subject:(hybridizable discontinuous Galerkin)

University of Minnesota

1. Stoter, Klaas. The variational multiscale method for mixed finite element formulations.

Degree: MS, Mathematics, 2018, University of Minnesota

URL: http://hdl.handle.net/11299/198352

► In this thesis, the variational multiscale method is explored in the context of mixed formulations of partial differential equations. The domain decomposition variational multiscale method… (more)

▼ In this thesis, the variational multiscale method is explored in the context of mixed formulations of partial differential equations. The domain decomposition variational multiscale method that has recently been introduced by the author is used as a basis. The function spaces of both the primary and the auxiliary variable are decomposed in a coarse-scale and a fine-scale space. The mixed weak formulations are then derived on a per-element basis. The same scale decomposition is used to rewrite the transmission conditions, which are then incorporated into the weak formulations to couple the elements. The result is a mixed finite element formulation that includes all the fine-scale terms that capture the exact scale interaction, irrespective of the order of continuity of the coarse-scale and fine-scale function spaces. A closure model has to be substituted in place of the fine-scale terms. This closure model dictates the nature of the scale decomposition by imposing a constraint on the fine-scale solution. It is shown that, in the context of Poisson's equation, numerous existing discontinuous Galerkin formulations may be interpreted as particular choices of closure models. Due to the mixed origin of the formulation, a broad range of formulations may be retrieved. Also the Raviart-Thomas method, the Brezzi-Douglas-Marini method and hybridized formulations are investigated from this perspective. The associated fine-scale constraints are examined in depth. Similarly, an advection-diffusion problem is considered, and the fine-scale constraint associated with upwind finite element formulations are investigated. Finally, the residual-based modeling of the fine-scale solution is explored in the context of mixed formulations. Incorporation of the model for the one-dimensional advection-diffusion problem leads to a significant accuracy improvement. In particular does it mitigate the overshoot and the oscillation problems that are observed at boundary layers which occur for advection dominated problems.

Subjects/Keywords: Discontinuous Galerkin; Hybridizable discontinuous Galerkin; Mixed finite element formulation; Partial differential equation; Variational multiscale method

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

APA (6^th Edition):

Stoter, K. (2018). The variational multiscale method for mixed finite element formulations. (Masters Thesis). University of Minnesota. Retrieved from http://hdl.handle.net/11299/198352

Chicago Manual of Style (16^th Edition):

Stoter, Klaas. “The variational multiscale method for mixed finite element formulations.” 2018. Masters Thesis, University of Minnesota. Accessed February 28, 2021. http://hdl.handle.net/11299/198352.

MLA Handbook (7^th Edition):

Stoter, Klaas. “The variational multiscale method for mixed finite element formulations.” 2018. Web. 28 Feb 2021.

Vancouver:

Stoter K. The variational multiscale method for mixed finite element formulations. [Internet] [Masters thesis]. University of Minnesota; 2018. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/11299/198352.

Council of Science Editors:

Stoter K. The variational multiscale method for mixed finite element formulations. [Masters Thesis]. University of Minnesota; 2018. Available from: http://hdl.handle.net/11299/198352

University of Waterloo

2. Sosa Jones, Giselle. Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems.

Degree: 2020, University of Waterloo

URL: http://hdl.handle.net/10012/16192

► Free-surface problems arise in many real-world applications such as in the design of ships and offshore structures, modeling of tsunamis, and dam breaking. Mathematically, free-surface… (more)

