subject:(Krylov)

Anna University

1. Babu T. Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;.

Degree: Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system, 2015, Anna University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/38623

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In this work a controller is designed for a reduced order interval newlinesystem model using heuristic algorithm newlineIndustrial processes with large number of state variables… (more)

Subjects/Keywords: Kharitonov theorem; Krylov subspace

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

APA (6^th Edition):

T, B. (2015). Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;. (Thesis). Anna University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/38623

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):

T, Babu. “Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;.” 2015. Thesis, Anna University. Accessed March 08, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/38623.

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

MLA Handbook (7^th Edition):

T, Babu. “Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;.” 2015. Web. 08 Mar 2021.

Vancouver:

T B. Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;. [Internet] [Thesis]. Anna University; 2015. [cited 2021 Mar 08]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/38623.

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

Council of Science Editors:

T B. Heuristic algorithm based Controller design and stability Analysis using model order Reduction of interval system;. [Thesis]. Anna University; 2015. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/38623

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

Virginia Tech

2. Renardy, Marissa. Analysis of the BiCG Method.

Degree: MS, Mathematics, 2013, Virginia Tech

URL: http://hdl.handle.net/10919/50922

► The Biconjugate Gradient (BiCG) method is an iterative Krylov subspace method that utilizes a 3-term recurrence. BiCG is the basis of several very popular methods,… (more)

Subjects/Keywords: Krylov methods; BiCG; GMRES; FOM

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APA (6^th Edition):

Renardy, M. (2013). Analysis of the BiCG Method. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/50922

Chicago Manual of Style (16^th Edition):

Renardy, Marissa. “Analysis of the BiCG Method.” 2013. Masters Thesis, Virginia Tech. Accessed March 08, 2021. http://hdl.handle.net/10919/50922.

MLA Handbook (7^th Edition):

Renardy, Marissa. “Analysis of the BiCG Method.” 2013. Web. 08 Mar 2021.

Vancouver:

Renardy M. Analysis of the BiCG Method. [Internet] [Masters thesis]. Virginia Tech; 2013. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10919/50922.

Council of Science Editors:

Renardy M. Analysis of the BiCG Method. [Masters Thesis]. Virginia Tech; 2013. Available from: http://hdl.handle.net/10919/50922

3. Silva, Tiago Filipe Leitão. Métodos numéricos para resolução de equações de Lyapunov.

Degree: 2010, Universidade da Beira Interior

URL: http://www.rcaap.pt/detail.jsp?id=oai:ubibliorum.ubi.pt:10400.6/1851

► O objectivo desta dissertação é descrever, analisar e aplicar alguns métodos numéricos para resolver a equação clássica de Lyapunov. Estudamos condições que garantem a solubilidade… (more)

Subjects/Keywords: Métodos numéricos; Equações matriciais; Kronecker; Krylov

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APA (6^th Edition):

Silva, T. F. L. (2010). Métodos numéricos para resolução de equações de Lyapunov. (Thesis). Universidade da Beira Interior. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:ubibliorum.ubi.pt:10400.6/1851

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):

Silva, Tiago Filipe Leitão. “Métodos numéricos para resolução de equações de Lyapunov.” 2010. Thesis, Universidade da Beira Interior. Accessed March 08, 2021. http://www.rcaap.pt/detail.jsp?id=oai:ubibliorum.ubi.pt:10400.6/1851.

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

MLA Handbook (7^th Edition):

Silva, Tiago Filipe Leitão. “Métodos numéricos para resolução de equações de Lyapunov.” 2010. Web. 08 Mar 2021.

Vancouver:

Silva TFL. Métodos numéricos para resolução de equações de Lyapunov. [Internet] [Thesis]. Universidade da Beira Interior; 2010. [cited 2021 Mar 08]. Available from: http://www.rcaap.pt/detail.jsp?id=oai:ubibliorum.ubi.pt:10400.6/1851.

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

Council of Science Editors:

Silva TFL. Métodos numéricos para resolução de equações de Lyapunov. [Thesis]. Universidade da Beira Interior; 2010. Available from: http://www.rcaap.pt/detail.jsp?id=oai:ubibliorum.ubi.pt:10400.6/1851

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

Delft University of Technology

4. Zimmerling, J.T. (author). Modeling of wave propagation in open domains: A Krylov subspace approach.

Degree: 2014, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:aea44c4e-2658-474d-b9ea-c046066ac881

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Simulating electromagnetic or acoustic wave propagation in complex open structures is extremely important in many areas of science and engineering. In a wide range of… (more)

Subjects/Keywords: Computational Electromagnetics; Krylov subspace; model order reduction

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APA (6^th Edition):

Zimmerling, J. T. (. (2014). Modeling of wave propagation in open domains: A Krylov subspace approach. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:aea44c4e-2658-474d-b9ea-c046066ac881

Chicago Manual of Style (16^th Edition):

Zimmerling, J T (author). “Modeling of wave propagation in open domains: A Krylov subspace approach.” 2014. Masters Thesis, Delft University of Technology. Accessed March 08, 2021. http://resolver.tudelft.nl/uuid:aea44c4e-2658-474d-b9ea-c046066ac881.

MLA Handbook (7^th Edition):

Zimmerling, J T (author). “Modeling of wave propagation in open domains: A Krylov subspace approach.” 2014. Web. 08 Mar 2021.

Vancouver:

Zimmerling JT(. Modeling of wave propagation in open domains: A Krylov subspace approach. [Internet] [Masters thesis]. Delft University of Technology; 2014. [cited 2021 Mar 08]. Available from: http://resolver.tudelft.nl/uuid:aea44c4e-2658-474d-b9ea-c046066ac881.

Council of Science Editors:

Zimmerling JT(. Modeling of wave propagation in open domains: A Krylov subspace approach. [Masters Thesis]. Delft University of Technology; 2014. Available from: http://resolver.tudelft.nl/uuid:aea44c4e-2658-474d-b9ea-c046066ac881

Delft University of Technology

5. de Bruycker, Deborah (author). Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:87ad4bb3-61b5-4a55-a956-1db361f133c1

► Maritime hydrodynamics involves strong inertia-driven flows, including free-surface waves, and with Reynolds numbers as high as 109. Numerical modelling of these flows is therefore a… (more)

▼ Maritime hydrodynamics involves strong inertia-driven flows, including free-surface waves, and with Reynolds numbers as high as 109. Numerical modelling of these flows is therefore a true challenge. Especially for the optimization of the design of the aft part of the ship, where viscous effects cannot be discarded. At MARIN, the viscous flow solver PARNASSOS has been developed for this purpose. Over the years, this solver has been optimized with respect to robustness, accuracy and efficiency, which has resulted in a tool capable of doing fast viscous flow computations. However, if the ship's generated wave pattern has to be taken into account, a complete hull form evaluation can still take hours, or even days. For automatic optimization purposes, where hundreds or thousands of calculations are needed, it is thus desired to further accelerate the computing time of this solver. Most of the CPU time for a computation with PARNASSOS is spent on solving the large sparse linear systems of the form Ax=b. These are currently solved using an iterative solver such as GMRES, in combination with a preconditioner to improve convergence rates. Due to the increase in computational capability of modern computers, the performance of the linear system solver could be further improved through use of high performance computing. Especially the Graphical Processing Unit (GPU) seems to have great potential for speeding up such scientific computations. The aim of the work is therefore to investigate whether it is possible to achieve reasonable speedup of PARNASSOS' linear system solver by making use of GPU computing. This investigation was done using both model- and full-scale test cases, both for increasing size of the systems to solve. Performance of different iterative solvers has been analysed on different GPU cards and has been compared against the performance, currently used on the CPU. Advisors/Committee Members: van Zuijlen, Alexander (mentor), Delft University of Technology (degree granting institution).

Subjects/Keywords: GPU computing; Preconditioning; CFD; Krylov solvers

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APA (6^th Edition):

de Bruycker, D. (. (2017). Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:87ad4bb3-61b5-4a55-a956-1db361f133c1

Chicago Manual of Style (16^th Edition):

de Bruycker, Deborah (author). “Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware.” 2017. Masters Thesis, Delft University of Technology. Accessed March 08, 2021. http://resolver.tudelft.nl/uuid:87ad4bb3-61b5-4a55-a956-1db361f133c1.

MLA Handbook (7^th Edition):

de Bruycker, Deborah (author). “Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware.” 2017. Web. 08 Mar 2021.

Vancouver:

de Bruycker D(. Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Mar 08]. Available from: http://resolver.tudelft.nl/uuid:87ad4bb3-61b5-4a55-a956-1db361f133c1.

Council of Science Editors:

de Bruycker D(. Efficiency improvement of viscous ship flow computations through use of the Graphics Processing Unit: A performance analysis on different hardware. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:87ad4bb3-61b5-4a55-a956-1db361f133c1

6. Kaouane, Yassine. Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications.

Degree: Docteur es, Mathématiques. Systèmes dynamiques, 2018, Littoral; Université Cadi Ayyad (Marrakech, Maroc)

URL: http://www.theses.fr/2018DUNK0501

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Les simulations à grande dimension jouent un rôle crucial dans l'étude d'une grande variété de phénomènes physiques complexes, entraînant souvent des demandes écrasantes sur les… (more)

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Les simulations à grande dimension jouent un rôle crucial dans l'étude d'une grande variété de phénomènes physiques complexes, entraînant souvent des demandes écrasantes sur les ressources informatiques. La gestion de ces demandes constitue la principale motivation pour la réduction du modèle : produire des modèles de commande réduite plus simples, qui permettent une simulation plus rapide et moins coûteuse tout en se rapprochant avec précision du comportement du modèle d'origine. La présence des systèmes avec multiples entrées et multiples sorties (MIMO) rend le processus de réduction encore plus difficile. Dans cette thèse, nous nous intéressons aux méthodes de réduction de modèles à grande dimension en utilisant la projection sur des sous-espaces de Krylov tangentielles. Nous nous penchons sur le développement de techniques qui utilisent l'interpolation tangentielle. Celles-ci présentent une alternative efficace et intéressante à la troncature équilibrée qui est considérée comme référence dans le domaine et tout particulièrement la réduction pour les systèmes linéaire à temps invariants. Enfin, une attention particulière sera portée sur l'élaboration de nouveaux algorithmes efficaces et sur l'application à des problèmes pratiques.

