ACCURACY
248 CONTENTS , IX 12.6 IMPLICIT WAVE EQUATION 250 STABILITY 250 ACCURACY
251 12.7 ADVECTION EQUATION 251 EULER ADVECTION 252 TWO-LEVEL IMPLICIT
ADVECTION 253 LEAPFROG ADVECTION 253 12.8 ADVECTIVE-DIFFUSIVE EQUATION
255 EULER 256 2-LEVEL IMPLICIT 257 LEAPFROG 258 III INVERSE METHODS 263
13 INVERSE NOISE, SVD, AND LLS 265 13.1 MATRIX INVERSION AND INVERSE
NOISE 266 MEAN AND VARIABILITY. 266 COVARIANCE 266 VARIANCE 268 NOISE
MODELS 268 EIGENTHEORY 270 13.2 THE SINGULAR VALUE DECOMPOSITION 272 SVD
BASICS 273 THE SQUARE, NONSINGULAR CASE 274 THE SQUARE, SINGULAR CASE
275 THE SQUARE, NEARLY-SINGULAR CASE 277 THE OVER-DETERMINED CASE 277
THE UNDER-DETERMINED CASE 278 SVD COVARIANCE 278 SVD REFERENCES 279 13.3
LINEAR'LEAST SQUARES AND THE NORMAL EQUATIONS 279 QUADRATIC FORMS AND
GRADIENT 279 ORDINARY LEAST SQUARES 280 WEIGHTED LEAST SQUARES 281
GENERAL LEAST SQUARES 282 14 FITTING MODELS TO DATA 285 14.1 INVERTING
DATA 285 MODEL-DATA MISFIT 285 DIRECT SOLUTION STRATEGIES AND INVERSE
NOISE 287 MORE ON THE MODEL-DATA MISFIT 288 14.2 CONSTRAINED
MINIMIZATION AND GRADIENT DESCENT 289 GENERALIZED LEAST SQUARES AS
CONSTRAINED MINIMIZATION 289 THE ADJOINT METHOD 290 GRADIENT DESCENT 291
SUMMARY - ADJOINT METHOD WITH GRADIENT DESCENT 293 MONTE CARLO VARIANCE
ESTIMATION - INVERSE NOISE 293 14.3 INVERTING DATA WITH REPRESENTERS 294
X CONTENTS THE PROCEDURE 295 INVERSE NOISE 296 14.4 INVERTING DATA WITH
UNIT RESPONSES 296 PROCEDURE 296 14.5 SUMMARY: GLS DATA INVERSION 297
14.6 PARAMETER ESTIMATION 298 GLS OBJECTIVE 299 FIRST-ORDER CONDITIONS
FOR GLS EXTREMUM 299 THE GRADIENT IN PARAMETER SPACE 300 AN ADJOINT
METHOD FOR PARAMETER ESTIMATION 302 14.7 SUMMARY - TERMINOLOGY 302 15
DYNAMIC INVERSION 305 15.1 PARABOLIC MODEL: ADVECTIVE-DIFFUSIVE
TRANSPORT 305 FORWARD MODEL IN DISCRETE FORM 306 OBJECTIVE AND
FIRST-ORDER CONDITIONS 307 ADJOINT MODEL 308 DIRECT SOLUTION - AN
ELLIPTIC PROBLEM IN TIME 309 ITERATIVE SOLUTION BY GRADIENT DESCENT 310
SPECIAL CASE #1: "SHOOTING" 312 SPECIAL CASE #2: AGNOSTIC P 313
PARAMETER ESTIMATION 313 15.2 HYPERBOLIC MODEL: TELEGRAPH EQUATION 315
PROBLEM STATEMENT 315 OPTIMAL FIT: GLS OBJECTIVE AND FIRST-ORDER
CONDITIONS 316 GRADIENT DESCENT ALGORITHMS 318 CONJUGATE GRADIENT
DESCENT 319 SOLUTION BY REPRESENTERS 319 15.3 REGULARIZATION 321
REDUCTION OF THE DOF'S 321 THE WEIGHT MATRIX 322 HEURISTIC SPECIFICATION
OF [W] USING FEM 322 15.4 EXAMPLE: NONLINEAR INVERSION 323 16 TIME
CONVENTIONS FOR REAL-TIME ASSIMILATION 329 16.1 TIME 329 16.2
OBSERVATIONAL DATA 329 16.3 SIMULATION DATA PRODUCTS 330 16.4 SEQUENTIAL
SIMULATION 331 16.5 WHAT TIME IS IT? 332 16.6 EXAMPLE: R-T OPERATIONS,
CRUISE EL 9904 332 17 SKILL ASSESSMENT FOR DATA ASSIMILATIVE MODELS 335
17.1 VOCABULARY 335 FORWARD AND INVERSE MODELS 335 TRUTH, DATA,
PREDICTION 335 SKILL 336 ACCURACY/BIAS, PRECISION/NOISE 336 17.2
OBSERVATIONAL SYSTEM SIMULATION EXPERIMENTS: EXAMPLE 337 CONTENTS , XI
18 STATISTICAL INTERPOLATION 341 18.1 INTRODUCTION: POINT ESTIMATION 341
18.2 INTERPOLATION AND THE GAUSS-MARKOV THEOREM 343 18.3 INTERPOLATING
AND SAMPLING FINITE FIELDS 345 18.4 ANALYTIC COVARIANCE FUNCTIONS 348
18.5 STOCHASTICALLY-FORCED DIFFERENTIAL EQUATION (SDE) 350 EXAMPLE 1 351
EXAMPLE 2 356 18.6 OA-GLS EQUIVALENCE 356 18.7 KRIGING 358 18.8
CONCLUDING REMARKS 359 APPENDICES 361 AL. VECTOR IDENTITIES 363 A2.