▼ Free-surface problems arise in many real-world applications such as in the design of ships and offshore structures, modeling of tsunamis, and dam breaking. Mathematically, free-surface wave problems are described by a set of partial differential equations that govern the movement of the fluid together with certain boundary conditions that describe the free-surface. The numerical solution of such problems is challenging because the boundary of the computational domain depends on the solution of the problem. This implies that there is a strong coupling between the fluid and the free-surface, and the domain must be continuously updated to track the changes in the free-surface. In this thesis we explore and develop space-time hybridizable discontinuous Galerkin (HDG) methods for free-surface problems. First, we focus on a linear free-surface problem in which the amplitude of the waves is assumed to be small enough so that the domain can remain fixed. We initially consider a traditional approach for the numerical discretization of time-dependent partial differential equations: we discretize in space using, in this case, an HDG method to obtain an ordinary differential equation. Then, we use a second order backward differentiation formula to discretize in time. We see that in comparison to an interior penalty discontinuous Galerkin discretization, this HDG discretization results in smaller linear systems (in general), and produces better approximations to the velocity of the fluid. Next, we consider the solution of the same linear free-surface problem with a space-time hybridizable discontinuous Galerkin method. Unlike previous finite element discretizations of this problem, we consider a mixed formulation in which the velocity of the flow can be approximated with an optimal order of convergence. We develop a set of space-time analysis tools that allow us to obtain a priori error estimates in which the dependency on the spatial mesh size and the time step is explicit. This is in contrast to previous space-time error analyses in which the error bounds depend on the size of the space-time elements. Finally, we move on to incompressible nonlinear free-surface flow. We consider the two-fluid (gas and liquid) Navier-Stokes equations and use a level set method in which the flow and the level set equations are solved subsequently until a certain stopping criterion has been met. The flow equations are solved with a space-time HDG method which is exactly mass conserving. Furthermore, a space-time embedded discontinuous Galerkin method is employed for the solution of the level set equation. This discretization possesses the same conservation and stability properties as discontinuous Galerkin methods, but produces a continuous approximation to the free-surface elevation. When a discontinuous approximation to the free-surface elevation is obtained, smoothing techniques have to be applied in order to move the mesh and track the interface. It has been shown in the past that such techniques can lead to instabilities and…

Subjects/Keywords: free-surface waves; space-time methods; hybridizable discontinuous Galerkin methods

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

APA (6^th Edition):

Sosa Jones, G. (2020). Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16192

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):

Sosa Jones, Giselle. “Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems.” 2020. Thesis, University of Waterloo. Accessed February 28, 2021. http://hdl.handle.net/10012/16192.

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

MLA Handbook (7^th Edition):

Sosa Jones, Giselle. “Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems.” 2020. Web. 28 Feb 2021.

Vancouver:

Sosa Jones G. Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10012/16192.

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

Council of Science Editors:

Sosa Jones G. Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16192

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

Penn State University

3. Sheldon, Jason Paul. A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction.

Degree: 2016, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/27574

► As computational methods have matured and computing power has increased over the years, simulations have grown in complexity by attempting to accurately model both larger… (more)

▼ As computational methods have matured and computing power has increased over the years, simulations have grown in complexity by attempting to accurately model both larger and more involved physical systems. Although the computational demand of these simulations has increased, the required accuracy of the solution has not decreased, resulting in simulations that can become prohibitively computationally expensive. New computational tools need to be developed that both maintain solution accuracy while minimizing the ever increasing computational cost in time and resources. This dissertation presents a novel application of the recently developed hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid-structure interaction (FSI) problems. Current applications of the HDG method are reviewed and shown to be limited in scope to single-physics scenarios; however, they do include both solid and fluid problems, which are necessary for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, linear elastodynamics, nonlinear elastodynamics, Eulerian Navier-Stokes, and arbitrary Lagrangian-Eulerian Navier-Stokes are derived. The elasticity formulations are all written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid-solid interface. In past work (Sheldon, 2012; Sheldon et al., 2014), a continuous Galerkin FSI model with a variety of coupling strategies was implemented, which greatly facilitated the process of creating a novel HDG FSI model. HDG FSI modeling comes with its own unique challenges, however, which are discussed and then addressed by modifications to the established component formulations. The resultant HDG FSI model is then presented. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then numerically validated against benchmark problems proposed by Turek and Hron (Turek and Hron, 2006). The HDG results show increasing accuracy compared to the benchmark’s measured quantities as simulations are refined. Finally, concluding remarks are presented and the future work necessary to turn this HDG FSI model into a production level tool is outlined. Advisors/Committee Members: Jonathan S Pitt, Dissertation Advisor/Co-Advisor, Scott Miller, Dissertation Advisor/Co-Advisor, Jonathan S Pitt, Committee Chair/Co-Chair, Scott Miller, Committee Chair/Co-Chair, Panagiotis Michaleris, Committee Member, Francesco Costanzo, Committee Member, Paris R Vonlockette, Special Member.

Subjects/Keywords: Hybridizable discontinuous Galerkin; Fluid-Structure Interaction; Arbitrary Lagrangian-Eulerian Navier-Stokes; Elastodynamics

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

APA (6^th Edition):

Sheldon, J. P. (2016). A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/27574

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):

Sheldon, Jason Paul. “A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction.” 2016. Thesis, Penn State University. Accessed February 28, 2021. https://submit-etda.libraries.psu.edu/catalog/27574.

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

MLA Handbook (7^th Edition):

Sheldon, Jason Paul. “A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction.” 2016. Web. 28 Feb 2021.