Large-scale simulations play a crucial role in the study of a great variety of complex physical phenomena, leading often to overwhelming demands on computational resources. Managing these demands constitutes the main motivation for model reduction : produce simpler reduced-order models, which allow for faster and cheaper simulation while accurately approximating the behaviour of the original model. The presence of multiple inputs and outputs (MIMO) systems, makes the reduction process even more challenging. In this thesis we are interested in methods of reducing large-scale models, using projection on tangential Krylov subspaces. We are looking at the development of techniques using tangential interpolation. These present an effective and interesting alternative to the balanced truncation which is considered as a reference in the field and especially for the reduction of linear time invariant systems. Finally, special attention will be focused on the development of new efficient algorithms and application to practical problems.

Advisors/Committee Members: Jbilou, Khalid (thesis director), Bentbib, Abdeslem Hafid (thesis director).

Subjects/Keywords: Réduction de modèle; Interpolation; Sous-espace de Krylov; Model reduction; Interpolation; Krylov subspace

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

APA (6^th Edition):

Kaouane, Y. (2018). Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications. (Doctoral Dissertation). Littoral; Université Cadi Ayyad (Marrakech, Maroc). Retrieved from http://www.theses.fr/2018DUNK0501

Chicago Manual of Style (16^th Edition):

Kaouane, Yassine. “Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications.” 2018. Doctoral Dissertation, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Accessed March 08, 2021. http://www.theses.fr/2018DUNK0501.

MLA Handbook (7^th Edition):

Kaouane, Yassine. “Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications.” 2018. Web. 08 Mar 2021.

Vancouver:

Kaouane Y. Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications. [Internet] [Doctoral dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2018. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2018DUNK0501.

Council of Science Editors:

Kaouane Y. Méthodes tangentielles pour les réductions de modèles et applications : Tangential methods for model reductions and applications. [Doctoral Dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2018. Available from: http://www.theses.fr/2018DUNK0501

7. Abidi, Oussama. Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions.

Degree: Docteur es, Mathématiques appliquées, 2016, Littoral

URL: http://www.theses.fr/2016DUNK0419

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Beaucoup de phénomènes physiques sont modélisés par des équations aux dérivées partielles, la discrétisation de ces équations conduit souvent à des systèmes dynamiques (continus ou… (more)

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Beaucoup de phénomènes physiques sont modélisés par des équations aux dérivées partielles, la discrétisation de ces équations conduit souvent à des systèmes dynamiques (continus ou discrets) dépendant d'un vecteur de contrôle dont le choix permet de stabiliser le système dynamique. Comme ces problèmes sont, dans la pratique, de grandes tailles, il est intéressant de les étudier via un autre problème dérivé réduit et plus proche du modèle initial. Dans cette thèse, on introduit et on étudie de nouvelles méthodes basées sur les processus de type Krylov rationnel afin d'extraire un modèle réduit proche du modèle original. Des applications numériques seront faites à partir de problèmes pratiques. Après un premier chapitre consacré au rappel de quelques outils mathématiques, on s'intéresse aux méthodes basées sur le processus d'Arnoldi rationnel par blocs pour réduire la taille d'un système dynamique de type Multi-Input/Multi-Output (MIMO). On propose une sélection adaptative de choix de certains paramètres qui sont cruciaux pour l'efficacité de la méthode. On introduit aussi un nouvel algorithme adaptatif de type Arnoldi rationnel par blocs afin de fournir une nouvelle relation de type Arnoldi. Dans la deuxième partie de ce travail, on introduit la méthode d'Arnoldi rationnelle globale, comme alternative de la méthode d'Arnoldi rationnel par blocs. On définit la projection au sens global, et on applique cette méthode pour approcher les fonctions de transfert. Dans la troisième partie, on s'intéresse à la méthode d'Arnoldi étendue (qui est un cas particulier de la méthode d'Arnoldi rationnelle) dans les deux cas (global et par blocs), on donnera quelques nouvelles propriétés algébriques qui sont appliquées aux problèmes des moments. On consièdère dans la quatrième partie la méthode de troncature balancée pour la réduction de modèle. Ce procédé consiste à résoudre deux grandes équations algébriques de Lyapunov lorsque le système est stable ou à résoudre deux équations de Riccati lorsque le système est instable. Comme ces équations sont de grandes tailles, on va appliquer la méthode de Krylov rationnel par blocs pour approcher la solution de ces équations. Le travail de cette thèse sera cloturé par une nouvelle idée, dans laquelle on définit un nouvel espace sous le nom de sous-espace de Krylov rationnelle étendue qui sera utilisée pour la réduction du modèle.

Many physical phenomena are modeled by PDEs. The discretization of these equations often leads to dynamical systems (continuous or discrete) depending on a control vector whose choice can stabilize the dynamical system. As these problems are, in practice, of a large size, it is interesting to study the problem through another one which is reduced and close to the original model. In this thesis, we develop and study new methods based on rational Krylov-based processes for model reduction techniques in large-scale Multi-Input Multi-Output (MIMO) linear time invariant dynamical systems. In chapter 2 the methods are based on the rational block Arnoldi process to reduce…

Advisors/Committee Members: Jbilou, Khalid (thesis director).

Subjects/Keywords: Sous-espaces de Krylov; Arnoldi rationnel; Systèmes dynamiques; Réduction de modèles; Contrôle; Krylov subspaces; Rational Arnoldi; Dynamical systems; Model reductions; Control

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

APA (6^th Edition):

Abidi, O. (2016). Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions. (Doctoral Dissertation). Littoral. Retrieved from http://www.theses.fr/2016DUNK0419

Chicago Manual of Style (16^th Edition):

Abidi, Oussama. “Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions.” 2016. Doctoral Dissertation, Littoral. Accessed March 08, 2021. http://www.theses.fr/2016DUNK0419.

MLA Handbook (7^th Edition):

Abidi, Oussama. “Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions.” 2016. Web. 08 Mar 2021.

Vancouver:

Abidi O. Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions. [Internet] [Doctoral dissertation]. Littoral; 2016. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2016DUNK0419.

Council of Science Editors:

Abidi O. Méthodes de sous-espaces de Krylov rationnelles pour le contrôle et la réduction de modèles : Rational Krylov subspace methods for the control and model reductions. [Doctoral Dissertation]. Littoral; 2016. Available from: http://www.theses.fr/2016DUNK0419

Delft University of Technology

8. Diao, H. (author). Fourier Analysis of Iterative Methods for the Helmholtz Problem.

Degree: 2012, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

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This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues… (more)

Subjects/Keywords: Helmholtz problem; Krylov subspace methods; multigrid method; multilevel Krylov multigrid method; shifted Laplacian preconditioner; deflation operator; Fourier analysis

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APA (6^th Edition):

Diao, H. (. (2012). Fourier Analysis of Iterative Methods for the Helmholtz Problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Chicago Manual of Style (16^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Masters Thesis, Delft University of Technology. Accessed March 08, 2021. http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

MLA Handbook (7^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Web. 08 Mar 2021.

Vancouver:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Mar 08]. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

Council of Science Editors:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

9. Badahmane, Achraf. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.

Degree: Docteur es, Mathématiques. Mathématiques appliquées, 2019, Littoral; Université Cadi Ayyad (Marrakech, Maroc)

URL: http://www.theses.fr/2019DUNK0543

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La résolution numérique des problèmes de point-selle a eu une attention particulière ces dernières années. À titre d'exemple, la mécanique des fluides et solides conduit… (more)

Subjects/Keywords: Point-selle; Préconditionnement; Krylov; Produit de Kronecker; Produit de diamant; Saddle point; Preconditioner; Global Krylov subspace method; Kronecker product; Diamond product

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

APA (6^th Edition):

Badahmane, A. (2019). Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. (Doctoral Dissertation). Littoral; Université Cadi Ayyad (Marrakech, Maroc). Retrieved from http://www.theses.fr/2019DUNK0543

Chicago Manual of Style (16^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Doctoral Dissertation, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Accessed March 08, 2021. http://www.theses.fr/2019DUNK0543.

MLA Handbook (7^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Web. 08 Mar 2021.

Vancouver:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Internet] [Doctoral dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2019DUNK0543.

Council of Science Editors:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Doctoral Dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. Available from: http://www.theses.fr/2019DUNK0543

University of California – Merced

10. Loffeld, John. Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications.

Degree: Applied Mathematics, 2013, University of California – Merced

URL: http://www.escholarship.org/uc/item/559821rq

► Exponential integrators have received renewed interest in recent years as a means to approximate stiff systems of ODEs, but are not currently widely used in… (more)

Subjects/Keywords: Mathematics; EPIRK methods; exponential integrators; Krylov; Stiff systems

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APA (6^th Edition):

Loffeld, J. (2013). Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications. (Thesis). University of California – Merced. Retrieved from http://www.escholarship.org/uc/item/559821rq

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):

Loffeld, John. “Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications.” 2013. Thesis, University of California – Merced. Accessed March 08, 2021. http://www.escholarship.org/uc/item/559821rq.

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

MLA Handbook (7^th Edition):

Loffeld, John. “Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications.” 2013. Web. 08 Mar 2021.

Vancouver:

Loffeld J. Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications. [Internet] [Thesis]. University of California – Merced; 2013. [cited 2021 Mar 08]. Available from: http://www.escholarship.org/uc/item/559821rq.

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

Council of Science Editors:

Loffeld J. Design, Implementation and Performance of Exponential Integrators for High Performance Computing Applications. [Thesis]. University of California – Merced; 2013. Available from: http://www.escholarship.org/uc/item/559821rq

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

Temple University

11. Shank, Stephen David. Low-rank solution methods for large-scale linear matrix equations.

Degree: PhD, 2014, Temple University

URL: http://digital.library.temple.edu/u?/p245801coll10,273331

►

Mathematics

We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on… (more)

Subjects/Keywords: Applied mathematics;

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APA (6^th Edition):

Shank, S. D. (2014). Low-rank solution methods for large-scale linear matrix equations. (Doctoral Dissertation). Temple University. Retrieved from http://digital.library.temple.edu/u?/p245801coll10,273331

Chicago Manual of Style (16^th Edition):

Shank, Stephen David. “Low-rank solution methods for large-scale linear matrix equations.” 2014. Doctoral Dissertation, Temple University. Accessed March 08, 2021. http://digital.library.temple.edu/u?/p245801coll10,273331.

