Computational optimization of systems governed by partial differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
SIAM, Soc. for Indust. and Appl. Math.
2012
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| Series: | Computational science & engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 282 S. Ill., graph. Darst. |
| ISBN: | 9781611972047 |
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MARC
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| adam_text | Titel: Computational optimization of systems governed by partial differential equations
Autor: Borzì, Alfio
Jahr: 2012
Contents
List of Figures xi
List of Tables xv
List of Algorithms xvii
Preface xix
1 Introduction 1
2 Optimality Conditions 3
2.1 Introduction................................. 3
2.2 Optimality Conditions........................... 3
2.3 The Formal Lagrangian Approach..................... 17
2.4 Control Constraints............................. 22
3 Discretization of Optimality Systems 27
3.1 Introduction................................. 27
3.2 Discretization of Elliptic Optimization Problems............. 28
3.3 Discretization of Parabolic Optimization Problems............ 34
3.4 Discretization of Optimization Problems with Integral Equations..... 37
4 Single-Grid Optimization 41
4.1 Introduction................................. 41
4.2 Black-Box Methods............................ 41
4.2.1 Steepest Descent and NCG Methods............... 43
4.2.2 Quasi-Newton Methods...................... 45
4.2.3 Krylov-Newton Methods..................... 47
4.2.4 Cascadic Black-Box Schemes................... 48
4.3 Semismooth Newton Methods....................... 49
4.4 Preconditioning............................... 53
4.5 SQP Methods and Variants......................... 59
4.6 Reduced SQP and One-Shot Methods................... 62
5 Multigrid Methods 67
5.1 Introduction................................. 67
Contents
5.2 Multigrid Methods for Linear Problems.................. 67
5.2.1 Iterative Methods and the Smoothing Property.......... 68
5.2.2 Iterative Methods as Minimization Schemes........... 72
5.2.3 The Twogrid Scheme and the Approximation Property...... 74
5.2.4 The Multigrid Scheme ...................... 79
5.2.5 The Algebraic Multigrid Method................. 84
5.3 Multigrid Methods for Nonlinear Problems................ 87
5.3.1 The FAS Multigrid Method.................... 87
5.3.2 The Full Multigrid Method .................... 89
5.4 The Multigrid Optimization Scheme.................... 92
5.4.1 Convergence of the MGOPT Method............... 94
5.4.2 The Construction of the MGOPT Components.......... 97
5.5 Multigrid and Reduced SQP for Parameter Optimization......... 99
5.6 Schur-Complement-Based Multigrid Smoothers ............. 101
5.7 The Collective Smoothing Multigrid Approach.............. 106
5.7.1 CSMG Schemes for Elliptic Control Problems.......... 108
5.7.2 Algebraic Multigrid Methods for Optimality Systems ...... 125
5.7.3 A CSMG Scheme with FEM Discretization............ 133
5.7.4 CSMG Schemes for Parabolic Control Problems......... 142
5.7.5 Projected Collective Smoothing Schemes and the Semismooth
Newton Method.......................... 163
5.7.6 Multigrid Receding-Horizon Approach.............. 167
5.7.7 A CSMG Scheme for Fredholm Control Problems........ 169
5.7.8 Optimization Properties of the CSMG Scheme.......... 174
PDE Optimization with Uncertainty 177
6.1 Introduction................................. 177
6.2 PDE Control Problems with Uncertain Coefficients............ 179
6.2.1 Discretization of the Probabilistic Space............. 182
6.2.2 Sparse-Grid CSMG Methods................... 183
6.2.3 Experiments with a Parabolic Control Problem.......... 184
6.3 Aerodynamic Design under Geometric Uncertainty............ 186
6.3.1 Modeling Geometric Uncertainty................. 186
6.3.2 Semi-infinite Robust Design.................... 187
6.3.3 The Use of a Goal-Oriented KL Basis............... 188
6.3.4 Adaptive Sparse Grids for High-Dimensional Integration..... 188
6.3.5 Numerically Computed Robust Aerodynamic Designs...... 189
6.4 A Proper Orthogonal Decomposition Framework to Determine Robust
Controls................................... 190
6.4.1 POD Analysis of the Control Space................ 193
6.4.2 A Robust Control for Elliptic Control Problems ......... 195
