Adaptive hierarchical isogeometric finite element methods
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| Sprache: | English |
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Wiesbaden
Vieweg & Teubner
2012
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| Schriftenreihe: | Springer Spektrum Research
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| 245 | 1 | 0 | |a Adaptive hierarchical isogeometric finite element methods |c Anh-Vu Vuong |
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Datensatz im Suchindex
| _version_ | 1819589314371125248 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE V
ACKNOWLEDGMENT VII
LIST O F FIGURES XIII
LIST O F TABLES XVII
LIST O F ALGORITHMS XIX
1 INTRODUCTION 1
2 PREREQUISITES FROM APPLIED GEOMETRY A N D SPLINE THEORY 7
2.1 PARAMETRIC CURVES. SURFACES A N D VOLUMES 8
2.2 SPLINE FUNCTIONS 9
2.2.1 POLYNOMIAL SPACES 9
2.2.2 SPLINE SPACES 10
2.2.3 B-SPLINES 10
2.2.4 NON-UNIFORM RATIONAL B-SPLINES 13
2.3 MULTIVARIATE TENSOR-PRODUCT SPLINES 15
2.4 ALGORITHMIC ASPECTS 16
2.4.1 EVALUATIONS 16
2.4.2 REFINEMENT 17
3 MATHEMATICAL MODELS A N D FINITE ELEMENT ANALYSIS 19
3.1 MATHEMATICAL MODELS 20
3.1.1 HEAT A N D POTENTIAL FLOW 20
3.1.2 CONTINUUM MECHANICS 20
3.2 VARIATIONAL FORMULATION 24
3.2.1 A B S T R A C T SETTING 24
3.2.2 APPLICATION T O MODELS 25
3.3 FINITE ELEMENT FOUNDATIONS 27
3.3.1 GALERKIN PROJECTION 27
3.3.2 FINITE ELEMENT FUNCTION SPACES 28
3.3.3 REFERENCE ELEMENTS 30
3.3.4 CONVERGENCE ANALYSIS 31
3.4 FINITE ELEMENTS IN USE 32
3.4.1 SOME FINITE ELEMENT SPACES 32
3.4.2 ISOPARAMETRIC FINITE ELEMENTS 34
HTTP://D-NB.INFO/1021360031
IMAGE 2
X CONTENTS
3.4.3 MESH REFINEMENT 36
3.4.4 ADAPTIVE FINITE ELEMENTS A N D ERROR ESTIMATION 3 7
3.5 IMPLEMENTATION ISSUES 39
3.5.1 D A T A REPRESENTATION 40
3.5.2 ASSEMBLY OF SYSTEM MATRICES 41
3.5.3 BOUNDARY CONDITIONS 44
3.5.4 POSTPROCESSING 44
4 ISOGEOMETRIC ANALYSIS 4 7
4.1 BASIC IDEA A N D FUNDAMENTALS 4 8
4.2 ISOGEOMETRIC ANALYSIS IN DETAIL 50
4.2.1 B-SPLINES A N D N U R B S AS BASIS FUNCTIONS 50
4.2.2 ISOGEOMETRIC MESH A N D RELATIONSHIP T O FINITE ELEMENT METHODS 51
4.2.3 GEOMETRY MAPPING - T H E RELATION T O C A G D 54
4.2.4 SHARED CONCEPTS BETWEEN T H E COMPONENTS 56
4.3 CONVERGENCE ANALYSIS 57
4.4 ISOGEOMETRIC ELEMENT CONCEPT 59
4.4.1 ISOGEOMETRIC REFERENCE ELEMENT 59
4.4.2 BEZIER EXTRACTION 61
4.5 UNIFORM REFINEMENT 62
4.6 IMPLEMENTATION ISSUES 6 3
4.6.1 D A T A REPRESENTATION 64
4.6.2 ELEMENT STRUCTURE A N D ENUMERATION 64
4.6.3 MATRIX ASSEMBLY 66
4.6.4 BOUNDARY CONDITIONS 68
4.6.5 VISUALIZATION 69
4.7 SIMULATION EXAMPLES 70
4.7.1 HEAT CONDUCTION ON A HALF-DISK 70
4.7.2 HEAT CONDUCTION ON A N L-SHAPE 71
4.7.3 P L A T E WITH A HOLE 72
4.7.4 TURBINE BLADE 74
4.7.5 WHEEL DISK 75
4.8 CONCLUSION A N D APPLICATIONS 77
5 LOCAL REFINEMENT FOR ISOGEOMETRIC ANALYSIS 7 9
5.1 INTRODUCTION T O ADAPTIVE SIMULATION 80
5.1.1 ASPECTS OF REFINEMENT IN ISOGEOMETRIC ANALYSIS 80
5.1.2 ISOGEOMETRIC ANALYSIS REFINEMENT TECHNIQUES 81
5.2 HIERARCHICAL B-SPLINES 84
5.2.1 BASIC DEFINITIONS 84
