Adaptive multilevel methods for PDAE-constrained optimal control problems:
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| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Verl. Dr. Hut
2013
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 189 S. Ill., graph. Darst. |
| ISBN: | 9783843908788 |
Internformat
MARC
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| 100 | 1 | |a Clever, Debora |d 1980- |e Verfasser |0 (DE-588)1033534072 |4 aut | |
| 245 | 1 | 0 | |a Adaptive multilevel methods for PDAE-constrained optimal control problems |c Debora Clever |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a München |b Verl. Dr. Hut |c 2013 | |
| 300 | |a XXVIII, 189 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematik | |
| 502 | |a Zugl.: Darmstadt, Techn. Univ., Diss. | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025969375&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804150314706665472 |
|---|---|
| adam_text | Adaptive Multilevel Methods for PDAE-Constrained
Optimal Control Problems
Vom Fachbereich Mathematik
der Technischen Universität Darmstadt
zur Erlangung des Grades eines Doktors der Naturwissenschaften
(Dr -rer nat )
genehmigte Dissertation
von
Dipl -Math Debora Clever, B Sc
aus Darmstadt
Referent: Prof Dr Jens Lang
Korreferenten: Prof Dr Stefan Ulbrich
Prof Dr Andrea Walther
Tag der Einreichung: 12 Oktober 2012
Tag der mündlichen Prüfung: 21 Januar 2013
Darmstadt 2013
D 17
xiii
Contents
1 Introduction 1
1 The All-In-One Optimization Environment 5
2 Optimal Control Theory for PDAEs 7
2 1 Introduction to DAEs and PDAEs 8
211 Classification Based of Different Concepts of Indices 8
212 Linear Implicit Runge-Kutta Methods of Rosenbrock type for PDAEs 11
213 Consistent Initial Conditions for DAEs and PDAEs 16
2 2 Introduction to Optimal Control Theory 17
2 3 Discretized Adjoint versus Adjoint Discretization 20
2 4 Notation 22
3 Optimization Methods 23
3 1 Reduced Optimal Control Problem 24
311 Reduced Gradient 25
312 Reduced Hessian 26
3 2 Gradient Method with Armijo Rule 28
3 3 Newton-Type Methods 31
331 Unidirectional Trust Region Method 34
332 Quasi-Newton Trust Region Method with BFGS Update 35
333 Newton-Iterative Trust Region Method 37
3 4 Control Constraints 42
341 Projected Gradient and Unidirectional Trust Region Methods 42
342 Projected Quasi-Newton and Newton-Iterative Trust Region Methods 43
3 5 Multilevel Strategy 48
4 Combination of Optimization Tools with the PDAE Solver KARDOS 53
4 1 KARDOS 53
411 Time Discretization: Adaptive Rosenbrock Methods 55
412 Space Discretization: Multilevel Stabilized Finite Elements 56
4 2 From Local to Global Error Estimates 59
4 3 The Coupling 61
xiv
Contents
431 Data Exchange and Grid Management within a KARDOS Based Envi-
ronment 63
432 Realization of a Multilevel Strategy within a KARDOS Based Environ-
ment 65
4 4 Multilevel Newton-Iterative Method for Control Constrained Problems 66
II Application to Radiative Heat Transfer 69
5 Optimal Boundary Control for Glass Cooling 71
5 1 Glass Cooling 71
511 The Objective 71
512 The Glass Cooling Model 72
513 Model Simplification 75
5 2 Theoretical Background 78
521 Index Analysis 81
522 Reduced Problem and Optimality System 82
5 3 The Choice of Models 89
6 Practical Issues 95
6 1 Verification of the Reduced Derivatives 95
611 Verification Tools for the Reduced Gradient 96
612 Verification Tools for Actings of the Reduced Hessian 98
613 Symmetry Verification of the Reduced Hessian 99
614 Derivative Transformation with Gauss 101
6 2 Implementational Aspects 102
621 Implementation of Second-Order Space Derivatives 103
622 Hj regularization for control 106
623 Consistent Initial Values 107
7 Numerical Experiments 111
7 1 Experiments Concerning the Algorithm Ill
711 Selection of Rosenbrock Methods 112
712 Adaptivity 113
713 Second Order Information 117
714 Multilevel Strategy 122
7 2 Experiments Concerning the Glass Cooling Problem 126
721 Basic Objective 128
Contents
xv
722 Control Constraints 134
723 Mean Internal Stresses 136
724 Extension of Cooling Time 143
725 Time Dependent Weights 147
7 3 Prolongation to Three Spatial Dimensions 150
731 Case 1: Computations on 153
732 Case 2: Computations on 158
733 Comparison of 3d Results to Computations on 161
8 Conclusions 167
8 1 Main Contributions 167
8 2 Main Conclusions 168
8 3 Future Research 168
A Appendix 171
Bibliography
|
| any_adam_object | 1 |
| author | Clever, Debora 1980- |
| author_GND | (DE-588)1033534072 |
| author_facet | Clever, Debora 1980- |
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| bvnumber | BV040991574 |
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| ctrlnum | (OCoLC)844104627 (DE-599)BVBBV040991574 |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:36:58Z |
| institution | BVB |
| isbn | 9783843908788 |
| language | English |
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| series2 | Mathematik |
| spelling | Clever, Debora 1980- Verfasser (DE-588)1033534072 aut Adaptive multilevel methods for PDAE-constrained optimal control problems Debora Clever 1. Aufl. München Verl. Dr. Hut 2013 XXVIII, 189 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: Darmstadt, Techn. Univ., Diss. (DE-588)4113937-9 Hochschulschrift gnd-content HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025969375&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clever, Debora 1980- Adaptive multilevel methods for PDAE-constrained optimal control problems |
| subject_GND | (DE-588)4113937-9 |
| title | Adaptive multilevel methods for PDAE-constrained optimal control problems |
| title_auth | Adaptive multilevel methods for PDAE-constrained optimal control problems |
| title_exact_search | Adaptive multilevel methods for PDAE-constrained optimal control problems |
| title_full | Adaptive multilevel methods for PDAE-constrained optimal control problems Debora Clever |
| title_fullStr | Adaptive multilevel methods for PDAE-constrained optimal control problems Debora Clever |
| title_full_unstemmed | Adaptive multilevel methods for PDAE-constrained optimal control problems Debora Clever |
| title_short | Adaptive multilevel methods for PDAE-constrained optimal control problems |
| title_sort | adaptive multilevel methods for pdae constrained optimal control problems |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025969375&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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