MLA Handbook (7^th Edition):

Shank, Stephen David. “Low-rank solution methods for large-scale linear matrix equations.” 2014. Web. 08 Mar 2021.

Vancouver:

Shank SD. Low-rank solution methods for large-scale linear matrix equations. [Internet] [Doctoral dissertation]. Temple University; 2014. [cited 2021 Mar 08]. Available from: http://digital.library.temple.edu/u?/p245801coll10,273331.

Council of Science Editors:

Shank SD. Low-rank solution methods for large-scale linear matrix equations. [Doctoral Dissertation]. Temple University; 2014. Available from: http://digital.library.temple.edu/u?/p245801coll10,273331

Universidade do Rio Grande do Norte

12. Silva, Josimara Tatiane da. Precondicionamento do método GMRES para Z-matrizes .

Degree: 2016, Universidade do Rio Grande do Norte

URL: http://repositorio.ufrn.br/handle/123456789/22016

► This study aims to investigate the convergence behavior of the GMRES (Generalized Minimal Residual) method and its version GMRES(m), without and with preconditioner ILU(0) applied… (more)

Subjects/Keywords: Z-matrizes; Métodos de Krylov; GMRES; GMRES(m); Precondicionador ILU (0)

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APA (6^th Edition):

Silva, J. T. d. (2016). Precondicionamento do método GMRES para Z-matrizes . (Masters Thesis). Universidade do Rio Grande do Norte. Retrieved from http://repositorio.ufrn.br/handle/123456789/22016

Chicago Manual of Style (16^th Edition):

Silva, Josimara Tatiane da. “Precondicionamento do método GMRES para Z-matrizes .” 2016. Masters Thesis, Universidade do Rio Grande do Norte. Accessed March 08, 2021. http://repositorio.ufrn.br/handle/123456789/22016.

MLA Handbook (7^th Edition):

Silva, Josimara Tatiane da. “Precondicionamento do método GMRES para Z-matrizes .” 2016. Web. 08 Mar 2021.

Vancouver:

Silva JTd. Precondicionamento do método GMRES para Z-matrizes . [Internet] [Masters thesis]. Universidade do Rio Grande do Norte; 2016. [cited 2021 Mar 08]. Available from: http://repositorio.ufrn.br/handle/123456789/22016.

Council of Science Editors:

Silva JTd. Precondicionamento do método GMRES para Z-matrizes . [Masters Thesis]. Universidade do Rio Grande do Norte; 2016. Available from: http://repositorio.ufrn.br/handle/123456789/22016

Universidade do Estado do Rio de Janeiro

13. Marcelo Xavier Guterres. Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards.

Degree: PhD, 2013, Universidade do Estado do Rio de Janeiro

URL: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6749 ;

►

A engenharia geotécnica é uma das grandes áreas da engenharia civil que estuda a interação entre as construções realizadas pelo homem ou de fenômenos naturais… (more)

▼

A engenharia geotécnica é uma das grandes áreas da engenharia civil que estuda a interação entre as construções realizadas pelo homem ou de fenômenos naturais com o ambiente geológico, que na grande maioria das vezes trata-se de solos parcialmente saturados. Neste sentido, o desempenho de obras como estabilização, contenção de barragens, muros de contenção, fundações e estradas estão condicionados a uma correta predição do fluxo de água no interior dos solos. Porém, como a área das regiões a serem estudas com relação à predição do fluxo de água são comumente da ordem de quilômetros quadrados, as soluções dos modelos matemáticos exigem malhas computacionais de grandes proporções, ocasionando sérias limitações associadas aos requisitos de memória computacional e tempo de processamento. A fim de contornar estas limitações, métodos numéricos eficientes devem ser empregados na solução do problema em análise. Portanto, métodos iterativos para solução de sistemas não lineares e lineares esparsos de grande porte devem ser utilizados neste tipo de aplicação. Em suma, visto a relevância do tema, esta pesquisa aproximou uma solução para a equação diferencial parcial de Richards pelo método dos volumes finitos em duas dimensões, empregando o método de Picard e Newton com maior eficiência computacional. Para tanto, foram utilizadas técnicas iterativas de resolução de sistemas lineares baseados no espaço de Krylov com matrizes pré-condicionadoras com a biblioteca numérica Portable, Extensible Toolkit for Scientific Computation (PETSc). Os resultados indicam que quando se resolve a equação de Richards considerando-se o método de PICARD-KRYLOV, não importando o modelo de avaliação do solo, a melhor combinação para resolução dos sistemas lineares é o método dos gradientes biconjugados estabilizado mais o pré-condicionador SOR. Por outro lado, quando se utiliza as equações de van Genuchten deve ser optar pela combinação do método dos gradientes conjugados em conjunto com pré-condicionador SOR. Quando se adota o método de NEWTON-KRYLOV, o método gradientes biconjugados estabilizado é o mais eficiente na resolução do sistema linear do passo de Newton, com relação ao pré-condicionador deve-se dar preferência ao bloco Jacobi. Por fim, há evidências que apontam que o método PICARD-KRYLOV pode ser mais vantajoso que o método de NEWTON-KRYLOV, quando empregados na resolução da equação diferencial parcial de Richards.

Geotechnical Engineering is the area of Civil Engineering that studies the interaction between constructions carried out by man or natural phenomena with geological environment, which most of times is partially saturated soil. In this sense, work developing as stabilization, dam containing, retaining walls, foundations and highways are conditioned to a right prediction of water flow into the soil. However, considering the water flow, the studied region areas are commonly on the order of square kilometers, mathematical models solutions require computational meshes of large proportions, causing serious limitations linked to…

Advisors/Committee Members: Antônio José da Silva Neto, João Flávio Vieira de Vasconcellos, Leôncio Diógenes Tavares Câmara, Carlos Antonio de Moura, Carlos Alexandre Bastos de Vasconcellos, Claudia Mazza Dias.

Subjects/Keywords: Dinâmica dos fluidos Modelos matemáticos; Método dos volumes finitos; Equações diferenciais parciais; Permeabilidade Modelos matemáticos; Newton-Krylov, Método; Picard-Krylov, Método; Fluidodinâmica computacional; Richards, Equação de; PETSc; Richards equation; Picard-Krylov; Newton-Krylov; PETSc; AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES

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

APA (6^th Edition):

Guterres, M. X. (2013). Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards. (Doctoral Dissertation). Universidade do Estado do Rio de Janeiro. Retrieved from http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6749 ;

Chicago Manual of Style (16^th Edition):

Guterres, Marcelo Xavier. “Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards.” 2013. Doctoral Dissertation, Universidade do Estado do Rio de Janeiro. Accessed March 08, 2021. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6749 ;.

MLA Handbook (7^th Edition):

Guterres, Marcelo Xavier. “Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards.” 2013. Web. 08 Mar 2021.

Vancouver:

Guterres MX. Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards. [Internet] [Doctoral dissertation]. Universidade do Estado do Rio de Janeiro; 2013. [cited 2021 Mar 08]. Available from: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6749 ;.

Council of Science Editors:

Guterres MX. Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards. [Doctoral Dissertation]. Universidade do Estado do Rio de Janeiro; 2013. Available from: http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6749 ;

Baylor University

14. Nguyen, Huy V., 1986-. Krylov methods for solving a sequence of large systems of linear equations.

Degree: PhD, Baylor University. Dept. of Mathematics., 2015, Baylor University

URL: http://hdl.handle.net/2104/9511

► Consider solving a sequence of linear systems A_(i)x⁽ⁱ⁾=b⁽ⁱ⁾, i=1, 2, ... where A₍ᵢ₎ ϵℂⁿᵡⁿ and b⁽ⁱ⁾ϵℂⁿ using some variations of Krylov subspace methods, like GMRES.… (more)

Subjects/Keywords: GMRES. Krylov subspace. Deflation. GMRES-DR. GMRES-E. Subspace recycling.

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

APA (6^th Edition):

Nguyen, Huy V., 1. (2015). Krylov methods for solving a sequence of large systems of linear equations. (Doctoral Dissertation). Baylor University. Retrieved from http://hdl.handle.net/2104/9511

Chicago Manual of Style (16^th Edition):

Nguyen, Huy V., 1986-. “Krylov methods for solving a sequence of large systems of linear equations.” 2015. Doctoral Dissertation, Baylor University. Accessed March 08, 2021. http://hdl.handle.net/2104/9511.

MLA Handbook (7^th Edition):

Nguyen, Huy V., 1986-. “Krylov methods for solving a sequence of large systems of linear equations.” 2015. Web. 08 Mar 2021.

Vancouver:

Nguyen, Huy V. 1. Krylov methods for solving a sequence of large systems of linear equations. [Internet] [Doctoral dissertation]. Baylor University; 2015. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/2104/9511.

Council of Science Editors:

Nguyen, Huy V. 1. Krylov methods for solving a sequence of large systems of linear equations. [Doctoral Dissertation]. Baylor University; 2015. Available from: http://hdl.handle.net/2104/9511

Delft University of Technology

15. Brahma, Sherine (author). Signal Modelling and Imaging of Low Field MRI.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:9c7ebf36-9bc6-41e1-b2c7-55d61c2c6c19

►

MRI machines are devices that are used to non-invasively obtain images of the internal anatomy and physiological processes of the human body. It is safe… (more)

Subjects/Keywords: MRI; Signal Processing; Krylov solvers; portable; low field; imaging

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APA (6^th Edition):

Brahma, S. (. (2019). Signal Modelling and Imaging of Low Field MRI. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:9c7ebf36-9bc6-41e1-b2c7-55d61c2c6c19

Chicago Manual of Style (16^th Edition):

Brahma, Sherine (author). “Signal Modelling and Imaging of Low Field MRI.” 2019. Masters Thesis, Delft University of Technology. Accessed March 08, 2021. http://resolver.tudelft.nl/uuid:9c7ebf36-9bc6-41e1-b2c7-55d61c2c6c19.

