Modeling and simulation: an application-oriented introduction
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Berlin
Springer
[2014]
|
| Schriftenreihe: | Springer Undergraduate Texts in Mathematics and Technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xiv, 413 Seiten Diagramme 235 mm x 155 mm |
| ISBN: | 3642395236 9783642395239 |
Internformat
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| 245 | 1 | 0 | |a Modeling and simulation |b an application-oriented introduction |c Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk Pflüger ; translated from the German by Sabine and Richard Le Borne |
| 264 | 1 | |a Berlin |b Springer |c [2014] | |
| 264 | 4 | |c © 2014 | |
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Datensatz im Suchindex
| _version_ | 1809768971048583168 |
|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 1
1.1 THE SIMULATION PIPELINE 1
1.2 INTRODUCTION TO MODELING 4
1.2.1 GENERAL PREREQUISITES 5
1.2.2 DERIVATION OF MODELS 7
1.2.3 ANALYSIS OF MODELS 9
1.2.4 CLASSIFICATION OF MODELS 11
1.2.5 SCALES 11
1.3 INTRODUCTION TO SIMULATION 13
1.3.1 GENERAL REMARKS 13
1.3.2 ASSESSMENT 14
2 REQUIRED TOOLS IN SHORT 17
2.1 ELEMENTARY AND DISCRETE TOPICS 18
2.2 CONTINUOUS ASPECTS 19
2.2.1 LINEAR ALGEBRA 19
2.2.2 ANALYSIS 21
2.2.3 SIGNIFICANCE FOR MODELING AND SIMULATION 28
2.3 STOCHASTIC AND STATISTICAL ISSUES 29
2.3.1 WHY RANDOMNESS? 29
2.3.2 DISCRETE PROBABILITY SPACES 30
2.3.3 CONTINUOUS PROBABILITY SPACES 36
2.3.4 ASYMPTOTICS 41
2.3.5 STATISTICAL INFERENCE 43
2.4 NUMERICAL ASPECTS 47
2.4.1 BASICS 47
2.4.2 INTERPOLATION AND QUADRATURE 51
2.4.3 DIRECT SOLUTION OF LINEAR SYSTEMS OF EQUATIONS 59
2.4.4 ITERATION METHODS 61
HTTP://D-NB.INFO/1035829231
X
CONTENTS
2.4.5 ORDINARY DIFFERENTIAL EQUATIONS 68
2.4.6 PARTIAL DIFFERENTIAL EQUATIONS 78
2.5 INTERRELATIONSHIPS BETWEEN TOOLS AND APPLICATIONS 83
PART I GAMING*DECIDING*PLANNING: A WARM-UP
FOR MODELING
3 GAME THEORY 87
3.1 GAMES IN STRATEGIC NORMAL FORM 88
3.2 GAMES WITHOUT ASSUMPTIONS ON THE OPPONENT 90
3.3 RESPONSE MAPPINGS 91
3.4 DOMINANT STRATEGIES 93
3.5 NASH EQUILIBRIA 94
3.6 MIXED STRATEGIES 95
3.7 OUTLOOK 97
4 GROUP DECISION MAKING 99
4.1 INDIVIDUAL PREFERENCES AND GROUP DECISION MAKING 100
4.2 EXAMPLES FOR DECISION MAKING METHODS 103
4.3 CONDITIONS FOR CHOICE FUNCTIONS, ARROW'S THEOREM 106
5 SCHEDULING ILL
5.1 PROCESS SCHEDULING (DETERMINISTIC) 112
5.2 PROCESS-SCHEDULING (STOCHASTIC) 118
5.3 JOB-SHOP PROBLEMS 124
5.4 FURTHER SCHEDULING PROBLEMS 128
6 WIENER PROCESSES 131
6.1 FROM THE BERNOULLI EXPERIMENT TO THE NORMAL DISTRIBUTION 132
6.2 NORMALLY DISTRIBUTED INPUT PARAMETERS 134
6.3 WIENER PROCESSES 135
6.4 APPLICATION: DEVELOPMENT OF MONEY INVESTMENTS 138
