subject:(PDE Constraints)

1. Laurent-Brouty, Nicolas. Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws.

Degree: Docteur es, Mathématiques, 2019, Université Côte d'Azur (ComUE)

URL: http://www.theses.fr/2019AZUR4056

► Cette thèse se consacre à la modélisation mathématique du trafic routier à l'aide des lois de conservation hyperboliques. Nous nous intéressons plus particulièrement à l’application… (more)

▼ Cette thèse se consacre à la modélisation mathématique du trafic routier à l'aide des lois de conservation hyperboliques. Nous nous intéressons plus particulièrement à l’application des modèles macroscopiques en milieu urbain. Les zones urbaines sont désormais régulièrement confrontées à des niveaux de congestion record et à des épisodes de pollution atmosphérique causés par le trafic routier. L’objectif de cette thèse est alors de développer des modèles de trafic qui représentent de manière réaliste l’évolution des véhicules en milieu urbain. Dans un premier temps, nous considérons le modèle Aw-Rascle-Zhang avec relaxation. Nous construisons une suite de solutions approchées à l'aide de la méthode de suivi des fronts (wave-front tracking en anglais) couplée à une méthode de décomposition temporelle (splitting en anglais) en référentiel Lagrangien. Pour chaque valeur du paramètre de relaxation, nous montrons que cette suite converge vers une solution faible et entropique du système pour une donnée initiale à variation bornée. Par la suite, nous calculons une borne supérieure sur la décroissance des ondes positives. Nous démontrons que les solutions du système convergent vers une solution faible du modèle Lighthill-Whitham-Richards (LWR), c'est à dire vers la solution de la loi de conservation scalaire, lorsque le paramètre de relaxation tend vers zéro. Nous concluons par une discussion sur le caractère entropique de cette solution faible du modèle LWR. Dans un second temps, nous proposons un nouveau modèle macroscopique de trafic routier qui préserve le caractère borné de l'accélération des véhicules. Notre modèle couple une Équation aux Dérivées Partielles (EDP), la loi de conservation scalaire, à plusieurs Équations aux Dérivées Ordinaires (EDO), décrivant la trajectoire de véhicules accélérant à taux constant. Ces véhicules sont traités dans le modèle comme des goulots d'étranglement mobiles. Nous proposons la construction de solutions approchées avec un algorithme de suivi des fronts d'ondes et prouvons l'existence et l'unicité de la solution pour le problème de Cauchy associé à une donnée initiale constante par morceaux. Nous produisons ensuite des simulations numériques de notre modèle dans différentes situations urbaines, allant de la résolution du problème de Riemann à la simulation d'un axe urbain comportant plusieurs feux de signalisation. Enfin nous comparons ces simulations aux solutions du modèle LWR appliqué aux mêmes situations. Pour terminer, nous proposons un nouveau modèle macroscopique de trafic routier avec des stockages tampon (buffers en anglais) aux intersections afin de résoudre le modèle LWR sur des réseaux routiers. Ce modèle utilise des buffers de dimension finie, qui garantissent la propagation de la congestion au sein du réseau. Il comporte également des fonctions de répartition de véhicules aux jonctions qui sont dépendantes du temps, et peuvent dès lors être contrôlées au cours du temps. La dynamique du trafic est d'abord établie à l'aide des lois de conservation hyperboliques,… Advisors/Committee Members: Goatin, Paola (thesis director).

Subjects/Keywords: Lois de conservation hyperboliques; Systèmes de conservation hyperboliques avec relaxation; Modèles macroscopiques de trafic routier; Suivi de fronts d'onde; Systèmes de Temple; Couplage EDP-EDO; Contraintes de flux; Trafic routier sur les réseaux; Équations d'Hamilton-Jacobi; Méthodes de point fixe; Hyperbolic conservation laws; Hyperbolic systems of conservation laws with relaxation; Macroscopic traffic flow models; Wave-front tracking; Temple class systems; PDE-ODE coupling; Flux constraints; Traffic flow on networks; Hamilton-Jacobi equations; Fixed-point problems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Laurent-Brouty, N. (2019). Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws. (Doctoral Dissertation). Université Côte d'Azur (ComUE). Retrieved from http://www.theses.fr/2019AZUR4056

Chicago Manual of Style (16^th Edition):

Laurent-Brouty, Nicolas. “Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws.” 2019. Doctoral Dissertation, Université Côte d'Azur (ComUE). Accessed April 13, 2021. http://www.theses.fr/2019AZUR4056.

MLA Handbook (7^th Edition):

Laurent-Brouty, Nicolas. “Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws.” 2019. Web. 13 Apr 2021.