COORDINATE SYSTEMS 365 A3. STABILITY OF QUADRATIC ROOTS 367 A4.
INVERSION NOTES 369 A5. TIME CONVENTIONS 371 BIBLIOGRAPHY 377 INDEX 385 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Lynch, Daniel R. |
| author_facet | Lynch, Daniel R. |
| author_role | aut |
| author_sort | Lynch, Daniel R. |
| author_variant | d r l dr drl |
| building | Verbundindex |
| bvnumber | BV021997910 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 |
| callnumber-search | QA374 |
| callnumber-sort | QA 3374 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)56686622 (DE-599)BVBBV021997910 |
| dewey-full | 518/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.64 |
| dewey-search | 518/.64 |
| dewey-sort | 3518 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV021997910 |
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| index_date | 2024-07-02T16:11:02Z |
| indexdate | 2024-07-09T20:49:00Z |
| institution | BVB |
| isbn | 0387236198 |
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| physical | XXIV, 388 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Springer |
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| spelling | Lynch, Daniel R. Verfasser aut Numerical partial differential equations for environmental scientist and engineers a first practical course New York, NY Springer 2005 XXIV, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [377] - 384 Differential equations, Partial Numerical solutions Finite differences Finite element method Inverse problems (Differential equations) Inverse Methode (DE-588)4162226-1 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Umweltwissenschaften (DE-588)4137364-9 gnd rswk-swf Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Partielle Differentiation (DE-588)4464177-1 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Partielle Differentiation (DE-588)4464177-1 s Numerisches Verfahren (DE-588)4128130-5 s Inverses Problem (DE-588)4125161-1 s Finite-Differenzen-Methode (DE-588)4194626-1 s Umweltwissenschaften (DE-588)4137364-9 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Numerische Mathematik (DE-588)4042805-9 s Ingenieurwissenschaften (DE-588)4137304-2 s Finite-Elemente-Methode (DE-588)4017233-8 s Inverse Methode (DE-588)4162226-1 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015212558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lynch, Daniel R. Numerical partial differential equations for environmental scientist and engineers a first practical course Differential equations, Partial Numerical solutions Finite differences Finite element method Inverse problems (Differential equations) Inverse Methode (DE-588)4162226-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Umweltwissenschaften (DE-588)4137364-9 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Partielle Differentiation (DE-588)4464177-1 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4162226-1 (DE-588)4137304-2 (DE-588)4128130-5 (DE-588)4017233-8 (DE-588)4044779-0 (DE-588)4137364-9 (DE-588)4194626-1 (DE-588)4042805-9 (DE-588)4464177-1 (DE-588)4125161-1 (DE-588)4151278-9 |
| title | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_auth | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_exact_search | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_exact_search_txtP | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_full | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_fullStr | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_full_unstemmed | Numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_short | Numerical partial differential equations for environmental scientist and engineers |
| title_sort | numerical partial differential equations for environmental scientist and engineers a first practical course |
| title_sub | a first practical course |
| topic | Differential equations, Partial Numerical solutions Finite differences Finite element method Inverse problems (Differential equations) Inverse Methode (DE-588)4162226-1 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Umweltwissenschaften (DE-588)4137364-9 gnd Finite-Differenzen-Methode (DE-588)4194626-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Partielle Differentiation (DE-588)4464177-1 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Differential equations, Partial Numerical solutions Finite differences Finite element method Inverse problems (Differential equations) Inverse Methode Ingenieurwissenschaften Numerisches Verfahren Finite-Elemente-Methode Partielle Differentialgleichung Umweltwissenschaften Finite-Differenzen-Methode Numerische Mathematik Partielle Differentiation Inverses Problem Einführung |
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