PART II TRAFFIC ON HIGHWAYS AND DATA HIGHWAYS: ONCE
THROUGH THE SIMULATION PIPELINE
7 MACROSCOPIC SIMULATION OF ROAD TRAFFIC 149
7.1 MODEL APPROACH 150
7.2 HOMOGENEOUS TRAFFIC FLOW 152
7.2.1 AN INITIAL RESULT 152
7.2.2 VELOCITY, FLOW AND DENSITY 153
7.2.3 FUNDAMENTAL DIAGRAM 154
7.2.4 MODEL REFINEMENTS 155
7.3 INHOMOGENEOUS TRAFFIC FLOW 158
7.4 SIMULATION OF A SIMPLE CIRCULAR ROAD 160
7.4.1 A FIRST ATTEMPT 161
7.4.2 AN IMPROVED SIMULATION 163
CONTENTS XI
7.5 SIGNAL AND TRAFFIC VELOCITY 165
7.6 SUMMARY AND OUTLOOK 169
8 MICROSCOPIC SIMULATION OF ROAD TRAFFIC 171
8.1 MODEL APPROACH 172
8.1.1 CELLULAR AUTOMATA 172
8.1.2 ROAD TRAFFIC 174
8.2 A FIRST SIMULATION 176
8.3 STOCHASTIC EXTENSION: RANDOMIZATION 178
8.3.1 FREE TRAFFIC FLOW 179
8.3.2 HIGHER DENSITIES, TRAFFIC JAMS OUT OF NOWHERE 180
8.3.3 VALIDATION AND CALIBRATION: FUNDAMENTAL DIAGRAMS 182
8.4 MODELING OF TRAFFIC NETWORKS 186
8.4.1 TRAFFIC GRAPH 186
8.4.2 INTERSECTIONS 188
8.4.3 PLANS AND INTENTIONS 193
8.5 MODEL REFINEMENTS 199
8.6 SUMMARY AND OUTLOOK 201
9 STOCHASTIC TRAFFIC SIMULATION 203
9.1 MODEL APPROACH 204
9.2 QUEUING SYSTEMS 206
9.2.1 STOCHASTIC PROCESSES 207
9.2.2 CLASSIFICATION OF ELEMENTARY QUEUING SYSTEMS 213
9.2.3 EXAMPLES FOR THE KENDALL NOTATION 214
9.2.4 PERFORMANCE INDICES AND FIRST RESULTS 215
9.3 QUEUING NETWORKS 218
9.3.1 PARAMETERS IN QUEUING NETWORKS 219
9.3.2 ASYMPTOTIC ANALYSIS 220
9.4 ANALYSIS AND SIMULATION 222
9.4.1 MARKOV PROCESSES AND MARKOV CHAINS 223
9.4.2 QUEUING SYSTEMS 229
9.4.3 QUEUING NETWORKS 234
9.4.4 SIMULATION 235
9.5 SUMMARY AND OUTLOOK 237
PART III DYNAMICAL SYSTEMS: CAUSE, EFFECT, AND INTERPLAY
10 POPULATION DYNAMICS 241
10.1 MALTHUSIAN GROWTH MODEL 242
10.2 REFINED SINGLE SPECIES MODELS 242
10.2.1 LINEAR MODEL WITH SATURATION 243
10.2.2 LOGISTIC GROWTH 243
10.3 TWO SPECIES MODELS 245
10.4 A DISCRETE SINGLE SPECIES MODEL 250
XII CONTENTS
11 CONTROL ENGINEERING 255
11.1 THE BASICS OF CONTROL THEORY 256
11.1.1 CONTROL LOOP 257
11.1.2 DESCRIPTION OF LINEAR DYNAMICAL SYSTEMS 258
11.1.3 REQUIREMENTS FOR THE CONTROLLER 258
11.1.4 PID CONTROLLER 259
11.2 EXEMPLARY MODELING OF A MULTIBODY SYSTEM 261
11.2.1 LINEARIZED MODEL WITH CONSERVATION
OF LINEAR AND ANGULAR MOMENTUM 263
11.2.2 COMPLETE MODEL WITH LAGRANGE EQUATIONS 266
11.2.3 SIMULATION OF THE PENDULUM 270
11.3 FUZZY SET THEORY 271
11.3.1 MEMBERSHIP IN FUZZY SETS 271
11.3.2 OPERATIONS WITH FUZZY SETS 274
11.3.3 LINGUISTIC VARIABLES 276
11.3.4 FUZZY LOGIC 277
11.4 RULE-BASED FUZZY SYSTEM 280
11.4.1 FUZZIFICATION 281
11.4.2 INFERENCE 282
11.4.3 DEFUZZIFICATION 283
11.4.4 EXAMPLE 284
11.5 FUZZY CONTROL OF THE INVERTED PENDULUM 284
11.5.1 PARAMETERS AND CONSTRAINTS 285
11.5.2 SWINGING UP THE PENDULUM 286
11.5.3 STABILIZING THE PENDULUM 288