Vancouver:

Laurent-Brouty N. Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws. [Internet] [Doctoral dissertation]. Université Côte d'Azur (ComUE); 2019. [cited 2021 Apr 13]. Available from: http://www.theses.fr/2019AZUR4056.

Council of Science Editors:

Laurent-Brouty N. Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques : Modeling traffic on urban road networks with hyperbolic conservation laws. [Doctoral Dissertation]. Université Côte d'Azur (ComUE); 2019. Available from: http://www.theses.fr/2019AZUR4056

Brno University of Technology

2. Mrázková, Eva. Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/1571

► Many optimum design problems in engineering areas lead to optimization models constrained by ordinary (ODE) or partial (PDE) differential equations, and furthermore, several elements of… (more)

▼ Many optimum design problems in engineering areas lead to optimization models constrained by ordinary (ODE) or partial (PDE) differential equations, and furthermore, several elements of the problems may be uncertain in practice. Three engineering problems concerning the optimization of vibrations and an optimal design of beam dimensions are considered. The uncertainty in the form of random load or random Young's modulus is involved. It is shown that two-stage stochastic programming offers a promising approach in solving such problems. Corresponding mathematical models involving ODE or PDE type constraints, uncertain parameters and multiple criteria are formulated and lead to (multi-objective) stochastic nonlinear optimization models. It is also proved for which type of problems stochastic programming approach (EO reformulation) should be used and when it is sufficient to solve simpler deterministic problem (EV reformulation). This fact has the big importance in practice in term of computational intensity of large scale problems. Computational schemes for this type of problems are proposed, including discretization methods for random elements and ODE or PDE constraints. By means of derived approximations the mathematical models are implemented and solved in GAMS. The solution quality is determined by an interval estimate of the optimality gap computed via Monte Carlo bounding technique. Parametric analysis of multi-criteria model results in efficient frontier computation. The alternatives of approximations of the model with reliability-related probabilistic terms including mixed-integer nonlinear programming and penalty reformulations are discussed. Furthermore, the progressive hedging algorithm is implemented and tested for the selected problems with respect to future possibilities of parallel computing of large engineering problems. The results show that it can be used even when the mathematical conditions for convergence are not fulfilled. Finite difference method and finite element method are compared for deterministic version of ODE constrained problem by using GAMS and ANSYS with quite comparable results. Advisors/Committee Members: Karpíšek, Zdeněk (advisor), Horová, Ivana (referee), Štěpánek, Petr (referee).

Subjects/Keywords: optimální inženýrský návrh; ODR a PDR omezení; stochastické programování; optimalizace s pravděpodobnostními omezeními; vícekriteriální optimalizace; metoda Monte Carlo; PHA algoritmus; optimum engineering design; ODE and PDE constraints; stochastic programming; chance constrained programming; multi-objective programming; Monte Carlo method; progressive hedging algorithm

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mrázková, E. (2019). Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/1571

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mrázková, Eva. “Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications.” 2019. Thesis, Brno University of Technology. Accessed April 13, 2021. http://hdl.handle.net/11012/1571.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mrázková, Eva. “Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications.” 2019. Web. 13 Apr 2021.

Vancouver:

Mrázková E. Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/11012/1571.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mrázková E. Approximations in Stochastic Optimization and Their Applications: Approximations in Stochastic Optimization and Their Applications. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/1571

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Mejeur, Joel M. Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints .

Degree: 2017, George Mason University

URL: http://hdl.handle.net/1920/11279

State inequality constraints in PDE Constrained Optimization (PDECO) arise in many areas of science and engineering. Unfortunately these constraints, and the resulting Lagrange multipliers, are known to negatively influence the behavior of many existing optimization methods. Advisors/Committee Members: Griva, Igor (advisor).

Subjects/Keywords: Applied mathematics; Augmented Lagrangian; Control Constraints; Elliptic Control; Nonlinear Rescaling; PDE Constrained Optimization; State Constraints

…Director: Dr. Igor Griva State inequality constraints in PDE Constrained Optimization (… …optimization for problems with Partial Differential Equation (PDE) constraints has been an… …constraints, and therefore optimization problems do often arise with these PDE constraints. Elliptic… …List of Tables Table Page 7.1 7.2 State and Control Constraints… …AND CONTROL CONSTRAINTS Joel M Mejeur, PhD George Mason University, 2017 Dissertation…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mejeur, J. M. (2017). Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints . (Thesis). George Mason University. Retrieved from http://hdl.handle.net/1920/11279

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mejeur, Joel M. “Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints .” 2017. Thesis, George Mason University. Accessed April 13, 2021. http://hdl.handle.net/1920/11279.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mejeur, Joel M. “Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints .” 2017. Web. 13 Apr 2021.