Vancouver:

Sheldon JP. A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction. [Internet] [Thesis]. Penn State University; 2016. [cited 2021 Feb 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/27574.

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

Council of Science Editors:

Sheldon JP. A Hybridizable Discontinuous Galerkin Method For Modeling Fluid–structure Interaction. [Thesis]. Penn State University; 2016. Available from: https://submit-etda.libraries.psu.edu/catalog/27574

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

4. Bonnasse-Gahot, Marie. Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics.

Degree: Docteur es, Mathématiques appliquées, 2015, Nice

URL: http://www.theses.fr/2015NICE4125

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Le contexte scientifique de cette thèse est l'imagerie sismique dont le but est de reconstituer la structure du sous-sol de la Terre. Comme le forage… (more)

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Le contexte scientifique de cette thèse est l'imagerie sismique dont le but est de reconstituer la structure du sous-sol de la Terre. Comme le forage a un coût assez élevé, l'industrie pétrolière s'intéresse à des méthodes capables de reconstituer les images de la structure terrestre interne avant de le faire. La technique d'imagerie sismique la plus utilisée est la technique de sismique-réflexion qui est basée sur le modèle de l'équation d'ondes. L'imagerie sismique est un problème inverse qui requiert de résoudre un grand nombre de problèmes directs. Dans ce contexte, nous nous intéressons dans cette thèse à la résolution du problème direct en régime harmonique, soit à la résolution des équations d'Helmholtz. L'objectif principal est de proposer et de développer un nouveau type de solveur élément fini (EF) caractérisé par un opérateur discret de taille réduite (comparée à la taille des solveurs déjà existants) sans pour autant altérer la précision de la solution numérique. Nous considérons les méthodes de Galerkine discontinues (DG). Comme les méthodes DG classiques sont plus coûteuses que les méthodes EF continues si l'on considère un même problème à cause d'un grand nombre de degrés de liberté couplés, résultat des approximations discontinues, nous développons une nouvelle classe de méthode DG réduisant ce problème : la méthode DG hybride (HDG). Pour valider l'efficacité de la méthode HDG proposée, nous comparons les résultats obtenus avec ceux obtenus avec une méthode DG basée sur des flux décentrés en 2D. Comme l'industrie pétrolière s'intéresse au traitement de données réelles, nous développons ensuite la méthode HDG pour les équations élastiques d'Helmholtz 3D.

The scientific context of this thesis is seismic imaging which aims at recovering the structure of the earth. As the drilling is expensive, the petroleum industry is interested by methods able to reconstruct images of the internal structures of the earth before the drilling. The most used seismic imaging method in petroleum industry is the seismic-reflection technique which uses a wave equation model. Seismic imaging is an inverse problem which requires to solve a large number of forward problems. In this context, we are interested in this thesis in the modeling part, i.e. the resolution of the forward problem, assuming a time-harmonic regime, leading to the so-called Helmholtz equations. The main objective is to propose and develop a new finite element (FE) type solver characterized by a reduced-size discrete operator (as compared to existing such solvers) without hampering the accuracy of the numerical solution. We consider the family of discontinuous Galerkin (DG) methods. However, as classical DG methods are much more expensive than continuous FE methods when considering steady-like problems, because of an increased number of coupled degrees of freedom as a result of the discontinuity of the approximation, we develop a new form of DG method that specifically address this issue: the hybridizable DG (HDG) method. To validate the efficiency of the…

Advisors/Committee Members: Calandra, Henri (thesis director), Diaz, Julien (thesis director), Lanteri, Stéphane (thesis director).

Subjects/Keywords: Méthodes Galerkine discontinues; Méthode Galerkine discontinue hybride; Ondes élastiques; Domaine fréquentiel; Imagerie sismique; Discontinuous Galerkin methods; Hybridizable discontinuous Galerkin method; Elastic waves; Harmonic domain; Seismic imaging

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

APA (6^th Edition):

Bonnasse-Gahot, M. (2015). Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics. (Doctoral Dissertation). Nice. Retrieved from http://www.theses.fr/2015NICE4125

Chicago Manual of Style (16^th Edition):

Bonnasse-Gahot, Marie. “Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics.” 2015. Doctoral Dissertation, Nice. Accessed February 28, 2021. http://www.theses.fr/2015NICE4125.

MLA Handbook (7^th Edition):

Bonnasse-Gahot, Marie. “Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics.” 2015. Web. 28 Feb 2021.

