Advanced finite element methods and applications:
Gespeichert in:
Weitere beteiligte Personen: | |
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Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
Schriftenreihe: | Lecture notes in applied and computational mechanics
66 |
Schlagwörter: | |
Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=4012617&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=026040426&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Beschreibung: | Literaturangaben |
Umfang: | XV, 374 S. Ill., graph. Darst. 235 mm x 155 mm |
ISBN: | 9783642303159 |
Internformat
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Datensatz im Suchindex
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adam_text | IMAGE 1
CONTENTS
A BRIEF HISTORY O F THE PARALLEL DAWN IN KARL-MARX-STADT/CHEMNITZ 1
GUNDOLF HAASE AND MATTHIAS PESTER 1 INTRODUCTION 1
2 ANCIENT HARDWARE AND ITS DEVELOPMENT 2
2.1 TRANSPUTER 2
2.2 AVAILABLE PARALLEL COMPUTERS 4
2.3 SOME REMARKS ON PERFORMANCE 12
3 THE SCIENTIFIC ENVIRONMENT 13
3.1 SUMMER SCHOOL 1988 14
3.2 SUMMER SCHOOL 1989 14
3.3 SUMMER SCHOOL 1990 16
3.4 MULTIGRID SEMINARS 16
3.5 FEM SYMPOSIA 18
3.6 HISTORIC NUMERICAL EXAMPLES 19
4 PARALLEL COMPUTING IN 2012 2 0
4.1 STATE O F HARDWARE 2 0
4.2 PERFORMANCE NUMBERS 2 1
5 CONCLUSIONS 2 3
REFERENCES 2 3
DOMAIN DECOMPOSITION PRECONDITIONING FOR HIGH ORDER HYBRID DISCONTINUOUS
GALERKIN METHODS ON TETRAHEDRAL MESHES 27
JOACHIM SCHOBERL AND CHRISTOPH LEHRENFELD 1 INTRODUCTION 27
2 HDG DISCRETIZATION 29
3 DOMAIN DECOMPOSITION PRECONDITIONING 33
3.1 SCHWARZ TYPE DOMAIN DECOMPOSITION 34
3.2 BDDC PRECONDITIONERS 35
4 TRACES AND POLYNOMIAL EXTENSIONS ON THE INTERVAL 36
5 EXTENSION FROM A VERTEX 4 3
6 EXTENSION FROM AN EDGE 45
HTTP://D-NB.INFO/1021597856
IMAGE 2
X
CONTENTS
7 NUMERICAL RESULTS 53
REFERENCES 5 4
FAST DOMAIN DECOMPOSITION ALGORITHMS FOR ELLIPTIC PROBLEMS WITH
PIECEWISE VARIABLE ORTHOTROPISM 57
VADIM G. KORNEEV 1 INTRODUCTION 57
2 SINGLE THIN RECTANGLE 63
2.1 DISCRETE ANALOGUES OF BOUNDARY NORMS FOR HARMONIC FUNCTIONS IN THIN
RECTANGLES 63
2.2 FINITE-DIFFERENCE SHAPE DEPENDENT BOUNDARY NORM FOR FINITE ELEMENT
FUNCTIONS 67
2.3 PRECONDITIONING BY NONOVERLAPPING DOMAIN DECOMPOSITION 70
3 ORTHOTOPIC DISCRETIZATION WITH ARBITRARY ASPECT RATIO ON THIN
RECTANGLES 72
3.1 FINITE ELEMENT SPACE DECOMPOSITION 72
3.2 REDUCING TO ISOTROPIC DISCRETIZATION 73
4 COMPATIBLE SCHUR COMPLEMENT PRECONDITIONER 79
5 PIECEWISE ORTHOTOPIC DISCRETIZATIONS ON DOMAINS COMPOSED OF RECTANGLES
