Verfügbarkeit: Numerical partial differential equations for environmental scientist and engineers

Numerical partial differential equations for environmental scientist and engineers: a first practical course

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Bibliographische Detailangaben
1. Verfasser:	Lynch, Daniel R. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York, NY Springer 2005
Schlagworte:	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
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Literaturverz. S. [377] - 384
Beschreibung:	XXIV, 388 S. graph. Darst.
ISBN:	0387236198

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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
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genre	(DE-588)4151278-9 Einführung gnd-content
genre_facet	Einführung
id	DE-604.BV021997910
illustrated	Illustrated
index_date	2024-07-02T16:11:02Z
indexdate	2024-07-09T20:49:00Z
institution	BVB
isbn	0387236198
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015212558
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owner	DE-706
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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
url	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
work_keys_str_mv	AT lynchdanielr numericalpartialdifferentialequationsforenvironmentalscientistandengineersafirstpracticalcourse

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