Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2015
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| Series: | Berichte aus der Mathematik
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | 200 S. Ill., graph. Darst. 21 cm, 300 g |
| ISBN: | 9783844037005 |
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MARC
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| 245 | 1 | 0 | |a Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |c Markus Dihlmann |
| 264 | 1 | |a Aachen |b Shaker |c 2015 | |
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| 490 | 0 | |a Berichte aus der Mathematik | |
| 502 | |a Zugl.: Stuttgart, Univ., Diss., 2014 | ||
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| 653 | |a Reduced Basis Method | ||
| 653 | |a model reduction | ||
| 653 | |a data assimilation | ||
| 653 | |a partial differential equation | ||
| 653 | |a error estimation | ||
| 653 | |a Kalman filter | ||
| 653 | |a state estimation | ||
| 653 | |a pde-constrained optimization | ||
| 653 | |a adaptive | ||
| 653 | |a parameterized | ||
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Record in the Search Index
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| adam_text |
CONTENTS
ZUSAMMENFASSUNG / ABSTRACT 5
1 INTRODUCTION 13
1 ADAPTIVE REDUCED BASIS METHODS FOR EVOLUTION PROBLEMS 23
2 INTRODUCTION TO THE REDUCED BASIS METHOD FOR EVOLUTION PROBLEMS 25
'2.1 GENERAL PROBLEM SETTING 25
2.2 REDUCED BASIS APPROXIMATION 27
2.3 ERROR ESTIMATION 28
2.4 BASIS GENERATION 29
2.4.1 ADAPTIVE TRAINING SET EXTENSION 31
2.5 OFFLINE-/ONLINE-DECOMPOSITION 32
2.6 EXAMPLE PROBLEM 33
3 BASIS GENERATION WITH PARAMETER DOMAIN PARTITIONING 37
3.1 INTRODUCTION 37
3.2 ADAPTIVE PARAMETER DOMAIN PARTITIONING 38
3.3 NUMERICAL EXPERIMENTS 41
3.4 CONCLUSION 45
4 BASIS GENERATION WITH TIME DOMAIN PARTITIONING 47
4.1 INTRODUCTION 47
4.2 TIME DOMAIN PARTITIONING 48
4.2.1 OFFLINE-PHASE 49
4.2.2 ONLINE-PHASE 50
4.2.3 ERROR ANALYSIS 50
4.3 ADAPTIVE TIME DOMAIN PARTITIONING 51
4.4 NUMERICAL EXPERIMENTS 52
4.5 CONCLUSION 56
9
HTTP://D-NB.INFO/1071470647
10
CONTENTS
5 ONLINE REDUCED BASIS ASSEMBLING 57
5.1 INTRODUCTION 57
5.2 RAPID ONLINE CONSTRUCTION OF A REDUCED SPACE 58
5.2.1 OFFLINE-PHASE: CONSTRUCTION OF THE DICTIONARY -58
5.2.2 ONLINE-PHASE 1: ONLINE CONSTRUCTION ALGORITHMS FOR THE LOCALIZED
REDUCED SPACE 59
5.2.3 ONLINE-PHASE 2: PERFORMING ONLINE SIMULATIONS 62
5.3 NUMERICAL EXPERIMENTS 63
5.4 CONCLUSION 65
II APPLICATION OF THE REDUCED BASIS METHOD TO PARAMETER
OPTIMIZATION AND STATE ESTIMATION 67
6 CERTIFIED PARAMETER OPTIMIZATION USING REDUCED BASIS MODELS 69
6.1 INTRODUCTION 69
6.2 REDUCED BASIS SURROGATE MODELS FOR PARAMETER OPTIMIZATION 71
6.3 ERROR ESTIMATOR FOR PARAMETER SUBOPTIMALITY 73
6.4 REDUCED BASIS OPTIMIZATION OF AN INSTATIONARY LINEAR PROBLEM 78
6.4.1 PROBLEM SETTING 79
6.4.2 EVOLUTION SCHEMES FOR SENSITIVITY DERIVATIVES 80
6.4.3 ERROR ANALYSIS 83
6.4.4 NUMERICAL EXPERIMENTS 91
6.5 REDUCED BASIS OPTIMIZATION OF A STATIONARY-QUADRATIC PROBLEM 99
6.5.1 PROBLEM SETTING 100
6.5.2 SENSITIVITY DERIVATIVES 101
6.5.3 ERROR ANALYSIS 101
6.5.4 NUMERICAL EXPERIMENTS 103
6.6 CONCLUSION 106
7 A REDUCED BASIS KALMAN FILTER 109
7.1 INTRODUCTION 109
7.2 PROBLEM SETTING 112
7.2.1 THE STOCHASTICALLY FORCED PARAMETERIZED PARABOLIC PDE 114
7.2.2 THE OPTIMAL FILTER IN WEAK FORMULATION 116
7.3 REDUCED BASIS KALMAN FILTER 119
7.3.1 BASIS GENERATION WITH THE NOISE-POD-GREEDY 121
7.3.2 COMPUTATIONAL PROCEDURE AND OFFLINE-/ONLINE-DECOMPOSITION . . .
123
7.4 ERROR ESTIMATION 124
7.4.1 PRELIMINARIES 125
CONTENTS
11
7.4.2 ERROR DECOMPOSITION 127
7.4.3 ERROR ESTIMATION FOR A NOISY REDUCED BASIS MODEL (COMPONENT
EJ)130
7.4.4 ERROR BOUNDS FOR THE DEVIATION (COMPONENTS E