Vancouver:

Bonnasse-Gahot M. Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics. [Internet] [Doctoral dissertation]. Nice; 2015. [cited 2021 Feb 28]. Available from: http://www.theses.fr/2015NICE4125.

Council of Science Editors:

Bonnasse-Gahot M. Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues : High order discontinuous Galerkin methods for time-harmonic elastodynamics. [Doctoral Dissertation]. Nice; 2015. Available from: http://www.theses.fr/2015NICE4125

Penn State University

5. Kauffman, Justin A. An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method.

Degree: 2018, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/15005jak5378

► Computational simulations contain discretizations of both a physical domain and a mathematical model. In this dissertation, an overset mesh framework is used to discretize the… (more)

▼ Computational simulations contain discretizations of both a physical domain and a mathematical model. In this dissertation, an overset mesh framework is used to discretize the physical domain, and the hybridizable discontinuous Galerkin (HDG) finite element method is used to discretize the mathematical model. It is proposed that using an overset mesh framework for the HDG method enables stable solutions to be computed for complex geometries and dynamic meshes. Overset mesh methods are chosen because they are efficient at decomposing geometrically complex domains. The HDG method was chosen because it provides solutions that are arbitrarily high-order accurate, reduces the size of the global discrete problem, and has the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. An overset mesh method can utilize an inherent property of the HDG method, the decomposition of the solution into global (face) and local (volume) parts. The global solution exists only on the cell boundaries; while, the local solution exists in the interior of each cell and is decoupled between neighboring cells. This decomposition introduces face-volume coupling in the weak form for degrees of freedom on cell boundaries, which is used as the foundation for the overset communication between subdomains. Ultimately, the goal of this work is to simulate full-scale hydrodynamic and fluid-structure interaction (FSI) problems. To achieve these simulations, the necessary building blocks must first be verified and validated in the overset-HDG framework. The building blocks demonstrated in this dissertation are steady convection-diffusion, linear elasticostatics, and pseudo-compressible Navier-Stokes in both Eulerian and arbitrary Lagrangian-Eulerian frames. Computational simulations are performed to demonstrate the applicability and accuracy of the overset-HDG algorithm. Advisors/Committee Members: Jonathan S Pitt, Dissertation Advisor/Co-Advisor, Jonathan S Pitt, Committee Chair/Co-Chair, Francesco Costanzo, Committee Member, Corina Stefania Drapaca, Committee Member, James Joseph Brannick, Outside Member, Scott Miller, Special Member.

Subjects/Keywords: Overset Mesh Methods; Hybridizable discontinuous Galerkin; HDG; Finite Element Method; Pseudo-compressibility; Arbitrary Lagrangian-Eulerian; Navier-Stokes; Elasticity

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

APA (6^th Edition):

Kauffman, J. A. (2018). An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/15005jak5378

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):

Kauffman, Justin A. “An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method.” 2018. Thesis, Penn State University. Accessed February 28, 2021. https://submit-etda.libraries.psu.edu/catalog/15005jak5378.

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

MLA Handbook (7^th Edition):

Kauffman, Justin A. “An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method.” 2018. Web. 28 Feb 2021.

Vancouver:

Kauffman JA. An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method. [Internet] [Thesis]. Penn State University; 2018. [cited 2021 Feb 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/15005jak5378.

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

Council of Science Editors:

Kauffman JA. An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method. [Thesis]. Penn State University; 2018. Available from: https://submit-etda.libraries.psu.edu/catalog/15005jak5378

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

Universitat Politècnica de Catalunya

6. Gürkan, Ceren. Extended hybridizable discontinuous Galerkin method.

Degree: Departament d'Enginyeria Civil i Ambiental, 2018, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/664035

► Esta tesis propone una nueva técnica numérica: eXtended Hybridizable Discontinuous Galerkin (X-HDG), para resolver eficazmente problemas incluyendo fronteras en movimiento e interfaces. Su objetivo es… (more)