MLA Handbook (7^th Edition):

Brahma, Sherine (author). “Signal Modelling and Imaging of Low Field MRI.” 2019. Web. 08 Mar 2021.

Vancouver:

Brahma S(. Signal Modelling and Imaging of Low Field MRI. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2021 Mar 08]. Available from: http://resolver.tudelft.nl/uuid:9c7ebf36-9bc6-41e1-b2c7-55d61c2c6c19.

Council of Science Editors:

Brahma S(. Signal Modelling and Imaging of Low Field MRI. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:9c7ebf36-9bc6-41e1-b2c7-55d61c2c6c19

Universitat Politècnica de València

16. Campos González, María Carmen. Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios .

Degree: 2017, Universitat Politècnica de València

URL: http://hdl.handle.net/10251/86134

► The polynomial eigenvalue problem appears in many areas of scientific and technical computing. It can be seen as a generalization of the linear eigenvalue problem… (more)

▼ The polynomial eigenvalue problem appears in many areas of scientific and technical computing. It can be seen as a generalization of the linear eigenvalue problem in which the equation P(lambda)x = 0, that defines the problem, involves a polynomial P(lambda), of degree d, in the parameter lambda (the eigenvalue), and d+1 matrix coefficients. In its turn, the polynomial eigenvalue problem is a particular case of the nonlinear eigenvalue problem, T(lambda)x = 0, in which T is a nonlinear matrix function. These problems appear in diverse areas of application such as acoustics, fluid mechanics, structure analysis, or photonics. This thesis focuses on the study of methods for the numerical resolution of the polynomial eigenvalue problem, as well as the adaptation of such methods to the most general nonlinear case. Mainly, we consider methods of projection, that are appropriate for the case of sparse matrices of large dimension, where only a small percentage of eigevalues and eigenvectors are required. The algorithms are studied from the point of view of high-performance computing, considering issues like (computational and memory) efficiency and parallel computation. SLEPc, Scalable Library for Eigenvalue Problem Computations, is a software library for the parallel solution of large-scale eigenvalue problems. It is of general purpose and can be used for standard and generalized problems, both symmetric and nonsymmetric, with real or complex arithmetic. As a result of this thesis, we have developed several solvers for polynomial an nonlinear eigenproblems, which have included in the last versions of this software. On one hand, we consider methods based on the linearization of the polynomial problem, that solves an equivalent linear eigenproblem of dimension several times the initial size. Among them, the TOAR method stands out, that repre- sents the search subspace basis in an efficient way in terms of memory, and is appropriate to handle the increase of dimension of the linear problem. The thesis also proposes specific variants for the particular case of symmetric matrices. In all these methods we consider several aspects to provide the implementations with robustness and flexibility, such as spectral transformations, scaling, and techniques of extraction. In addition to the methods of linearization, we propose methods of Newton type, such as the method of Jacobi-Davidson with deflation and the method of Newton for invariant pairs. Due to its characteristics, the latter is not usually employed as a proper method, but as a technique for refinement of the solutions obtained with another method. The previous methods can also be applied to the resolution of the nonlinear problem, using techniques like polynomial or rational interpolation, being necessary in some cases to adapt the algorithms. This thesis covers also these cases. For all the considered algorithms we have made parallel implementations in SLEPc, and have studied its numerical behaviour and its parallel performance in problems coming from real… Advisors/Committee Members: Román Moltó, José Enrique (advisor).

Subjects/Keywords: computación paralela; valores propios; SLEPc; polinomios de matrices; métodos de Krylov

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

APA (6^th Edition):

Campos González, M. C. (2017). Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/86134

Chicago Manual of Style (16^th Edition):

Campos González, María Carmen. “Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios .” 2017. Doctoral Dissertation, Universitat Politècnica de València. Accessed March 08, 2021. http://hdl.handle.net/10251/86134.

MLA Handbook (7^th Edition):

Campos González, María Carmen. “Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios .” 2017. Web. 08 Mar 2021.

Vancouver:

Campos González MC. Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2017. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10251/86134.

Council of Science Editors:

Campos González MC. Implementación paralela de métodos iterativos para la resolución de problemas polinómicos de valores propios . [Doctoral Dissertation]. Universitat Politècnica de València; 2017. Available from: http://hdl.handle.net/10251/86134

University of New Mexico

17. Hobbs, Edward L. Asymptotic Neutronic Solutions for Fast Burst Reactor Design.

Degree: Nuclear Engineering, 2017, University of New Mexico

URL: https://digitalrepository.unm.edu/ne_etds/72

► Deterministic numerical methodologies for solving time-eigenvalue problems are valuable in characterizing the inherent rapid transient neutron behavior of a Fast Burst Reactor (FBR). New… (more)

▼ Deterministic numerical methodologies for solving time-eigenvalue problems are valuable in characterizing the inherent rapid transient neutron behavior of a Fast Burst Reactor (FBR). New nonlinear solution techniques used to solve eigenvalue problems show great promise in modeling the neutronics of reactors. This research utilizes nonlinear solution techniques to solve for the dominant time-eigenvalue associated with the asymptotic (exponential) solution to the neutron diffusion and even-parity form of the neutron transport equation, and lays the foundation for coupling with other physics phenomena associated with FBRs. High security costs and proliferation risks associated with Highly Enriched Uranium (HEU) fueled FBRs are the motivation for this research. Use of Low Enriched Uranium (LEU) as fuel reduces these risks to acceptable levels. However, the use of LEU fuel introduces complexities such as, increased volume, and longer neutron lifetimes. Numerical techniques are sought to explore these complexities and determine the limitations and potential of a LEU fueled FBR. A combination of deterministic and stochastic computational modeling techniques are tools used to investigate the effects these complexities have on reactor design and performance. Monte Carlo N-Particle (MCNP) code is useful to determine criticality and calculate reactor kinetics parameters of current and proposed designs. New deterministic methods are developed to directly calculate the fundamental time-eigenvalue in a way that will support multi-physics coupling. The methods incorporate Jacobian Free Newton Krylov solution techniques to address the nonlinear nature of the neutronics equations. These new deterministic models produce data to determine LEU designs that may meet the performance requirements of proven HEU FBRs in terms of neutron burst yield and burst duration (pulse width) based on the Nordheim-Fuchs model. This computational data and measured performance characteristics of historical LEU FBRs show that LEU designs can generate pulses that are beneficial for meeting Research and Development (R&D) requirements. These modern computational neutronic results indicate that a LEU fueled FBR is a plausible alternative to current HEU fueled reactors. Advisors/Committee Members: Cassiano R. Endres de Oliveira, Adam Hecht, Barry D. Ganapol, Patrick J. McDaniel.

Subjects/Keywords: burst reactor; Newton Krylov; Jacobian; time-eigenvalue; Nuclear Engineering

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

APA (6^th Edition):

Hobbs, E. L. (2017). Asymptotic Neutronic Solutions for Fast Burst Reactor Design. (Doctoral Dissertation). University of New Mexico. Retrieved from https://digitalrepository.unm.edu/ne_etds/72

Chicago Manual of Style (16^th Edition):

Hobbs, Edward L. “Asymptotic Neutronic Solutions for Fast Burst Reactor Design.” 2017. Doctoral Dissertation, University of New Mexico. Accessed March 08, 2021. https://digitalrepository.unm.edu/ne_etds/72.

MLA Handbook (7^th Edition):

Hobbs, Edward L. “Asymptotic Neutronic Solutions for Fast Burst Reactor Design.” 2017. Web. 08 Mar 2021.

Vancouver:

Hobbs EL. Asymptotic Neutronic Solutions for Fast Burst Reactor Design. [Internet] [Doctoral dissertation]. University of New Mexico; 2017. [cited 2021 Mar 08]. Available from: https://digitalrepository.unm.edu/ne_etds/72.

Council of Science Editors:

Hobbs EL. Asymptotic Neutronic Solutions for Fast Burst Reactor Design. [Doctoral Dissertation]. University of New Mexico; 2017. Available from: https://digitalrepository.unm.edu/ne_etds/72

University of Maryland

18. Forstall, Virginia Hardy. Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations.

Degree: Applied Mathematics and Scientific Computation, 2015, University of Maryland

URL: http://hdl.handle.net/1903/17232

► This dissertation considers efficient computational algorithms for solving parameterized discrete partial differential equations (PDEs) using techniques of reduced-order modeling. Parameterized equations of this type arise… (more)

▼ This dissertation considers efficient computational algorithms for solving parameterized discrete partial differential equations (PDEs) using techniques of reduced-order modeling. Parameterized equations of this type arise in numerous mathematical models. In some settings, e.g. sensitivity analysis, design optimization, and uncertainty quantification, it is necessary to compute discrete solutions of the PDEs at many parameter values. Accuracy considerations often lead to algebraic systems with many unknowns whose solution via traditional methods can be expensive. Reduced-order models use a reduced space to approximate the parameterized PDE, where the reduced space is of a significantly smaller dimension than that of the discrete PDE. Solving an approximation of the problem on the reduced space leads to reduction in cost, often with little loss of accuracy. In the reduced basis method, an offline step finds an approximation of the solution space and an online step utilizes this approximation to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it is more effective to use iterative methods to solve the reduced problem. To demonstrate this we construct preconditioners for the reduced-order models or construct well-conditioned reduced-order models. We demonstrate that by using iterative methods, reduced-order models of larger dimension can be effective. There are several reasons that iterative methods are well suited to reduced- order modeling. In particular, we take advantage of the similarity of the realizations of parameterized systems, either by reusing preconditioners or by recycling Krylov vectors. These two approaches are shown to be effective when the underlying PDE is linear. For nonlinear problems, we utilize the discrete empirical interpolation method (DEIM) to cheaply evaluate the nonlinear components of the reduced model. The method identifies points in the PDE discretization necessary for representing the nonlinear component of the reduced model accurately. This approach incurs online computational costs that are independent of the spatial dimension of the discretized PDE. When this method is used to assemble the reduced model cheaply, iterative methods are shown to further improve efficiency in the online step. Finally, when the traditional offline/online approach is ineffective for a given problem, reduced-order models can be used to accelerate the solution of the full model. We follow the solution model of Krylov subspace recycling methods for sequences of linear systems where the coefficient matrices vary. A Krylov subspace recycling method contains a reduced-order model and an iterative method that… Advisors/Committee Members: Elman, Howard C (advisor).