2
. EJJ
3
. EJ
4
) . 135
7.4.5 COMPLETE RBKF OUTPUT ERROR ESTIMATION 141
7.4.6 LINK BETWEEN OBSERVABILITY AND STABILITY OF THE RBKF 143
7.5 NUMERICAL EXPERIMENTS 144
7.5.1 EXPERIMENT CONSIDERING THE BASIS GENERATION 150
7.6 CONCLUSION 151
CONCLUSION AND OUTLOOK 153
A LEMMAS AND QUANTITIES FOR CHAPTER 6 157
A.L LEMMAS 157
A.2 MATRICES FOR THE ERROR ESTIMATOR OF D
PI
UJ\ IN THE INSTATIONARY OPTIMIZATION 159
B PROOFS FOR THE REDUCED BASIS KALMAN FILTER 161
B.L PROOF OF COROLLARY 7.2.1 161
B.2 PROOF OF COROLLARY 7.2.3 162
B.3 PROOF OF LEMMA 7.2.4 163
B.4 PROOF OF PROPOSITION 7.2.6 166
B.5 LEMMA USED IN PROOF OF LEMMA 7.4.1 170
B.6 PROOF OF LEMMA 7.4.7 171
B.7 PROOF OF PROPOSITION 7.4.8 173
B.8 PROOF OF LEMMA 7.4.12 175
B.9 PROOF OF PROPOSITION 7.4.14 177
LIST OF FIGURES 184
LIST OF TABLES 186
LIST OF ALGORITHMS 187
BIBLIOGRAPHY 189 |
| any_adam_object | 1 |
| author | Dihlmann, Markus |
| author_GND | (DE-588)1072851091 |
| author_facet | Dihlmann, Markus |
| author_role | aut |
| author_sort | Dihlmann, Markus |
| author_variant | m d md |
| building | Verbundindex |
| bvnumber | BV042943618 |
| ctrlnum | (OCoLC)910333011 (DE-599)DNB1071470647 |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-09-10T01:54:54Z |
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| institution_GND | (DE-588)1064118135 |
| isbn | 9783844037005 |
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| physical | 200 S. Ill., graph. Darst. 21 cm, 300 g |
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| spelling | Dihlmann, Markus Verfasser (DE-588)1072851091 aut Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation Markus Dihlmann Aachen Shaker 2015 200 S. Ill., graph. Darst. 21 cm, 300 g txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Zugl.: Stuttgart, Univ., Diss., 2014 Ordnungsreduktion (DE-588)4136085-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Reduced Basis Method model reduction data assimilation partial differential equation error estimation Kalman filter state estimation pde-constrained optimization adaptive parameterized (DE-588)4113937-9 Hochschulschrift gnd-content Evolutionsgleichung (DE-588)4129061-6 s Ordnungsreduktion (DE-588)4136085-0 s DE-604 Shaker Verlag (DE-588)1064118135 pbl Erscheint auch als Online-Ausgabe Dihlmann, Markus Adaptive Reduced Basis Methods for Parameterized Evolution Problems with Application in Optimization and State Estimation X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5275873&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=028370008&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dihlmann, Markus Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation Ordnungsreduktion (DE-588)4136085-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4136085-0 (DE-588)4129061-6 (DE-588)4113937-9 |
| title | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |
| title_auth | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |
| title_exact_search | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |
| title_full | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation Markus Dihlmann |
| title_fullStr | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation Markus Dihlmann |
| title_full_unstemmed | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation Markus Dihlmann |
| title_short | Adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |
| title_sort | adaptive reduced basis methods for parameterized evolution problems with application in optimization and state estimation |
| topic | Ordnungsreduktion (DE-588)4136085-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Ordnungsreduktion Evolutionsgleichung Hochschulschrift |
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