WITH ARBITRARY ASPECT RATIOS 82
5.1 SCHUR COMPLEMENT AND DOMAIN DECOMPOSITION ALGORITHMS 82
6 CONCLUDING REMARKS 86
REFERENCES 86
INEXACT ADDITIVE SCHWARZ SOLVERS FOR /I/?-FEM DISCRETIZATIONS IN THREE
DIMENSIONS 91
SVEN BEUCHLER 1 INTRODUCTION 91
2 SETTING OF THE PROBLEM, DISCRETIZATION 93
3 THE SOLUTION O F THE LINEAR SYSTEM 9 4
3.1 THE SCALAR ELLIPTIC CASE 9 4
3.2 THE PRECONDITIONER FOR LAME 99
4 NUMERICAL EXPERIMENTS 99
4.1 SCALAR ELLIPTIC PROBLEMS 100
4.2 LAME EQUATIONS O F LINEAR ELASTICITY 103
5 CONCLUSIONS 105
REFERENCES 106
A RIGOROUS ERROR ANALYSIS O F COUPLED FEM-BEM PROBLEMS WITH ARBITRARY
MANY SUBDOMAINS 109
CLEMENS PECHSTEIN AND CLEMENS HOFREITHER 1 INTRODUCTION 109
2 MODEL PROBLEM AND FEM-BEM COUPLING I L L
2.1 MODEL PROBLEM 112
2.2 SUBDOMAIN DECOMPOSITION 112
IMAGE 3
CONTENTS X I
2.3 OPERATORS ASSOCIATED TO THE POTENTIAL EQUATION 113
2.4 BOUNDARY INTEGRAL OPERATORS 114
2.5 CONTINUOUS DOMAIN-SKELETON FORMULATION 115
2.6 SYMMETRIC FEM-BEM COUPLING 116
3 MAIN RESULT 118
4 EXPLICIT BOUNDS FOR THE CONSTANTS CO,; 119
4.1 EXPLICIT BOUNDS FOR POINCARE CONSTANTS 120
4.2 AN EXTENSION OPERATOR FOR POLY TOPES 120
4.3 EXPLICIT BOUNDS FOR BOUNDARY INTEGRAL OPERATORS 123
5 ERROR ANALYSIS 124
5.1 A LEMMA A LA STRANG 125
5.2 ERROR ESTIMATE FOR THE DIRICHLET DATA 126
5.3 ERROR ESTIMATE FOR THE NEUMANN DATA 127
5.4 PROOF O F THEOREM 1 129
6 CONCLUSION AND EXTENSIONS 129
REFERENCES 130
A REVIEW O F ANISOTROPIC REFINEMENT METHODS FOR TRIANGULAR MESHES IN FEM
133
RENE SCHNEIDER 1 INTRODUCTION 133
2 BACKGROUND 134
3 REFINEMENT CRITERIA 139
3.1 INTERPOLATION ERROR ESTIMATES 140
3.2 POST-PROCESSING AND RECOVERY TECHNIQUES 140
3.3 RESIDUAL ESTIMATES 141
3.4 LOCAL PROBLEM ESTIMATES 142
3.5 HIERARCHICAL ESTIMATES 142
3.6 DUAL WEIGHTED RESIDUAL (DWR) ESTIMATES 142
4 REFINEMENT STRATEGIES 143
4.1 NODE RELOCATION 143
4.2 ANISOTROPIC RE-MESHING 145
4.3 SPLITTING OF ELEMENTS 145
4.4 SUMMARY OF PROPERTIES OF THE THREE REFINEMENT STRATEGIES 148
5 CONCLUSIONS 149
REFERENCES 150
A POSTPROCESSING FINITE ELEMENT STRATEGY FOR POISSON S EQUATION IN
POLYGONAL DOMAINS: COMPUTING THE STRESS INTENSITY FACTORS 153
BONIFACE NKEMZI AND MICHAEL JUNG 1 INTRODUCTION 153
2 ANALYTICAL PRELIMINARIES 155
2.1 THE MODEL BOUNDARY VALUE PROBLEM AND NOTATIONS 155
2.2 SINGULAR DECOMPOSITION O F SOLUTION 157
3 THE FINITE ELEMENT APPROXIMATION 159
IMAGE 4
XII CONTENTS
3.1 APPROXIMATION ON QUASI UNIFORM MESH 160
3.2 IMPROVING THE ACCURACY O F THE APPROXIMATION 161
4 NUMERICAL EXPERIMENTS 163