Vancouver:

Mejeur JM. Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints . [Internet] [Thesis]. George Mason University; 2017. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/1920/11279.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mejeur JM. Function Space Nonlinear Rescaling Methods for Elliptic Control Problems with Point-wise State and Control Constraints . [Thesis]. George Mason University; 2017. Available from: http://hdl.handle.net/1920/11279

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

4. Letona Bolivar, Cristina Felicitas. On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.

Degree: PhD, Mathematics, 2016, Virginia Tech

URL: http://hdl.handle.net/10919/73308

► The methods for solving domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but… (more)

Subjects/Keywords: Domain Optimization; Shape Derivatives; PDE Constraints; Mixed Boundary Conditions.

…optimization problems with elliptic PDE constraints. As for any other optimization problem, solving a… …These studies vary in the choice of functionals or the form of the PDE constraints. The… …boundary conditions. Few results on finding the minimizing domain subject to PDE constraints with… …optimization problems that contain specific PDE constraints. Thus, the definition of the admissible… …setting to the domain optimization problem subject to PDE constraints. In that chapter, we begin…

9 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Letona Bolivar, C. F. (2016). On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/73308

Chicago Manual of Style (16^th Edition):

Letona Bolivar, Cristina Felicitas. “On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.” 2016. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021. http://hdl.handle.net/10919/73308.

MLA Handbook (7^th Edition):

Letona Bolivar, Cristina Felicitas. “On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.” 2016. Web. 13 Apr 2021.

Vancouver:

Letona Bolivar CF. On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. [Internet] [Doctoral dissertation]. Virginia Tech; 2016. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/10919/73308.

Council of Science Editors:

Letona Bolivar CF. On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. [Doctoral Dissertation]. Virginia Tech; 2016. Available from: http://hdl.handle.net/10919/73308

5. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-6950

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan (advisor), Meyer, Christian (referee).

Subjects/Keywords: Block-Glätter; Czochralski; Elliptisch; EOJ Stabilisierung; Finite Elemente; Hierarchisch; Hierarchisches Lösungskonzept; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Kantenbasierte Stabilisierung; Kristallwachstum; Krylov; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithisch; Navier-Stokes; Nichtparametrische Finite Elemente; Optimierung; Raum-Zeit; Sattelpunkt; Schurkomplement-Vorkonditionierer; Stokes; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; Block smoother; CFD; Crank-Nicolson; Crystal growth; Distributed Control; Edge-oriented stabilisation; Elliptic; EOJ stabilisation; FEAT; FEATFLOW; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Inexact Newton; Inverse Problems; KKT system; Large-Scale; linear complexity; Monolithic; Multigrid; Multigrid-Krylov; Multilevel; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimisation; Optimization; PDE Constraints; saddle point; SAND; Schur complement preconditioning; Space-time; SQP; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-6950

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Doctoral Dissertation, Technische Universität Dortmund. Accessed April 13, 2021. http://dx.doi.org/10.17877/DE290R-6950.

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 13 Apr 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2011. [cited 2021 Apr 13]. Available from: http://dx.doi.org/10.17877/DE290R-6950.

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Doctoral Dissertation]. Technische Universität Dortmund; 2011. Available from: http://dx.doi.org/10.17877/DE290R-6950

6. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://hdl.handle.net/2003/29239

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan.

Subjects/Keywords: Block-Glätter; Block smoother; CFD; Crank-Nicolson; Crystal growth; Czochralski; Distributed Control; Edge-oriented stabilisation; Elliptic; Elliptisch; EOJ stabilisation; EOJ Stabilisierung; FEAT; FEATFLOW; Finite Elemente; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Hierarchisch; Hierarchisches Lösungskonzept; Inexact Newton; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Inverse Problems; Kantenbasierte Stabilisierung; KKT system; Kristallwachstum; Krylov; Large-Scale; linear complexity; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithic; Monolithisch; Multigrid; Multigrid-Krylov; Multilevel; Navier-Stokes; Nichtparametrische Finite Elemente; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimierung; Optimisation; Optimization; PDE Constraints; Raum-Zeit; saddle point; SAND; Sattelpunkt; Schur complement preconditioning; Schurkomplement-Vorkonditionierer; Space-time; SQP; Stokes; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Thesis). Technische Universität Dortmund. Retrieved from http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Thesis, Technische Universität Dortmund. Accessed April 13, 2021. http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 13 Apr 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Thesis]. Technische Universität Dortmund; 2011. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Thesis]. Technische Universität Dortmund; 2011. Available from: http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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Open Access Theses and Dissertations