5.2.2 PROPERTIES OF HIERARCHICAL B-SPLINES 87
5.3 ADAPTIVE HIERARCHICAL ISOGEOMETRIC ANALYSIS 88
5.3.1 HIERARCHICAL STRUCTURES 88
5.3.2 HIERARCHICAL REFINEMENT 9 3
5.3.3 HIERARCHICAL REFERENCE ELEMENT 97
5.3.4 REFINEMENT CRITERIUM A N D A POSTERIORI ERROR ESTIMATION . . . .
99
IMAGE 3
CONTENTS XI
5.4 IMPLEMENTATION ISSUES 100
5.4.1 D A T A STRUCTURES 101
5.4.2 HIERARCHICAL REFINEMENT 101
5.4.3 MATRIX ASSEMBLY 103
5.4.4 TREATMENT OF BOUNDARY CONDITIONS 104
5.4.5 VISUALIZATION 105
5.5 NUMERICAL SIMULATION CASES 105
5.5.1 ADVECTION-DIFFUSION 105
5.5.2 HEAT CONDUCTION OF A HALF-DISK 107
5.5.3 P L A T E WITH HOLE 108
5.5.4 CIRCULAR P L A T E 109
5.5.5 HEAT CONDUCTION ON A N L-SHAPE 110
6 CONCLUSIONS 1 1 5
A SOFTWARE 117
B GEOMETRIC D A T A 119
BIBLIOGRAPHY 1 2 1
|
| any_adam_object | 1 |
| author | Vuong, Anh-Vu |
| author_GND | (DE-588)1022875426 |
| author_facet | Vuong, Anh-Vu |
| author_role | aut |
| author_sort | Vuong, Anh-Vu |
| author_variant | a v v avv |
| building | Verbundindex |
| bvnumber | BV040242074 |
| classification_rvk | SK 910 |
| classification_tum | MAT 674d |
| ctrlnum | (OCoLC)796273733 (DE-599)DNB1021360031 |
| dewey-full | 518.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.25 |
| dewey-search | 518.25 |
| dewey-sort | 3518.25 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-12-24T02:43:18Z |
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| isbn | 9783834824448 3834824445 |
| language | English |
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| physical | XVI, 127 S. Ill., graph. Darst. 210 mm x 148 mm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Vieweg & Teubner |
| record_format | marc |
| series2 | Springer Spektrum Research |
| spellingShingle | Vuong, Anh-Vu Adaptive hierarchical isogeometric finite element methods Finite-Elemente-Methode (DE-588)4017233-8 gnd Rationaler B-Spline (DE-588)4384797-3 gnd Isogeometrische Analyse (DE-588)7718401-4 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4384797-3 (DE-588)7718401-4 (DE-588)4113937-9 |
| title | Adaptive hierarchical isogeometric finite element methods |
| title_auth | Adaptive hierarchical isogeometric finite element methods |
| title_exact_search | Adaptive hierarchical isogeometric finite element methods |
| title_full | Adaptive hierarchical isogeometric finite element methods Anh-Vu Vuong |
| title_fullStr | Adaptive hierarchical isogeometric finite element methods Anh-Vu Vuong |
| title_full_unstemmed | Adaptive hierarchical isogeometric finite element methods Anh-Vu Vuong |
| title_short | Adaptive hierarchical isogeometric finite element methods |
| title_sort | adaptive hierarchical isogeometric finite element methods |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Rationaler B-Spline (DE-588)4384797-3 gnd Isogeometrische Analyse (DE-588)7718401-4 gnd |
| topic_facet | Finite-Elemente-Methode Rationaler B-Spline Isogeometrische Analyse Hochschulschrift |
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| work_keys_str_mv | AT vuonganhvu adaptivehierarchicalisogeometricfiniteelementmethods |