Subjects/Keywords: Applied mathematics; iterative solvers; Krylov subspace recycling; reduced-order modeling

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APA (6^th Edition):

Forstall, V. H. (2015). Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/17232

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):

Forstall, Virginia Hardy. “Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations.” 2015. Thesis, University of Maryland. Accessed March 08, 2021. http://hdl.handle.net/1903/17232.

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

MLA Handbook (7^th Edition):

Forstall, Virginia Hardy. “Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations.” 2015. Web. 08 Mar 2021.

Vancouver:

Forstall VH. Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations. [Internet] [Thesis]. University of Maryland; 2015. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1903/17232.

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

Council of Science Editors:

Forstall VH. Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations. [Thesis]. University of Maryland; 2015. Available from: http://hdl.handle.net/1903/17232

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

Virginia Tech

19. Flagg, Garret Michael. Interpolation Methods for the Model Reduction of Bilinear Systems.

Degree: PhD, Mathematics, 2012, Virginia Tech

URL: http://hdl.handle.net/10919/27521

► Bilinear systems are a class of nonlinear dynamical systems that arise in a variety of applications. In order to obtain a sufficiently accurate representation of… (more)

Subjects/Keywords: Optimization; Model Reduction; Nonlinear systems; Interpolation theory; Rational Krylov subspace methods

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

APA (6^th Edition):

Flagg, G. M. (2012). Interpolation Methods for the Model Reduction of Bilinear Systems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/27521

Chicago Manual of Style (16^th Edition):

Flagg, Garret Michael. “Interpolation Methods for the Model Reduction of Bilinear Systems.” 2012. Doctoral Dissertation, Virginia Tech. Accessed March 08, 2021. http://hdl.handle.net/10919/27521.

MLA Handbook (7^th Edition):

Flagg, Garret Michael. “Interpolation Methods for the Model Reduction of Bilinear Systems.” 2012. Web. 08 Mar 2021.

Vancouver:

Flagg GM. Interpolation Methods for the Model Reduction of Bilinear Systems. [Internet] [Doctoral dissertation]. Virginia Tech; 2012. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10919/27521.

Council of Science Editors:

Flagg GM. Interpolation Methods for the Model Reduction of Bilinear Systems. [Doctoral Dissertation]. Virginia Tech; 2012. Available from: http://hdl.handle.net/10919/27521

Virginia Tech

20. Brown, Matthew Allen. On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems.

Degree: MS, Mathematics, 2015, Virginia Tech

URL: http://hdl.handle.net/10919/51546

► Iterative Krylov subspace methods have proven to be efficient tools for solving linear systems of equations. In the context of ill-posed inverse problems, they tend… (more)

Subjects/Keywords: Ill-posed inverse problems; Krylov subspace; Arnoldi process; Golub-Kahan bidiagonalization

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APA (6^th Edition):

Brown, M. A. (2015). On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/51546

Chicago Manual of Style (16^th Edition):

Brown, Matthew Allen. “On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems.” 2015. Masters Thesis, Virginia Tech. Accessed March 08, 2021. http://hdl.handle.net/10919/51546.

MLA Handbook (7^th Edition):

Brown, Matthew Allen. “On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems.” 2015. Web. 08 Mar 2021.

Vancouver:

Brown MA. On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems. [Internet] [Masters thesis]. Virginia Tech; 2015. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10919/51546.

Council of Science Editors:

Brown MA. On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems. [Masters Thesis]. Virginia Tech; 2015. Available from: http://hdl.handle.net/10919/51546

Virginia Tech

21. Wyatt, Sarah Alice. Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs.

Degree: PhD, Mathematics, 2012, Virginia Tech

URL: http://hdl.handle.net/10919/27668

► Dynamical systems are mathematical models characterized by a set of differential or difference equations. Model reduction aims to replace the original system with a reduced… (more)

▼ Dynamical systems are mathematical models characterized by a set of differential or difference equations. Model reduction aims to replace the original system with a reduced system of significantly smaller dimension that still describes the important dynamics of the large-scale model. Interpolatory model reduction methods define a reduced model that interpolates the full model at selected interpolation points. The reduced model may be obtained through a Krylov reduction process or by using the Iterative Rational Krylov Algorithm (IRKA), which iterates this Krylov reduction process to obtain an optimal \mathcal{H}₂ reduced model. This dissertation studies interpolatory model reduction for first-order descriptor systems, second-order systems, and DAEs. The main computational cost of interpolatory model reduction is the associated linear systems. Especially in the large-scale setting, inexact solves become desirable if not necessary. With the introduction of inexact solutions, however, exact interpolation no longer holds. While the effect of this loss of interpolation has previously been studied, we extend the discussion to the preconditioned case. Then we utilize IRKA's convergence behavior to develop preconditioner updates. We also consider the interpolatory framework for DAEs and second-order systems. While interpolation results still hold, the singularity associated with the DAE often results in unbounded model reduction errors. Therefore, we present a theorem that guarantees interpolation and a bounded model reduction error. Since this theorem relies on expensive projectors, we demonstrate how interpolation can be achieved without explicitly computing the projectors for index-1 and Hessenberg index-2 DAEs. Finally, we study reduction techniques for second-order systems. Many of the existing methods for second-order systems rely on the model's associated first-order system, which results in computations of a 2n system. As a result, we present an IRKA framework for the reduction of second-order systems that does not involve the associated 2n system. The resulting algorithm is shown to be effective for several dynamical systems. Advisors/Committee Members: Gugercin, Serkan (committeechair), de Sturler, Eric (committee member), Borggaard, Jeffrey T. (committee member), Beattie, Christopher A. (committee member).

Subjects/Keywords: Second-order Systems; Inexact Solves; Krylov reduction; DAEs

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

APA (6^th Edition):

Wyatt, S. A. (2012). Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/27668

Chicago Manual of Style (16^th Edition):

Wyatt, Sarah Alice. “Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs.” 2012. Doctoral Dissertation, Virginia Tech. Accessed March 08, 2021. http://hdl.handle.net/10919/27668.

MLA Handbook (7^th Edition):

Wyatt, Sarah Alice. “Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs.” 2012. Web. 08 Mar 2021.

Vancouver:

Wyatt SA. Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs. [Internet] [Doctoral dissertation]. Virginia Tech; 2012. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10919/27668.

Council of Science Editors:

Wyatt SA. Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs. [Doctoral Dissertation]. Virginia Tech; 2012. Available from: http://hdl.handle.net/10919/27668

Delft University of Technology

22. Belier, Joris (author). Wave Dynamics in Inverse Krylov Subspaces.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:e12eb0e2-67a2-4640-8598-3f639f12cea4

► Recent studies have shown an increased interest in modal solutions of wave problems with resonating structures. These studies demonstrate that resonating structures with physical dimensions… (more)

▼ Recent studies have shown an increased interest in modal solutions of wave problems with resonating structures. These studies demonstrate that resonating structures with physical dimensions close to a wavelength can be accurately described by a few relevant resonating modes. The physical dimensions of the demonstrated resonating structures were close to a wavelength, which suggests that these highly-resonating modes have relatively low eigenvalues. Those resonating-modes are therefore dominantly present in Krylov subspaces generated by inverse projections of the wave-operator. Relevant wave dynamics can, therefore, be effectively computed from inverse Krylov subspaces. Furthermore, inverse Krylov subspaces are computationally stable and are therefore a powerful way to compute high-fidelity modal solutions. With interesting applications in high Q-factor wave problems. The aim of this work is on improving the performance of inverse Krylov subspaces. Improvements to inverse Krylov subspace can be grouped into two approaches. In the first approach symmetry is exploited in the inverse wave-operator for reduced computational complexity and in the second approach the wave-operator is conditioned for desirable characteristics at the relatively low side of the spectrum. We will study several wave-operator configurations and optimize according to those approaches. Earlier studies have shown that in the dimensions with pseudo-periodic boundary conditions, the double-curl is efficiently eigendecomposed as spatial derivatives are diagonal operators acting on frequency representations. We extend this work by providing an alternative, more compact presentation in the continuous domain of the eigendecomposition of the double-curl. This eigendecomposition is used to create a nullspace free eigenvalue problem. Consecutively, we analyse the characteristics of the inverse wave-operator with Perfectly Matched Layers (PML). This analysis shows that in terms of inverse Krylov subspaces, the PML is not the obvious choice for the optimal absorbing boundary condition. Most notably, the PML introduces undesirable effects at the lower end of the spectrum, significantly impeding the performance of inverse Krylov subspaces, which leads to the conclusion that absorbing boundary conditions should be reassessed in terms of inverse Krylov subspaces behaviour. Lastly, we will study the so-called Fixed-Frequency PML (FF-PML), which is a PML inspired time-independent absorbing boundary condition. Our study has shown that the FF-PML is a more suitable absorbing boundary condition candidate for inverse Krylov subspaces. It does not have the undesirable effects at the lower end of the spectrum, which the traditional PML has. Furthermore, and even more importantly, we derive analytic expressions of the inverse wave operator with FF-PML absorbing boundary conditions. This simple and novel insight is easily exploited to invert the wave-operator efficiently, which enables a new approach to the computation of modal solutions of open scattering problems. The… Advisors/Committee Members: Remis, Rob (mentor), Delft University of Technology (degree granting institution).

Subjects/Keywords: Wave simulation; Reduced order model; Krylov; Modes; Periodic boundary condition; PML

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

APA (6^th Edition):

Belier, J. (. (2019). Wave Dynamics in Inverse Krylov Subspaces. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:e12eb0e2-67a2-4640-8598-3f639f12cea4

Chicago Manual of Style (16^th Edition):

Belier, Joris (author). “Wave Dynamics in Inverse Krylov Subspaces.” 2019. Masters Thesis, Delft University of Technology. Accessed March 08, 2021. http://resolver.tudelft.nl/uuid:e12eb0e2-67a2-4640-8598-3f639f12cea4.