6.5 Optimal Control of Probability Density Functions of Stochastic Processes 196
6.5.1 A Fokker-Planck Optimal Control Formulation.......... 199
6.5.2 An RH-MPC Scheme....................... 200
6.6 Bayesian Uncertainty Quantification.................... 202
6.6.1 Statistical Inverse Problems.................... 203
6.6.2 A Fast Scheme for Large-Scale Linear Inverse Problems..... 204
Contents
6.6.3 An Inverse Parabolic Problem...................207
7 Applications 209
7.1 Introduction.................................209
7.2 Aerodynamic Shape Design Supported by the Shape Calculus......210
7.2.1 Overview on Shape Sensitivity Analysis.............210
7.2.2 The Hadamard Formula......................211
7.2.3 Shape Optimization and the Incompressible Navier-Stokes
Equations .............................212
7.2.4 Shape Hessian Approximation and Operator Symbols......213
7.2.5 Aerodynamic Design Using Shape Calculus...........216
7.3 Quantum Control Problems........................219
7.3.1 Introduction to Quantum Control Problems............219
7.3.2 Finite-Level Quantum Systems..................220
7.3.3 Infinite-Dimensional Quantum Systems..............224
7.4 Electromagnetic Inverse Scattering ....................237
7.4.1 Introduction............................237
7.4.2 The Scattering Problem in the Time Domain...........238
7.4.3 The Maxwell Curl Equations...................242
7.4.4 The FDTD Discretization.....................244
7.4.5 Perfectly Matched Layer......................248
7.4.6 An Inverse Scattering Scenario..................253
Bibliography 255
Index 281
|
| any_adam_object | 1 |
| author | Borzì, Alfio 1965- Schulz, Volker 1965- |
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| dewey-full | 515/.353 |
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| discipline | Mathematik |
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| isbn | 9781611972047 |
| language | English |
| lccn | 2011033263 |
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| spelling | Borzì, Alfio 1965- Verfasser (DE-588)1019221909 aut Computational optimization of systems governed by partial differential equations Alfio Borzì ; Volker Schulz Philadelphia, PA SIAM, Soc. for Indust. and Appl. Math. 2012 XX, 282 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational science & engineering Mathematical optimization Differential equations, Partial Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Partielle Differentialgleichung (DE-588)4044779-0 s Wissenschaftliches Rechnen (DE-588)4338507-2 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Schulz, Volker 1965- Verfasser (DE-588)139783938 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024675924&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borzì, Alfio 1965- Schulz, Volker 1965- Computational optimization of systems governed by partial differential equations Mathematical optimization Differential equations, Partial Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4338507-2 (DE-588)4043664-0 (DE-588)4128130-5 (DE-588)4044779-0 |
| title | Computational optimization of systems governed by partial differential equations |
| title_auth | Computational optimization of systems governed by partial differential equations |
| title_exact_search | Computational optimization of systems governed by partial differential equations |
| title_full | Computational optimization of systems governed by partial differential equations Alfio Borzì ; Volker Schulz |
| title_fullStr | Computational optimization of systems governed by partial differential equations Alfio Borzì ; Volker Schulz |
| title_full_unstemmed | Computational optimization of systems governed by partial differential equations Alfio Borzì ; Volker Schulz |
| title_short | Computational optimization of systems governed by partial differential equations |
| title_sort | computational optimization of systems governed by partial differential equations |
| topic | Mathematical optimization Differential equations, Partial Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematical optimization Differential equations, Partial Wissenschaftliches Rechnen Optimierung Numerisches Verfahren Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024675924&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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