4.1 EXAMPLE 1 163
4.2 EXAMPLE 2 167
5 CONCLUSIONS 171
REFERENCES 172
MULTILEVEL PRECONDITIONERS FOR TEMPORAL-DIFFERENCE LEARNING METHODS
RELATED TO RECOMMENDATION ENGINES 175
MICHAEL THESS 1 INTRODUCTION 175
2 REINFORCEMENT LEARNING AND RECOMMENDATION ENGINES 176
2.1 REINFORCEMENT LEARNING 176
2.2 SOLUTION OF THE BELLMAN EQUATION 179
2.3 TEMPORAL-DIFFERENCE LEARNING 181
2.4 APPLICATION TO RECOMMENDATION ENGINES 182
3 A MULTILEVEL PRECONDITIONER FOR THE T D METHOD 185
4 EVALUATION ON REAL-LIFE DATA 192
5 SUMMARY 194
REFERENCES 194
EFFICIENT SOLVERS FOR SADDLE POINT PROBLEMS WITH APPLICATIONS TO
PDE-CONSTRAINED OPTIMIZATION 197
WALTER ZULEHNER 1 INTRODUCTION 197
2 THE GENERAL FRAMEWORK 199
3 PRECONDITIONERS BASED ON SCHUR COMPLEMENTS AND INTERPOLATION THEORY
201
4 PRECONDITIONERS BASED ON INEXACT SCHUR COMPLEMENTS 205
5 APPLICATION TO OPTIMAL CONTROL PROBLEMS 206
5.1 DISTRIBUTED OPTIMAL CONTROL FOR ELLIPTIC EQUATIONS 207
5.2 THE VELOCITY TRACKING PROBLEM FOR STOKES FLOW 209
6 NUMERICAL EXPERIMENTS 212
REFERENCES 214
CONVERGENCE ORDERS O F ITERATIVE METHODS FOR NONLINEAR EIGENVALUE
PROBLEMS 217
GERHARD UNGER 1 INTRODUCTION 217
2 BASICS O F HOLOMORPHIC EIGENVALUE PROBLEMS 219
3 NONLINEAR GENERALIZED RAYLEIGH QUOTIENT ITERATION 222
4 AUGMENTED NEWTON METHOD 226
4.1 NONLINEAR RAYLEIGH QUOTIENTS AND FUNCTIONALS 230
4.2 SIMPLIFIED NEWTON METHOD 232
5 EXAMPLES 232
IMAGE 5
CONTENTS XIII
6 CONCLUSIONS 235
REFERENCES 236
SENSITIVITY ANALYSIS FOR MAXWELL EIGENVALUE PROBLEMS IN INDUSTRIAL
APPLICATIONS 239
STEFAN REITZINGER, MARKUS WABRO, AND SABINE ZAGLMAYR 1 INTRODUCTION 239
2 PROBLEM FORMULATION, DISCRETIZATION AND SOLUTION STRATEGY 241
2.1 PROBLEM FORMULATION 241
2.2 DISCRETIZATION 243
2.3 ALGEBRAIC EIGENVALUE COMPUTATION 246
3 SENSITIVITY ANALYSIS 248
4 NUMERICAL RESULTS : 250
5 SUMMARY AND OUTLOOK 254
REFERENCES 254
NON-SEQUENTIAL OPTICAL FIELD TRACING 257
MICHAEL KUHN, FRANK WYROWSKI, AND CHRISTIAN HELLMANN 1 INTRODUCTION 257
2 THE TEARING AND INTERCONNECTING METHOD 259
3 THE LIGHT PATH TREE 262
4 FIELD TRACING METHODS 266
5 NUMERICAL EXAMPLES 269
6 CONCLUSIONS 272
REFERENCES 273
BOUNDARY ELEMENT METHOD FOR LINEAR ELASTICITY WITH CONSERVATIVE BODY
FORCES 275
HEIKO ANDRA, RICHARDS GRZHIBOVSKIS, AND SERGEJ RJASANOW 1 INTRODUCTION
275
2 SHORT REVIEW OF TECHNIQUES FOR TREATING VOLUME INTEGRALS IN BEM 276
3 DESCRIPTION O F THE PROBLEM 278
3.1 EXAMPLES O F THE BODY FORCES 279
3.2 BOUNDARY INTEGRAL FORMULATION 282
3.3 PARTICULAR SOLUTION 282
4 BOUNDARY ELEMENT METHOD 283