MLA Handbook (7^th Edition):

Belier, Joris (author). “Wave Dynamics in Inverse Krylov Subspaces.” 2019. Web. 08 Mar 2021.

Vancouver:

Belier J(. Wave Dynamics in Inverse Krylov Subspaces. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2021 Mar 08]. Available from: http://resolver.tudelft.nl/uuid:e12eb0e2-67a2-4640-8598-3f639f12cea4.

Council of Science Editors:

Belier J(. Wave Dynamics in Inverse Krylov Subspaces. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:e12eb0e2-67a2-4640-8598-3f639f12cea4

23. Hijazi, Abdallah. Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique.

Degree: Docteur es, Electronique des Hautes Fréquences et Optoélectronique, 2015, Limoges

URL: http://www.theses.fr/2015LIMO0139

►

MOR (Model Order Reduction) est devenu un domaine très répondu dans la recherche grâce à l'intérêt qu'il peut apporter dans la réduction des systèmes, ce… (more)

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MOR (Model Order Reduction) est devenu un domaine très répondu dans la recherche grâce à l'intérêt qu'il peut apporter dans la réduction des systèmes, ce qui permet d'économiser du temps, de la mémoire et le coût de CPU pour les outils de CAO. Ce domaine contient principalement deux branches: linéaires et non linéaires. MOR linéaire est un domaine mature avec des techniques numériques bien établie et bien connus dans la domaine de la recherche, par contre le domaine non linéaire reste vague, et jusqu'à présent il n'a pas montré des bons résultats dans la simulation des circuits électriques. La recherche est toujours en cours dans ce domaine, en raison de l’intérêt qu'il peut fournir aux simulateurs contemporains, surtout avec la croissance des puces électroniques en termes de taille et de complexité, et les exigences industrielles vers l'intégration des systèmes sur la même puce.Une contribution significative, pour résoudre le problème de Harmonic Balance (Equilibrage Harmonique) en utilisant la technique MOR, a été proposé en 2002 par E. Gad et M. Nakhla. La technique a montré une réduction substantielle de la dimension du système, tout en préservant, en sortie, la précision de l'analyse en régime permanent. Cette méthode de MOR utilise la technique de projection par l'intermédiaire de Krylov, et il préserve la passivité du système. Cependant, il souffre de quelques limitations importantes dans la construction de la matrice “pre-conditioner“ qui permettrait de réduire le système. La limitation principale est la nécessité d'une factorisation explicite comme une suite numérique de l'équation des dispositifs non linéaires . cette limitation rend la technique difficile à appliquer dans les conditions générales d'un simulateur. Cette thèse examinera les aspects non linéaires du modèle de réduction pour les équations de bilan harmoniques, et il étudiera les solutions pour surmonter les limitations mentionnées ci-dessus, en particulier en utilisant des approches de dérivateur numériques.

MOR recently became a well-known research field, due to the interest that it shows in reducing the system, which saves time, memory, and CPU cost for CAD tools. This field contains two branches, linear and nonlinear MOR, the linear MOR is a mature domain with well-established theory and numerical techniques. Meanwhile, nonlinear MOR domain is still stammering, and so far it didn’t show good and successful results in electrical circuit simulation. Some improvements however started to pop-up recently, and research is still going on this field because of the help that it can give to the contemporary simulators, especially with the growth of the electronic chips in terms of size and complexity due to industrial demands towards integrating systems on the same chip. A significant contribution in the MOR technique of HB solution has been proposed a decade ago by E. Gad and M. Nakhla. The technique has shown to provide a substantial system dimension reduction while preserving the precision of the output in steady state analysis. This MOR method…

Advisors/Committee Members: Ngoya, Edouard (thesis director).

Subjects/Keywords: Réduction de circuit; Equilibrage harmonique; Projection de Krylov; Circuit non-linéaires; MOR; Circuit reduction; Harmonic balance; Krylov-projection; Nonlinear circuits; MOR; 519.7

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

APA (6^th Edition):

Hijazi, A. (2015). Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique. (Doctoral Dissertation). Limoges. Retrieved from http://www.theses.fr/2015LIMO0139

Chicago Manual of Style (16^th Edition):

Hijazi, Abdallah. “Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique.” 2015. Doctoral Dissertation, Limoges. Accessed March 08, 2021. http://www.theses.fr/2015LIMO0139.

MLA Handbook (7^th Edition):

Hijazi, Abdallah. “Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique.” 2015. Web. 08 Mar 2021.

Vancouver:

Hijazi A. Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique. [Internet] [Doctoral dissertation]. Limoges; 2015. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2015LIMO0139.

Council of Science Editors:

Hijazi A. Implementation of harmonic balance reduce model order equation : Techniques de réduction d’ordre des modèles pour la mise en œuvre de la méthode de l'équilibrage harmonique. [Doctoral Dissertation]. Limoges; 2015. Available from: http://www.theses.fr/2015LIMO0139

INP Toulouse

24. Ferreira Lago, Rafael. A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique.

Degree: Docteur es, Sûreté de logiciel et calcul de haute performance, 2013, INP Toulouse

URL: http://www.theses.fr/2013INPT0041

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Les travaux de ce doctorat concernent le développement de méthodes itératives pour la résolution de systèmes linéaires creux de grande taille comportant de nombreux seconds… (more)

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Les travaux de ce doctorat concernent le développement de méthodes itératives pour la résolution de systèmes linéaires creux de grande taille comportant de nombreux seconds membres. L’application visée est la résolution d’un problème inverse en géophysique visant à reconstruire la vitesse de propagation des ondes dans le sous-sol terrestre. Lorsque de nombreuses sources émettrices sont utilisées, ce problème inverse nécessite la résolution de systèmes linéaires complexes non symétriques non hermitiens comportant des milliers de seconds membres. Dans le cas tridimensionnel ces systèmes linéaires sont reconnus comme difficiles à résoudre plus particulièrement lorsque des fréquences élevées sont considérées. Le principal objectif de cette thèse est donc d’étendre les développements existants concernant les méthodes de Krylov par bloc. Nous étudions plus particulièrement les techniques de déflation dans le cas multiples seconds membres et recyclage de sous-espace dans le cas simple second membre. Des gains substantiels sont obtenus en terme de temps de calcul par rapport aux méthodes existantes sur des applications réalistes dans un environnement parallèle distribué.

This PhD thesis concerns the development of flexible Krylov subspace iterative solvers for the solution of large sparse linear systems of equations with multiple right-hand sides. Our target application is the solution of the acoustic full waveform inversion problem in geophysics associated with the phenomena of wave propagation through an heterogeneous model simulating the subsurface of Earth. When multiple wave sources are being used, this problem gives raise to large sparse complex non-Hermitian and nonsymmetric linear systems with thousands of right-hand sides. Specially in the three-dimensional case and at high frequencies, this problem is known to be difficult. The purpose of this thesis is to develop a flexible block Krylov iterative method which extends and improves techniques already available in the current literature to the multiple right-hand sides scenario. We exploit the relations between each right-hand side to accelerate the convergence of the overall iterative method. We study both block deflation and single right-hand side subspace recycling techniques obtaining substantial gains in terms of computational time when compared to other strategies published in the literature, on realistic applications performed in a parallel environment.

Advisors/Committee Members: Gratton, Serge (thesis director), Vasseur, Xavier (thesis director).

Subjects/Keywords: Sous-espaces de Krylov; Méthodes itératives; Calcul de haute performance; Equation de Helmholtz; Imagerie sismique; Krylov subspace methods; Iterative methods; High performance computing; Helmholtz equation; Earth imaging

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

APA (6^th Edition):

Ferreira Lago, R. (2013). A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2013INPT0041

Chicago Manual of Style (16^th Edition):

Ferreira Lago, Rafael. “A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique.” 2013. Doctoral Dissertation, INP Toulouse. Accessed March 08, 2021. http://www.theses.fr/2013INPT0041.

MLA Handbook (7^th Edition):

Ferreira Lago, Rafael. “A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique.” 2013. Web. 08 Mar 2021.

Vancouver:

Ferreira Lago R. A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique. [Internet] [Doctoral dissertation]. INP Toulouse; 2013. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2013INPT0041.

Council of Science Editors:

Ferreira Lago R. A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics : Étude de méthodes itératives par bloc avec application à l’imagerie sismique en géophysique. [Doctoral Dissertation]. INP Toulouse; 2013. Available from: http://www.theses.fr/2013INPT0041

25. Barkouki, Houda. Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles.

Degree: Docteur es, Mathématiques, 2016, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Faculté des sciences et techniques Guéliz

URL: http://www.theses.fr/2016DUNK0440

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La solution numérique des systèmes dynamiques est un moyen efficace pour étudier des phénomènes physiques complexes. Cependant, dans un cadre à grande échelle, la dimension… (more)

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La solution numérique des systèmes dynamiques est un moyen efficace pour étudier des phénomènes physiques complexes. Cependant, dans un cadre à grande échelle, la dimension du système rend les calculs infaisables en raison des limites de mémoire et de temps, ainsi que le mauvais conditionnement. La solution de ce problème est la réduction de modèles. Cette thèse porte sur les méthodes de projection pour construire efficacement des modèles d'ordre inférieur à partir des systèmes linéaires dynamiques de grande taille. En particulier, nous nous intéressons à la projection sur la réunion de plusieurs sous-espaces de Krylov standard qui conduit à une classe de modèles d'ordre réduit. Cette méthode est connue par l'interpolation rationnelle. En se basant sur ce cadre théorique qui relie la projection de Krylov à l'interpolation rationnelle, quatre algorithmes de type Lanczos rationnel pour la réduction de modèles sont proposés. Dans un premier temps, nous avons introduit une méthode adaptative de type Lanczos rationnel par block pour réduire l'ordre des systèmes linéaires dynamiques de grande taille, cette méthode est basée sur l'algorithme de Lanczos rationnel par block et une méthode adaptative pour choisir les points d'interpolation. Une généralisation de ce premier algorithme est également donnée, où différentes multiplicités sont considérées pour chaque point d'interpolation. Ensuite, nous avons proposé une autre extension de la méthode du sous-espace de Krylov standard pour les systèmes à plusieurs-entrées plusieurs-sorties, qui est le sous-espace de Krylov global. Nous avons obtenu des équations qui décrivent cette procédure. Finalement, nous avons proposé une méthode de Lanczos étendu par block et nous avons établi de nouvelles propriétés algébriques pour cet algorithme. L'efficacité et la précision de tous les algorithmes proposés, appliqués sur des problèmes de réduction de modèles, sont testées dans plusieurs exemples numériques.