11.6 OUTLOOK 288
12 CHAOS THEORY 291
12.1 INTRODUCTION 292
12.2 FROM ORDER TO CHAOS 293
12.2.1 LOGISTIC MAPPING AND ITS FIXED POINTS 293
12.2.2 NUMERICAL ANALYSIS AND BIFURCATIONS 295
12.2.3 TRANSITION INTO CHAOS 298
12.3 STRANGE ATTRACTORS 301
12.3.1 SELF-SIMILARITY AND FRACTAL DIMENSION 302
12.3.2 HENON MAPPING 304
12.3.3 GENERAL TWO-DIMENSIONAL QUADRATIC MAPPING 305
12.4 CHAOTIC BEHAVIOR OF A DRIVEN PENDULUM 307
12.4.1 MODEL OF THE PENDULUM 308
12.4.2 DISCRETIZATION 309
12.4.3 CYCLES AND ATTRACTORS 310
CONTENTS
XLLL
PART IV PHYSICS IN THE COMPUTER: TAKE-OFF TOWARD NUMBER
CRUNCHING
13 MOLECULAR DYNAMICS 317
13.1 MODELING OF MOLECULES AND INTERACTIONS 318
13.1.1 FUNDAMENTAL PHYSICAL FORCES 318
13.1.2 POTENTIALS FOR UNCHARGED ATOMS 319
13.1.3 COMPUTATION OF THE FORCE ACTING ON AN ATOM 323
13.2 EQUATIONS OF MOTION AND THEIR SOLUTIONS 324
13.2.1 EQUATIONS OF MOTION 324
13.2.2 EULER'S METHOD 325
13.2.3 VELOCITY-STORMER-VERLET 326
13.2.4 REMARKS 327
13.3 SIMULATION DOMAIN 328
13.3.1 NVT ENSEMBLE 328
13.3.2 BOUNDARY CONDITIONS 329
13.4 IMPLEMENTATION 330
13.4.1 LINKED-CELLS DATA STRUCTURE 331
13.5 PARALLELIZATION 333
13.6 OUTLOOK 335
14 HEAT TRANSFER 337
14.1 DERIVATION OF THE HEAT EQUATION 338
14.1.1 NUMBER OF DIMENSIONS 340
14.2 DISCRETIZATION 341
14.2.1 3-POINT-STENCIL 342
14.2.2 5-POINT-STENCIL 344
14.2.3 BOUNDARY TREATMENT 346
14.3 NUMERICAL SOLUTION OF THE PDE 346
14.3.1 SIMPLE RELAXATION METHODS 347
14.3.2 MULTIGRID METHODS 348
15 FLUID DYNAMICS 355
15.1 FLUIDS AND FLOWS 356
15.2 MATHEMATICAL MODEL 357
15.2.1 NAVIER-STOKES EQUATIONS 357
15.2.2 REMARKS CONCERNING THE DERIVATION 360
15.3 DISCRETIZATION OF THE NAVIER-STOKES EQUATIONS 361
15.3.1 FINITE DIFFERENCES 361
15.3.2 TREATMENT OF SPATIAL DERIVATIVES 362
15.3.3 TREATMENT OF TEMPORAL DERIVATIVES 363
15.3.4 TREATMENT OF BOUNDARY CONDITIONS 364
15.4 NUMERICAL SOLUTION OF THE DISCRETIZED EQUATIONS 365
15.4.1 TIME STEP 365
15.4.2 SPATIALLY DISCRETE MOMENTUM EQUATIONS 367
XIV CONTENTS
15.4.3 SPATIALLY DISCRETE POISSON EQUATION FOR THE PRESSURE 367
15.4.4 REGARDING STABILITY 368
15.5 APPLICATION EXAMPLE: FLOW AROUND AN OBSTACLE 368
15.6 OUTLOOK 370
15.6.1 PROBLEM SETTINGS AND MODELS 370
15.6.2 DISCRETIZATIONS 371
15.6.3 STRUCTURED GRIDS 373
15.6.4 UNSTRUCTURED GRIDS 376
15.6.5 APPROACHES FOR THE TREATMENT OF CHANGING
GEOMETRIES 379
16 GLOBAL ILLUMINATION IN COMPUTER GRAPHICS 381
16.1 QUANTITIES FROM RADIOMETRY 382
16.2 THE RENDERING EQUATION 384
16.3 TECHNIQUES FOR THE SOLUTION OF THE RENDERING EQUATION 387
16.3.1 RAY TRACING 388
16.3.2 PATH-TRACING 390
16.3.3 FURTHER RAY-TRACING DERIVATES 391
16.4 THE RADIOSITY METHOD 392
16.4.1 BASIC PRINCIPLE 392
16.4.2 COMPUTATION OF THE FORM FACTORS 394
16.4.3 SOLUTION OF THE RADIOSITY EQUATION 396