▼ Esta tesis propone una nueva técnica numérica: eXtended Hybridizable Discontinuous Galerkin (X-HDG), para resolver eficazmente problemas incluyendo fronteras en movimiento e interfaces. Su objetivo es superar las limitaciones de los métodos disponibles y mejorar los resultados, heredando propiedades del método Hybridizable Discontinuous Galerkin method (HDG), junto con una definición de interfaz explícita. X-HDG combina el método HDG con la filosofía de eXtended Finite Element method (X-FEM), con una descripción level-set de la interfaz, para obtener un método numérico hp convergente de orden superior sin ajuste de la malla a la interfaz o frontera. HDG supera a otros métodos de DG para los problemas implícitos con operadores autoadjuntos, debido a sus propiedades de hibridación y superconvergencia. El proceso de hibridación reduce drásticamente el número de grados de libertad en el problema discreto, similar a la condensación estática en el contexto de Continuous Galerkin (CG) de alto orden. Por otro lado, HDG se basa en una formulación mixta que, a diferencia de CG u otros métodos DG, es estable incluso cuando todas las variables (incógnitas primitivas y derivadas) se aproximan con polinomios del mismo grado k. Como resultado, la convergencia de orden k + 1 en la norma L2 se demuestra no sólo para la incógnita primal sino también para sus derivadas. Por lo tanto, un simple post-proceso elemento-a-elemento de las derivadas conduce a una aproximación superconvergente de las variables primales, con convergencia de orden k+2 en la norma L2. X-HDG hereda estas propiedades. Por otro lado, gracias a la descripción level-set de la interfaz, se evita caro remallado tratando las interfaces móviles. Este trabajo demuestra que X-HDG mantiene la convergencia óptima y la superconvergencia de HDG sin la necesidad de ajustar la malla a la interfaz. En los capítulos 2 y 3, se deduce e implementa el método X-HDG para resolver la ecuación de Laplace estacionaria en un dominio donde la interfaz separa un solo material del vacío y donde la interfaz separa dos materiales diferentes. La precisión y convergencia de X-HDG se prueba con ejemplos de soluciones fabricadas y se demuestra que X-HDG supera las propuestas anteriores mostrando convergencia óptima y superconvergencia de alto orden, junto con una reducción del tamaño del sistema gracias a su naturaleza híbrida, pero sin ajuste de la malla. En los capítulos 4 y 5, el método X-HDG se desarrolla e implementa para resolver el problema de interfaz de Stokes para interfaces vacías y bimateriales. Con X-HDG, de nuevo se muestra una convergencia de alto orden en mallas no adaptadas, para problemas de flujo incompresible. X-HDG para interfaces móviles se discute en el Capítulo 6. Se considera un problema térmico transitorio, donde el término dependiente del tiempo es discretizado usando el método de backward Euler. Un ejemplo de una interfaz circulas que se reduce, junto con el problema de Stefan de dos fases, se discute en la sección de ejemplos numéricos. Se demuestra que X-HDG ofrece un… Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Fernández Méndez, Sonia (director), Kronbichler, Martin (director).

Subjects/Keywords: eXtended Finite Element method (X-FEM); Hybridizable Discontinuous Galerkin method (HDG); Àrees temàtiques de la UPC::Matemàtiques i estadística; 004; 51

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

APA (6^th Edition):

Gürkan, C. (2018). Extended hybridizable discontinuous Galerkin method. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/664035

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):

Gürkan, Ceren. “Extended hybridizable discontinuous Galerkin method.” 2018. Thesis, Universitat Politècnica de Catalunya. Accessed February 28, 2021. http://hdl.handle.net/10803/664035.

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

MLA Handbook (7^th Edition):

Gürkan, Ceren. “Extended hybridizable discontinuous Galerkin method.” 2018. Web. 28 Feb 2021.

Vancouver:

Gürkan C. Extended hybridizable discontinuous Galerkin method. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2018. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10803/664035.

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

Council of Science Editors:

Gürkan C. Extended hybridizable discontinuous Galerkin method. [Thesis]. Universitat Politècnica de Catalunya; 2018. Available from: http://hdl.handle.net/10803/664035

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

7. Paipuri, Mahendra. Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems.

Degree: Departament d'Enginyeria Civil i Ambiental, 2018, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/471530

► En esta tesis se propone una formulación acoplada del método de los elementos finitos clásico (CG) y el método Hybridizable Discontinuous Galerkin (HDG) para la… (more)