4.1 GALERKIN PROCEDURE 283
4.2 ADAPTIVE CROSS APPROXIMATION 284
5 EXACT SOLUTION FOR THE POLYNOMIAL BODY FORCES 285
6 APPROXIMATION OF THE BODY FORCE 286
6.1 RADIAL BASIS FUNCTIONS 287
6.2 EXACT SOLUTIONS 289
7 NUMERICAL EXAMPLES 290
8 CONCLUSIONS 295
REFERENCES 295
IMAGE 6
X I V
CONTENTS
TOWARDS THE DIRECT AND INVERSE ADAPTIVE MIXED FINITE ELEMENT
FORMULATIONS FOR NEARLY INCOMPRESSIBLE ELASTICITY AT LARGE STRAINS 299
ANKE BUCHER, UWE-JENS GORKE, AND REINER KREIBIG 1 INTRODUCTION 300
2 NEARLY INCOMPRESSIBLE ELASTICITY AT LARGE STRAINS 302
2.1 KINEMATICS 302
2.2 THERMODYNAMICALLY CONSISTENT CONSTITUTIVE EQUATION . . . 304 3
PARAMETER IDENTIFICATION AS OPTIMIZATION PROBLEM 305
3.1 OBJECTIVE FUNCTION 305
3.2 OPTIMIZATION PROCEDURE 307
4 WEAK FORMULATION OF THE COUPLED BOUNDARY VALUE PROBLEM OF NEARLY
INCOMPRESSIBLE ELASTICITY AT LARGE STRAINS 307
4.1 LINEARIZATION OF THE WEAK FORMULATION - DIRECT PROBLEM 308
4.2 PARAMETER DERIVATIVES O F THE WEAK FORMULATION - INVERSE PROBLEM 310
5 ADAPTIVE FINITE ELEMENT REALIZATION 311
5.1 STABLE ELEMENT FORMULATIONS 311
5.2. ERROR CONTROLLED MESH ADAPTATION 312
6 NUMERICAL EXAMPLES 313
6.1 ADAPTIVE NUMERICAL SOLUTION O F COOK S MEMBRANE PROBLEM 314
6.2 PARAMETER IDENTIFICATION FOR COOK S MEMBRANE PROBLEM 317
7 CONCLUSIONS 319
REFERENCES 321
APPLICATION O F THE RECIPROCITY PRINCIPLE FOR THE DETERMINATION O F
PLANAR CRACKS IN PIEZOELECTRIC MATERIAL 325
PETER STEINHORST AND BARBARA KALTENBACHER 1 INTRODUCTION 325
2 MATHEMATICAL FORMULATION 326
2.1 THE FORWARD PROBLEM 326
2.2 THE INVERSE PROBLEM 331
2.3 RECIPROCITY PRINCIPLE AND RECIPROCITY GAP 332
3 IDENTIFICATION O F THE CRACK NORMAL 334
3.1 METHODS O F IDENTIFICATION 334
3.2 STABILITY 336
4 DETERMINATION O F THE CRACK PLANE OR -LINE 17 339
4.1 VARIANTS FOR DETERMINING THE PLANE OFFSET 340
5 APPROXIMATIVE MID POINT DETERMINATION O F A SINGLE CRACK 342
6 NUMERICAL 2D-EXAMPLES 343
6.1 SETUP O F EXAMPLES 343
IMAGE 7
CONTENTS
X V
6.2 FE-MESHES AND REFINEMENT STRATEGIES IN THE FORWARD COMPUTATION 344
6.3 RESULTS WITH UNIFORM REFINEMENT 346
6.4 COMPARISON O F RESULTS WITH DIFFERENT REFINEMENT STRATEGIES 351
REFERENCES 352
P R O C R A C K : A SOFTWARE FOR SIMULATING THREE-DIMENSIONAL FATIGUE
CRACK GROWTH 355
FRANK RABOLD, MEINHARD KUNA, AND THOMAS LEIBELT 1 INTRODUCTION 355
2 FRACTURE-MECHANICAL FUNDAMENTALS 356
2.1 FATIGUE CRACK GROWTH 356
2.2 CALCULATION O F STRESS INTENSITY FACTORS 359
2.3 DETERMINATION O F CRACK DEFLECTION 361
2.4 DETERMINATION O F CRACK GROWTH INCREMENTS 362