Numerical solution of dynamical systems have been a successful means for studying complex physical phenomena. However, in large-scale setting, the system dimension makes the computations infeasible due to memory and time limitations, and ill-conditioning. The remedy of this problem is model reductions. This dissertations focuses on projection methods to efficiently construct reduced order models for large linear dynamical systems. Especially, we are interesting by projection onto unions of Krylov subspaces which lead to a class of reduced order models known as rational interpolation. Based on this theoretical framework that relate Krylov projection to rational interpolation, four rational Lanczos-type algorithms for model reduction are proposed. At first, an adaptative rational block Lanczos-type method for reducing the order of large scale dynamical systems is introduced, based on a rational block Lanczos algorithm and an adaptive approach for choosing the interpolation points. A generalization of the first algorithm is also given where different multiplicities are consider for each…

Advisors/Committee Members: Jbilou, Khalid (thesis director), Bentbib, Abdeslem Hafid (thesis director).

Subjects/Keywords: Algorithme de Lanczos; Fonction de transfert; Moment correspondant; Réduction de modèle; Sous-espace de Krylov rationnel; Lanczos algorithm; Transfer function; Moment matching; Model reduction; Rational Krylov subspace

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

APA (6^th Edition):

Barkouki, H. (2016). Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles. (Doctoral Dissertation). Littoral; Université Cadi Ayyad (Marrakech, Maroc). Faculté des sciences et techniques Guéliz. Retrieved from http://www.theses.fr/2016DUNK0440

Chicago Manual of Style (16^th Edition):

Barkouki, Houda. “Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles.” 2016. Doctoral Dissertation, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Faculté des sciences et techniques Guéliz. Accessed March 08, 2021. http://www.theses.fr/2016DUNK0440.

MLA Handbook (7^th Edition):

Barkouki, Houda. “Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles.” 2016. Web. 08 Mar 2021.

Vancouver:

Barkouki H. Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles. [Internet] [Doctoral dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc). Faculté des sciences et techniques Guéliz; 2016. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2016DUNK0440.

Council of Science Editors:

Barkouki H. Rational Lanczos-type methods for model order reduction : Méthodes de type Lanczos rationnel pour la réduction de modèles. [Doctoral Dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc). Faculté des sciences et techniques Guéliz; 2016. Available from: http://www.theses.fr/2016DUNK0440

26. Hached, Mustapha. Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations.

Degree: Docteur es, Mathématiques appliquées, 2012, Littoral

URL: http://www.theses.fr/2012DUNK0315

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Cette thèse porte sur des méthode de résolution d'équations matricielles appliquées à la résolution numérique d'équations aux dérivées partielles ou des problèmes de contrôle linéaire.… (more)

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Cette thèse porte sur des méthode de résolution d'équations matricielles appliquées à la résolution numérique d'équations aux dérivées partielles ou des problèmes de contrôle linéaire. On s'intéressen en premier lieu à des équations matricielles linéaires. Après avoir donné un aperçu des méthodes classiques employées pour les équations de Sylvester et de Lyapunov, on s'intéresse au cas d'équations linéaires générales de la forme M(X)=C, où M est un opérateur linéaire matriciel. On expose la méthode de GMRES globale qui s'avère particulièrement utile dans le cas où M(X) ne peut s'exprimer comme un polynôme du premier degré en X à coefficients matriciels, ce qui est le cas dans certains problèmes de résolution numérique d'équations aux dérivées partielles. Nous proposons une approche, noté LR-BA-ADI consistant à utiliser un préconditionnement de type ADI qui transforme l'équation de Sylvester en une équation de Stein que nous résolvons par une méthode de Krylox par blocs. Enfin, nous proposons une méthode de type Newton-Krylov par blocs avec préconditionnement ADI pour les équations de Riccati issues de problèmes de contrôle linéaire quadratique. Cette méthode est dérivée de la méthode LR-BA-ADI. Des résultats de convergence et de majoration de l'erreur sont donnés. Dans la seconde partie de ce travail, nous appliquons les méthodes exposées dans la première partie de ce travail à des problèmes d'équations aux dérivées partielles. Nous nous intéressons d'abord à la résolution numérique d'équations couplées de type Burgers évolutives en dimension 2. Ensuite, nous nous intéressons au cas où le domaine borné est choisi quelconque. Nous établissons des résultats théoriques de l'existence de tels interpolants faisant appel à des techniques d'algèbre linéaire.

This thesis deals with some matrix equations involved in numerical resolution of partial differential equations and linear control. We first consider some numerical resolution techniques of linear matrix equation. In the second part of this thesis, we apply these resolution techniques to problems related to partial differential equations.

Advisors/Committee Members: Jbilou, Khalid (thesis director), Bouhamidi, Abderrahman (thesis director).

Subjects/Keywords: Approximation; Arnoldi; Burgers; Chaleur; Equations aux dérivées partielles; GMRES; Krylov; Lyapunov; Meshless; Newton; RBF; Riccati; Sylvester; Approximation; Arnoldi; Burgers; Heat; PDE; GMRES; Krylov; Lyapunov; Meshless; Newton; RBF; Riccati; Sylvester

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

APA (6^th Edition):

Hached, M. (2012). Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations. (Doctoral Dissertation). Littoral. Retrieved from http://www.theses.fr/2012DUNK0315

Chicago Manual of Style (16^th Edition):

Hached, Mustapha. “Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations.” 2012. Doctoral Dissertation, Littoral. Accessed March 08, 2021. http://www.theses.fr/2012DUNK0315.

MLA Handbook (7^th Edition):

Hached, Mustapha. “Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations.” 2012. Web. 08 Mar 2021.

Vancouver:

Hached M. Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations. [Internet] [Doctoral dissertation]. Littoral; 2012. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2012DUNK0315.

Council of Science Editors:

Hached M. Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles : Matrix Krylov methods applied to partial differential equations. [Doctoral Dissertation]. Littoral; 2012. Available from: http://www.theses.fr/2012DUNK0315

INP Toulouse

27. Pinel, Xavier. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.

Degree: Docteur es, Mathématiques, Informatiques et Télécommunication, 2010, INP Toulouse

URL: http://www.theses.fr/2010INPT0033

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Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces… (more)

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Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces méthodes seront en particulier utilisées dans le cadre d'une application géophysique : la migration sismique visant à simuler la propagation d'ondes sous la surface de la terre. Le problème prend la forme d'une équation d'Helmholtz dans le domaine fréquentiel en trois dimensions, discrétisée par des différences finies et donnant lieu à un système linéaire creux, complexe, non-symétrique, non-hermitien. De plus, lorsque de grands nombres d'onde sont considérés, cette matrice possède une taille élevée et est indéfinie. Du fait de ces propriétés, nous nous proposons d'étudier des méthodes de Krylov préconditionnées par des techniques hiérarchiques deux niveaux. Un tel pre-conditionnement s'est montré particulièrement efficace en deux dimensions et le but de cette thèse est de relever le défi de l'adapter au cas tridimensionel. Pour ce faire, des méthodes de Krylov sont utilisées à la fois comme lisseur et comme méthode de résolution du problème grossier. Ces derniers choix induisent l'emploi de méthodes de Krylov dites flexibles.

The topic of this PhD thesis is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown efficient for two-dimensional applications and the purpose of this thesis is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver.

Advisors/Committee Members: Gratton, Serge (thesis director).

Subjects/Keywords: Equation d'Helmholtz; Méthodes de Krylov; Multigrille; Analyse de Fourier; Programmation parrallèle; Seconds membres multiples; Krylov methods; Multigrid; Helmholtz problems; Fourier analysis; Super computers; Geophysics; Multiple right-hand sides problems

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

APA (6^th Edition):

Pinel, X. (2010). A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2010INPT0033

Chicago Manual of Style (16^th Edition):

Pinel, Xavier. “A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.” 2010. Doctoral Dissertation, INP Toulouse. Accessed March 08, 2021. http://www.theses.fr/2010INPT0033.

MLA Handbook (7^th Edition):

Pinel, Xavier. “A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique.” 2010. Web. 08 Mar 2021.

Vancouver:

Pinel X. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. [Internet] [Doctoral dissertation]. INP Toulouse; 2010. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2010INPT0033.

Council of Science Editors:

Pinel X. A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics : Un preconditionnement perturbé à deux niveaux pour la résolution de problèmes d'Helmholtz hétérogènes dans le cadre d'une application en géophysique. [Doctoral Dissertation]. INP Toulouse; 2010. Available from: http://www.theses.fr/2010INPT0033

28. Al Daas, Hussam. Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling.

Degree: Docteur es, Mathématiques appliquées, 2018, Sorbonne université

URL: http://www.theses.fr/2018SORUS329

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Cette thèse présente un travail sur les méthodes itératives pour résoudre des systèmes linéaires en réduisant les communications pendant les calculs parallèles. Principalement, on est… (more)

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Cette thèse présente un travail sur les méthodes itératives pour résoudre des systèmes linéaires en réduisant les communications pendant les calculs parallèles. Principalement, on est intéressé par les systèmes linéaires qui proviennent des simulations de réservoirs. Trois approches, que l’on peut considérer comme indépendantes, sont présentées. Nous considérons les systèmes linéaires non-symétriques (resp. symétriques), cela correspond au schéma explicite (resp. implicite) du problème modèle. On commence par présenter une approche qui ajoute plusieurs directions de recherche à chaque itération au lieu d’une seule direction comme dans le cas des méthodes classiques. Ensuite, on considère les stratégies de recyclage des espaces de recherche. Ces stratégies réduisent, par un facteur considérable, le nombre d’itérations global pour résoudre une séquence de systèmes linéaires. On fait un rappel des stratégies existantes et l’on en présente une nouvelle. On introduit et détaille l’implémentation parallèle de ces méthodes en utilisant un langage bas niveau. On présente des résultats numériques séquentiels et parallèles. Finalement, on considère la méthode de décomposition de domaine algébrique. Dans un environnement algébrique, on étudie le préconditionneur de Schwarz additif à deux niveaux. On fournit la forme algébrique explicite d’une classe d’espaces grossiers locaux qui bornent le conditionnement par un nombre donné a priori.