▼ En esta tesis se propone una formulación acoplada del método de los elementos finitos clásico (CG) y el método Hybridizable Discontinuous Galerkin (HDG) para la a solución de problemas térmicos conjugados. El modelo se utiliza para determinar la respuesta al fuego de Polímeros Reforzados con Fibras de Vidrio (GFRP) con sección tubular. El primer paso de la tesis es la comparación de la eficiencia computacional de CG y HDG de alto orden para problemas de flujo incompresible para número de Reynolds (Re) bajo. Se consideran sólo ejemplos 2D y métodos de resolución de sistemas lineales directos. Se presenta una comparación en términos de tiempo de CPU y precisión en la solución para ambas discretizaciones, bajo la misma plataforma de implementación. Los resultados sugieren que HDG puede ser más eficiente computacionalmente que CG en tiempo de CPU, para un grado fijado. La estabilidad de HDG y CG para Re alto se estudia con una solución manufacturada que produce un frente pronunciado, confirmando que HDG proporciona soluciones convergidas suaves en presencia de frentes verticales, en casos en que las oscilaciones numéricas de CG no permiten llegar a convergencia. A continuación, se plantea la solución del problema acoplado Navier-Stokes/conveccióndifusión, con la aproximación de Boussinesq, en el contexto del método HDG, y se analiza con experimentos numéricos. Se propone una formulación acoplada HDG-CG para la ecuación del calor. Se comprueban numéricamente las propiedades de convergencia del método propuesto. Finalmente, se combina la formulación acoplada propuesta para la ecuación del calor con el acoplamiento con la ecuaciones de Navier-Stokes en el dominio del fluido, creando una nueva formulación CG-HDG para problemas térmicos conjugados. Se consideran ejemplos clásicos para validar los resultados comparando con la literatura existente. La parte final de la tesis aplica la formulación acoplada CG-HDG propuesta a la predicción de la respuesta térmica de secciones tubulares de GFRP, incluyendo radiosidad interna en el modelo. Se calculan estimas de los errores de discretización para determinar intervalos de confianza para las cantidades de interés. Se presentan resultados con geometría con esquinas curvas en la cavidad mostrando resultados dentro de los intervalos de incertidumbre estimados. El tiempo de CPU para la resolución de sistemas sugiere que el modelo CG-HDG propuesto es más eficiente que el clásico método CG-CG en todos los casos considerados. Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Fernández Méndez, Sonia (director), Fernandes, Carlos Manuel Tiago Tavares (director), true (authorsendemail).

Subjects/Keywords: Hybridizable discontinuous Galerkin; Coupling; Conjugate heat transfer; GFRP; Computational efficiency; Acoplamiento; Trasmisión del calor conjugada; Eficiencia computacional; Àrees temàtiques de la UPC::Matemàtiques i estadística; 004; 512

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APA (6^th Edition):

Paipuri, M. (2018). Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/471530

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):

Paipuri, Mahendra. “Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems.” 2018. Thesis, Universitat Politècnica de Catalunya. Accessed February 28, 2021. http://hdl.handle.net/10803/471530.

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

MLA Handbook (7^th Edition):

Paipuri, Mahendra. “Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems.” 2018. Web. 28 Feb 2021.

Vancouver:

Paipuri M. Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2018. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10803/471530.

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

Council of Science Editors:

Paipuri M. Comparison and coupling of continuous and hybridizable discontinuous Galerkin methods : application to multi-physics problems. [Thesis]. Universitat Politècnica de Catalunya; 2018. Available from: http://hdl.handle.net/10803/471530

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

Universitat Politècnica de Catalunya

8. Karkoulias, Alexandros. Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations.

Degree: 2020, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/669874

► Simulaciones de flujo incompresible se emplean a diario para resolver problemas de interés práctico e industrial en varios campos de la ingeniería, p.ej. en aplicaciones… (more)