3 T H E SIMULATION SOFTWARE P R O C R A C K 3 6 4
3.1 PROGRAM LAYOUT 364
3.2 PROCEDURE OF CRACK GENERATION 366
3.3 SUBMODEL TECHNIQUE 367
3.4 ADAPTATION OF THE CRACK DISCRETIZATION 368
4 APPLICATION EXAMPLES 369
4.1 CRACK GROWTH IN A THREE-POINT BENDING SPECIMEN 370
4.2 CRACK GROWTH IN A STEERING KNUCKLE 370
5 CONCLUSIONS 373
REFERENCES 373
|
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discipline | Maschinenbau / Maschinenwesen Mathematik |
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genre_facet | Aufsatzsammlung |
id | DE-604.BV041063347 |
illustrated | Illustrated |
indexdate | 2024-12-20T16:29:58Z |
institution | BVB |
isbn | 9783642303159 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026040426 |
oclc_num | 812569635 |
open_access_boolean | |
owner | DE-29T DE-83 |
owner_facet | DE-29T DE-83 |
physical | XV, 374 S. Ill., graph. Darst. 235 mm x 155 mm |
publishDate | 2013 |
publishDateSearch | 2013 |
publishDateSort | 2013 |
publisher | Springer |
record_format | marc |
series | Lecture notes in applied and computational mechanics |
series2 | Lecture notes in applied and computational mechanics |
spellingShingle | Advanced finite element methods and applications Lecture notes in applied and computational mechanics Finite-Integrations-Methode (DE-588)4639468-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
subject_GND | (DE-588)4639468-0 (DE-588)4017233-8 (DE-588)4143413-4 |
title | Advanced finite element methods and applications |
title_auth | Advanced finite element methods and applications |
title_exact_search | Advanced finite element methods and applications |
title_full | Advanced finite element methods and applications Thomas Apel ... (ed.) |
title_fullStr | Advanced finite element methods and applications Thomas Apel ... (ed.) |
title_full_unstemmed | Advanced finite element methods and applications Thomas Apel ... (ed.) |
title_short | Advanced finite element methods and applications |
title_sort | advanced finite element methods and applications |
topic | Finite-Integrations-Methode (DE-588)4639468-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
topic_facet | Finite-Integrations-Methode Finite-Elemente-Methode Aufsatzsammlung |
url | http://deposit.dnb.de/cgi-bin/dokserv?id=4012617&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=026040426&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV017110729 |
work_keys_str_mv | AT apelthomas advancedfiniteelementmethodsandapplications |