16.4.4 REMARKS AND IMPROVEMENTS 397
CONCLUDING REMARKS 401
REFERENCES 403
INDEX 407 |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| spelling | Bungartz, Hans-Joachim 1963- Verfasser (DE-588)112889832 aut Modellbildung und Simulation Modeling and simulation an application-oriented introduction Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk Pflüger ; translated from the German by Sabine and Richard Le Borne Berlin Springer [2014] © 2014 xiv, 413 Seiten Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Undergraduate Texts in Mathematics and Technology Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 s Computersimulation (DE-588)4148259-1 s DE-604 Zimmer, Stefan Verfasser aut Buchholz, Martin Verfasser aut Pflüger, Dirk Verfasser (DE-588)14255037X aut Erscheint auch als Online-Ausgabe 978-3-642-39524-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4363275&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026903469&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bungartz, Hans-Joachim 1963- Zimmer, Stefan Buchholz, Martin Pflüger, Dirk Modeling and simulation an application-oriented introduction Computersimulation (DE-588)4148259-1 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)7651795-0 |
| title | Modeling and simulation an application-oriented introduction |
| title_alt | Modellbildung und Simulation |
| title_auth | Modeling and simulation an application-oriented introduction |
| title_exact_search | Modeling and simulation an application-oriented introduction |
| title_full | Modeling and simulation an application-oriented introduction Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk Pflüger ; translated from the German by Sabine and Richard Le Borne |
| title_fullStr | Modeling and simulation an application-oriented introduction Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk Pflüger ; translated from the German by Sabine and Richard Le Borne |
| title_full_unstemmed | Modeling and simulation an application-oriented introduction Hans-Joachim Bungartz, Stefan Zimmer, Martin Buchholz, Dirk Pflüger ; translated from the German by Sabine and Richard Le Borne |
| title_short | Modeling and simulation |
| title_sort | modeling and simulation an application oriented introduction |
| title_sub | an application-oriented introduction |
| topic | Computersimulation (DE-588)4148259-1 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Computersimulation Mathematische Modellierung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4363275&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026903469&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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