▼ Simulaciones de flujo incompresible se emplean a diario para resolver problemas de interés práctico e industrial en varios campos de la ingeniería, p.ej. en aplicaciones automovilísticas, aeronáuticas, mecánicas y biomédicas. Aunque los métodos de volúmenes finitos (FV) siguen siendo la opción preferida por la industria debido a su eficiencia y robustez, la sensibilidad a la calidad de la malla y la baja precisión representan dos limitaciones importantes para estas técnicas. Estas limitaciones son todavía más críticas en el contexto de simulaciones de fenómenos transitorios, donde los FV están penalizados por su excesiva difusión numérica. En este contexto, las estrategias de discretización de alto orden han ganado una popularidad creciente en las últimas décadas para problemas transitorios dónde se necesitan soluciones precisas. Esta tesis propone un método de Galerkin discontinuo híbrido (HDG), de alto orden y adaptativo para la aproximación de las ecuaciones de Navier-Stokes incomprensible laminar, en el caso estacionario y transitorio en el entorno de aplicaciones ingenieriles. Para ello, la notación de Voigt para tensores simétricos de segundo orden (habituales en mecánica de los medios continuos) permite introducir un método HDG para la formulación de Cauchy de la ecuación de momento. La novedad de este resultado reside en la convergencia óptima alcanzada por el método, incluso para aproximaciones de orden polinómico bajo. Además, se desarrolla una estrategia de post-proceso local para construir elemento a elemento un campo de velocidad súper-convergente, tomando en cuenta los modos rígidos de traslación y rotación. La discrepancia entre el campo de velocidad calculado y el súper-convergente, obtenido a través del post-proceso, permite definir un indicador del error local. De esta forma, se desarrolla una estrategia para realizar adecuar elemento a elemento el grado de la aproximación polinómica y así mejorar la precisión adaptándose a las características localizadas del flujo. Seguidamente, se extiende el método HDG propuesto al tratamiento de problemas dependientes del tiempo. Más concretamente, se consideran los esquemas de integración temporal de alto orden explicit singly diagonal implicit Runge-Kutta (ESDIRK). En este contexto, se utiliza el paso explícito embedded para calcular una estimación computacionalmente eficiente del error temporal y definir una estrategia de adaptividad del paso de tiempo. Finalmente, se desarrolla un precondicionador adaptado a la estrategia HDG que acelera la convergencia del método iterativo empleado y, de esta forma, obtener resoluciones eficaces del problema global surgido de la discretización HDG. Es importante resaltar la importancia de una herramienta de resolución eficiente para problemas de gran escala en el contexto de aproximaciones de alto orden y en dominios tridimensionales. Estas herramientas se hacen aún más criticas en simulaciones transitorias. Más concretamente, se proponen un precondicionador diagonal por bloques y una aproximación eficiente del complemento… Advisors/Committee Members: Universitat Politècnica de Catalunya. Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports de Barcelona, [email protected] (authoremail), false (authoremailshow), Huerta, Antonio (director), Auricchio, Ferdinando (codirector), Giacomini, Matteo (codirector).

Subjects/Keywords: Hybridizable discontinuous Galerkin; Incompressible Navier-Stokes equations; Transient flows; High-order methods; Cauchy stress formulation; Voigt notation; Àrees temàtiques de la UPC::Enginyeria civil; 004; 512; 531/534

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

APA (6^th Edition):

Karkoulias, A. (2020). Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/669874

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):

Karkoulias, Alexandros. “Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations.” 2020. Thesis, Universitat Politècnica de Catalunya. Accessed February 28, 2021. http://hdl.handle.net/10803/669874.

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

MLA Handbook (7^th Edition):

Karkoulias, Alexandros. “Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations.” 2020. Web. 28 Feb 2021.

Vancouver:

Karkoulias A. Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2020. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10803/669874.

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

Council of Science Editors:

Karkoulias A. Adaptive low and high-order hybridized methods for unsteady incompressible flow simulations. [Thesis]. Universitat Politècnica de Catalunya; 2020. Available from: http://hdl.handle.net/10803/669874

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

9. Shi, Ke. Devising superconvergent HDG methods for partial differential equations.

Degree: PhD, Mathematics, 2012, University of Minnesota

URL: http://purl.umn.edu/139518

► The DG methods are ideally suited for numerically solving hyperbolic problems. However this is not the case for diffusion problems,even though they are ideally suited… (more)

Subjects/Keywords: Discontinuous Galerkin; Finite element; Fluid mechanics; Hybridizable; Numerical Analysis

…describe hybridizable discontinuous Galerkin (HDG) methods, we consider the following… …well as several hybridizable discontinuous Galerkin (HDG) methods. The novelty of… …testing our methods for Timoshenko beams. The first discontinuous Galerkin (DG)… …case of HDG methods whose local solvers are defined by the local discontinuous Galerkin… …classical continuous Galerkin methods on the same mesh, they have many more global degrees of…

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

APA (6^th Edition):

Shi, K. (2012). Devising superconvergent HDG methods for partial differential equations. (Doctoral Dissertation). University of Minnesota. Retrieved from http://purl.umn.edu/139518

Chicago Manual of Style (16^th Edition):

Shi, Ke. “Devising superconvergent HDG methods for partial differential equations.” 2012. Doctoral Dissertation, University of Minnesota. Accessed February 28, 2021. http://purl.umn.edu/139518.

MLA Handbook (7^th Edition):

Shi, Ke. “Devising superconvergent HDG methods for partial differential equations.” 2012. Web. 28 Feb 2021.

Vancouver:

Shi K. Devising superconvergent HDG methods for partial differential equations. [Internet] [Doctoral dissertation]. University of Minnesota; 2012. [cited 2021 Feb 28]. Available from: http://purl.umn.edu/139518.