This thesis presents a work on iterative methods for solving linear systems that aim at reducing the communication in parallel computing. The main type of linear systems in which we are interested arises from a real-life reservoir simulation. Both schemes, implicit and explicit, of modelling the system are taken into account. Three approaches are studied separately. We consider non-symmetric (resp. symmetric) linear systems. This corresponds to the explicit (resp. implicit) formulation of the model problem. We start by presenting an approach that adds multiple search directions per iteration rather than one as in the classic iterative methods. Then, we discuss different strategies of recycling search subspaces. These strategies reduce the global iteration count of a considerable factor during a sequence of linear systems. We review different existing strategies and present a new one. We discuss the parallel implementation of these methods using a low-level language. Numerical experiments for both sequential and parallel implementations are presented. We also consider the algebraic domain decomposition approach. In an algebraic framework, we study the two-level additive Schwarz preconditioner. We provide the algebraic explicit form of a class of local coarse spaces that bounds the spectral condition number of the preconditioned matrix by a number pre-defined.

Advisors/Committee Members: Grigori, Laura (thesis director), Hénon, Pascal (thesis director).

Subjects/Keywords: Krylov; Méthodes par bloc; Breakdown inexacte; Déflation; Recyclage; Décomposition de domaine; Krylov; Block methods; Inexact breakdown; Deflation; Recycling; Domain decomposition; 003.74; 518.26

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

APA (6^th Edition):

Al Daas, H. (2018). Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling. (Doctoral Dissertation). Sorbonne université. Retrieved from http://www.theses.fr/2018SORUS329

Chicago Manual of Style (16^th Edition):

Al Daas, Hussam. “Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling.” 2018. Doctoral Dissertation, Sorbonne université. Accessed March 08, 2021. http://www.theses.fr/2018SORUS329.

MLA Handbook (7^th Edition):

Al Daas, Hussam. “Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling.” 2018. Web. 08 Mar 2021.

Vancouver:

Al Daas H. Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling. [Internet] [Doctoral dissertation]. Sorbonne université; 2018. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2018SORUS329.

Council of Science Editors:

Al Daas H. Résolution de systèmes linéaires issus de la modélisation des réservoirs : Solving linear systems arising from reservoirs modelling. [Doctoral Dissertation]. Sorbonne université; 2018. Available from: http://www.theses.fr/2018SORUS329

29. Ul Jabbar, Absaar. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.

Degree: 2018, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-19859

► Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid… (more)

▼ Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid methods is that they have an asymptotically meshindependent convergence behavior. Multigrid with Vanka (or local multilevel pressure Schur complement method) as smoother have been frequently used for the construction of very effcient coupled monolithic solvers for the solution of the stationary incompressible Navier-Stokes equations in 2D and 3D. However, due to its innate Gauß-Seidel/Jacobi character, Vanka has a strong influence of the underlying mesh, and therefore, coupled multigrid solvers with Vanka smoothing very frequently face convergence issues on meshes with high aspect ratios. Moreover, even on very nice regular grids, these solvers may fail when the anisotropies are introduced from the differential operator. In this thesis, we develop a new class of robust and efficient monolithic finite element multilevel Krylov subspace methods (MLKM) for the solution of the stationary incompressible Navier-Stokes equations as an alternative to the coupled multigrid-based solvers. Different from multigrid, the MLKM utilizes a Krylov method as the basis in the error reduction process. The solver is based on the multilevel projection-based method of Erlangga and Nabben, which accelerates the convergence of the Krylov subspace methods by shifting the small eigenvalues of the system matrix, responsible for the slow convergence of the Krylov iteration, to the largest eigenvalue. Before embarking on the Navier-Stokes equations, we first test our implementation of the MLKM solver by solving scalar model problems, namely the convection-diffusion problem and the anisotropic diffusion problem. We validate the method by solving several standard benchmark problems. Next, we present the numerical results for the solution of the incompressible Navier-Stokes equations in two dimensions. The results show that the MLKM solvers produce asymptotically mesh-size independent, as well as Reynolds number independent convergence rates, for a moderate range of Reynolds numbers. Moreover, numerical simulations also show that the coupled MLKM solvers can handle (both mesh and operator based) anisotropies better than the coupled multigrid solvers. Advisors/Committee Members: Turek, Stefan (advisor), Blum, Heribert (referee).

Subjects/Keywords: Monolithic multilevel methods; Krylov subspaces; GMRES; FEM; Navier-Stokes equations; Saddle point problems; 510; Multi-level-Verfahren; Krylov-Verfahren; Finite-Elemente-Methode; Navier-Stokes-Gleichung

Record Details Similar Records Cite « Share

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

APA (6^th Edition):

Ul Jabbar, A. (2018). Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-19859

Chicago Manual of Style (16^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Doctoral Dissertation, Technische Universität Dortmund. Accessed March 08, 2021. http://dx.doi.org/10.17877/DE290R-19859.

MLA Handbook (7^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Web. 08 Mar 2021.

Vancouver:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2018. [cited 2021 Mar 08]. Available from: http://dx.doi.org/10.17877/DE290R-19859.

Council of Science Editors:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Doctoral Dissertation]. Technische Universität Dortmund; 2018. Available from: http://dx.doi.org/10.17877/DE290R-19859

30. Linel, Patrice. Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE.

Degree: Docteur es, Mathématiques appliquées, 2011, Université Claude Bernard – Lyon I

URL: http://www.theses.fr/2011LYO10102

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La complexification de la modélisation multi-physique conduit d’une part à devoir simuler des systèmes d’équations différentielles ordinaires et d’équations différentielles algébriques de plus en plus… (more)

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La complexification de la modélisation multi-physique conduit d’une part à devoir simuler des systèmes d’équations différentielles ordinaires et d’équations différentielles algébriques de plus en plus grands en nombre d’inconnues et sur des temps de simulation longs. D’autre part l’évolution des architectures de calcul parallèle nécessite d’autres voies de parallélisation que la décomposition de système en sous-systèmes. Dans ce travail, nous proposons de concevoir des méthodes de décomposition de domaine pour la résolution d’EDO en temps. Nous reformulons le problème à valeur initiale en un problème aux valeurs frontières sur l’intervalle de temps symétrisé, sous l’hypothèse de réversibilité du flot. Nous développons deux méthodes, la première apparentée à une méthode de complément de Schur, la seconde basée sur une méthode de type Schwarz dont nous montrons la convergence pouvant être accélérée par la méthode d’Aitken dans le cadre linéaire. Afin d’accélérer la convergence de cette dernière dans le cadre non-linéaire, nous introduisons les techniques d’extrapolation et d’accélération de la convergence des suites non-linéaires. Nous montrons les avantages et les limites de ces techniques. Les résultats obtenus nous conduisent à développer l’accélération de la méthode de type Schwarz par une méthode de Newton. Enfin nous nous intéressons à l’étude de conditions de raccord non-linéaires adaptées à la décomposition de domaine de problèmes non-linéaires. Nous nous servons du formalisme hamiltonien à ports, issu du domaine de l’automatique, pour déduire les conditions de raccord dans le cadre l’équation de Saint-Venant et de l’équation de la chaleur non-linéaire. Après une étude analytique de la convergence de la DDM associée à ces conditions de transmission, nous proposons et étudions une formulation de Lagrangien augmenté sous l’hypothèse de séparabilité de la contrainte.

Complexification of multi-physics modeling leads to have to simulate systems of ordinary differential equations and algebraic differential equations with increasingly large numbers of unknowns and over large times of simulation. In addition the evolution of parallel computing architectures requires other ways of parallelization than the decomposition of system in subsystems. In this work, we propose to design domain decomposition methods in time for the resolution of EDO. We reformulate the initial value problem in a boundary values problem on the symmetrized time interval, under the assumption of reversibility of the flow. We develop two methods, the first connected with a Schur complement method, the second based on a Schwarz type method for which we show convergence, being able to be accelerated by the Aitken method within the linear framework. In order to accelerate the convergence of the latter within the non-linear framework, we introduce the techniques of extrapolation and of acceleration of the convergence of non-linear sequences. We show the advantages and the limits of these techniques. The obtained results lead us to develop the…

Advisors/Committee Members: Lefèvre, Laurent (thesis director), Tromeur-Dervout, Damien (thesis director).

Subjects/Keywords: Complément de Schur; Décomposition de domaine en temps; Newton-Krylov; Parallélisation; Accélération non-linéaire; Condition interface; Domain decomposition; Schur complement; Time domain decomposition; Newton- Krylov; Parallelization; Nonlinear acceleration; Interface condition

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

APA (6^th Edition):

Linel, P. (2011). Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE. (Doctoral Dissertation). Université Claude Bernard – Lyon I. Retrieved from http://www.theses.fr/2011LYO10102

Chicago Manual of Style (16^th Edition):

Linel, Patrice. “Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE.” 2011. Doctoral Dissertation, Université Claude Bernard – Lyon I. Accessed March 08, 2021. http://www.theses.fr/2011LYO10102.

MLA Handbook (7^th Edition):

Linel, Patrice. “Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE.” 2011. Web. 08 Mar 2021.

Vancouver:

Linel P. Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE. [Internet] [Doctoral dissertation]. Université Claude Bernard – Lyon I; 2011. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2011LYO10102.

Council of Science Editors:

Linel P. Méthodes de décomposition de domaines en temps et en espace pour la résolution de systèmes d’EDOs non-linéaires : Time and space domain decomposition method for nonlinear ODE. [Doctoral Dissertation]. Université Claude Bernard – Lyon I; 2011. Available from: http://www.theses.fr/2011LYO10102

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