Galerkin methods for simulation of wave propagation on a network of pipes: Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Verlag Dr. Hut
2019
|
| Ausgabe: | 1. Auflage |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.dr.hut-verlag.de/978-3-8439-4184-6.html Inhaltsverzeichnis |
| Beschreibung: | vi, 141 Seiten Diagramme 21 cm x 14.8 cm, 236 g |
| ISBN: | 9783843941846 384394184X |
Internformat
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| 100 | 1 | |a Kugler, Thomas |d 1991- |0 (DE-588)1200356640 |4 aut | |
| 245 | 1 | 0 | |a Galerkin methods for simulation of wave propagation on a network of pipes |b Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |c Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Thomas Kugler aus Wiesbaden |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a München |b Verlag Dr. Hut |c 2019 | |
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| 502 | |b Dissertation |c Technische Universität Darmstadt |d 2019 | ||
| 653 | |a Galerkin methods | ||
| 653 | |a wave propagation | ||
| 653 | |a model reduction | ||
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Datensatz im Suchindex
| _version_ | 1804180766098194432 |
|---|---|
| adam_text | Galerkin methods for simulation of
wave propagation on a network of
pipes
Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken
Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr rer nat )
genehmigte Dissertation von Thomas Kugler aus Wiesbaden
September 12, 2019 — Darmstadt — D 17
jr~ ——-T3-
TECHNISCHE
UNIVERSITÄT
DARMSTADT
Fachbereich Mathematik
AG Numerik und
witienKhsftlichet Rechnen
Contents
1 Introduction 1
2 The continuous level 5
2 1 Preliminaries and notation 5
211 Network description 5
212 Function spaces 7
2 2 The stationary problem 9
221 Equivalence to weak formulation 10
222 Proof ofTheorem 2 18 14
2 3 The instationary problem 19
231 Reformulation of the instationary problem 20
232 Well-posedness of the instationary problem 21
2 4 Exponential decay to steady states 28
241 Decay of the energies £° and E1 28
242 Controlling the derivative d 29
243 Exponential decay of £° and E1 30
2 5 Comments on the special case of linear damping 33
3 Discretization in space 35
3 1 Galerkin discretization 35
311 The discrete stationary problem 35
312 The semi-discrete instationary problem 38
3 2 Exponential decay to steady states 41
321 Decay of the energies E® and E^ 41
322 Controlling the derivative d 42
323 Exponential decay of e£ and E^1 43
3 3 Abstract error estimates 45
331 Estimates for stationary problems 45
332 Estimates for instationary problem 49
3 4 Mixed finite element method 53
341 Approximation spaces and interpolation operators 53
342 Convergence rates 54
3 5 Comments on the special case of linear damping 55
4 Full discretization 57
4 1 Preliminaries and notation 58
4 2 Fully-discrete instationary problem 58
421 Existence of a unique solution 59
422 A-priori estimates 61
4 3 Exponential decay to steady states 65
431 Decay of the discrete energies E°’n and E^,n 66
432 Controlling the discrete representative of d 67
433 Exponential decay of £° and 67
4 4 Approximation error estimates 72
441 Error estimates for 6=1 72
442 Convergence rates 77
4 5 Comments on the special case of linear damping 78
v
4 6 Numerical validation 80
461 Implementations! aspects 80
462 Convergence rates in space and time 81
463 Exponential convergence to steady states 82
464 Non-uniform exponential convergence of the implicit midpoint rule 83
5 Structure preserving model order reduction 85
5 1 Preliminaries and basic strategy 86
511 Structural properties in the continuous case 87
512 Structure preserving Galerkin approximation 88
513 Algebraic representation 90
5 2 Basis construction and numerical realization 91
521 Basic model reduction: Moment matching 91
522 Basic model reduction: POD 93
523 Basis splitting 94
524 Basis modification 95
5 3 Numerical illustration 96
531 Modified moment matching on a single pipe with linear damping 97
532 Modified POD on a network of pipes with nonlinear damping 101
5 4 Summary and discussion 104
6 An optimal control problem of instationary gas transport on a network of pipes 107
6 1 The infinite dimensional problem 107
611 Motivation and model scenario 107
612 State equations 108
613 Existence of a unique state 116
614 Optimal control problem 116
6 2 Discretization 119
621 Semi-discretization of the state equations in space 119
622 Full-discretization of the state equations 120
623 Discrete optimal control problem 122
6 3 Realization of minimization procedure 124
631 Gauss-Newton approximation of objective function 124
632 Minimization of the Gauss-Newton approximation 125
6 4 Numerical example 128
641 Scenario 128
642 Method and parameters 128
643 Illustration of numerical results 129
7 Summary 131
8 Outlook 133
|
| any_adam_object | 1 |
| author | Kugler, Thomas 1991- |
| author_GND | (DE-588)1200356640 |
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| author_role | aut |
| author_sort | Kugler, Thomas 1991- |
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| building | Verbundindex |
| bvnumber | BV046298437 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)1128800828 (DE-599)DNB1200291476 |
| discipline | Mathematik |
| edition | 1. Auflage |
| format | Thesis Book |
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| spelling | Kugler, Thomas 1991- (DE-588)1200356640 aut Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Thomas Kugler aus Wiesbaden 1. Auflage München Verlag Dr. Hut 2019 vi, 141 Seiten Diagramme 21 cm x 14.8 cm, 236 g txt rdacontent n rdamedia nc rdacarrier Dissertation Technische Universität Darmstadt 2019 Galerkin methods wave propagation model reduction (DE-588)4113937-9 Hochschulschrift gnd-content Verlag Dr. Hut (München) (DE-588)10174118-2 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=40f961f95ec548c485f8e13be7d1a6e8&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.dr.hut-verlag.de/978-3-8439-4184-6.html HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031675808&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kugler, Thomas 1991- Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |
| subject_GND | (DE-588)4113937-9 |
| title | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |
| title_auth | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |
| title_exact_search | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |
| title_full | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Thomas Kugler aus Wiesbaden |
| title_fullStr | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Thomas Kugler aus Wiesbaden |
| title_full_unstemmed | Galerkin methods for simulation of wave propagation on a network of pipes Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Thomas Kugler aus Wiesbaden |
| title_short | Galerkin methods for simulation of wave propagation on a network of pipes |
| title_sort | galerkin methods for simulation of wave propagation on a network of pipes galerkin methoden zur simulation von wellenausbreitung auf rohrnetzwerken |
| title_sub | Galerkin Methoden zur Simulation von Wellenausbreitung auf Rohrnetzwerken |
| topic_facet | Hochschulschrift |
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