Council of Science Editors:

Shi K. Devising superconvergent HDG methods for partial differential equations. [Doctoral Dissertation]. University of Minnesota; 2012. Available from: http://purl.umn.edu/139518

10. Wang, Bin. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.

Degree: PhD, Mathematics, 2017, University of Kansas

URL: http://hdl.handle.net/1808/27005

► Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite… (more)

Subjects/Keywords: Mathematics; BDDC; domain decomposition; hybridizable discontinuous Galerkin; saddle point problems; Stokes; weak Galerkin

…hybridizable discontinuous Galerkin 2 (HDG) and weak Galerkin (WG) methods… …properties of the hybridizable discontinuous Galerkin (HDG) and weak Galerkin (WG… …respectively. Both hybridizable discontinuous Galerkin and weak Galerkin methods are used to… …method. 2.4 Hybridizable Discontinuous Galerkin Methods The interaction between ideas of DG… …Discontinuous Galerkin Methods Discontinuous Galerkin(DG) method was first introduced by…

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

APA (6^th Edition):

Wang, B. (2017). Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27005

Chicago Manual of Style (16^th Edition):

Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021. http://hdl.handle.net/1808/27005.

MLA Handbook (7^th Edition):

Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Web. 28 Feb 2021.

Vancouver:

Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/1808/27005.

Council of Science Editors:

Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/27005

11. Prada, Daniele. A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology.

Degree: 2016, IUPUI

URL: http://hdl.handle.net/1805/11877

►

Indiana University-Purdue University Indianapolis (IUPUI)

The interplay between biomechanics and blood perfusion in the optic nerve head (ONH) has a critical role in ocular pathologies,… (more)

Subjects/Keywords: hybridizable discontinuous Galerkin methods; optimal convergence; ocular biomechanics and hemodynamics; glaucoma; nonlinear porous media viscoelasticity

…Velocity GMRES Generalized Minimal Residual HDG Hybridizable Discontinuous Galerkin IOP… …University, December 2016. A Hybridizable Discontinuous Galerkin Method for Nonlinear Porous Media… …is solved via a numerical method based on a novel hybridizable discontinuous Galerkin… …and the displacement u by a family of discontinuous Galerkin methods. In this work, we adopt… …discontinuous Galerkin (HDG) methods [19], thus approximating all the variables at…

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APA (6^th Edition):

Prada, D. (2016). A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology. (Thesis). IUPUI. Retrieved from http://hdl.handle.net/1805/11877

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):

Prada, Daniele. “A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology.” 2016. Thesis, IUPUI. Accessed February 28, 2021. http://hdl.handle.net/1805/11877.

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

MLA Handbook (7^th Edition):

Prada, Daniele. “A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology.” 2016. Web. 28 Feb 2021.

Vancouver:

Prada D. A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology. [Internet] [Thesis]. IUPUI; 2016. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/1805/11877.

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

Council of Science Editors:

Prada D. A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology. [Thesis]. IUPUI; 2016. Available from: http://hdl.handle.net/1805/11877

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

12. HUYNH LE NGOC THANH. Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains.

Degree: 2010, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/23283

Subjects/Keywords: Hybridizable discontinuous Galerkin; immersed interface; Navier-Stokes; curved boundary; fast Fourier transform; arbitrary Lagrangian Eulerian

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

APA (6^th Edition):

THANH, H. L. N. (2010). Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/23283

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):

THANH, HUYNH LE NGOC. “Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains.” 2010. Thesis, National University of Singapore. Accessed February 28, 2021. http://scholarbank.nus.edu.sg/handle/10635/23283.

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

MLA Handbook (7^th Edition):

THANH, HUYNH LE NGOC. “Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains.” 2010. Web. 28 Feb 2021.

Vancouver:

THANH HLN. Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains. [Internet] [Thesis]. National University of Singapore; 2010. [cited 2021 Feb 28]. Available from: http://scholarbank.nus.edu.sg/handle/10635/23283.

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

Council of Science Editors:

THANH HLN. Immersed Hybridizable Discontinuous Galerkin Method for Multi-Viscosity Incompressible Navier-Stokes Flows on Irregular Domains. [Thesis]. National University of Singapore; 2010. Available from: http://scholarbank.nus.edu.sg/handle/10635/23283

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

13. Sala, Lorenzo. Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions.

Degree: Docteur es, Mathématiques appliquées, 2019, Université de Strasbourg

URL: http://www.theses.fr/2019STRAD021

►

Les neuropathies optiques comme le glaucome sont souvent des maladies tardives, évolutives et incurables. Malgré les progrès récents de la recherche clinique, de nombreuses questions… (more)

▼

Les neuropathies optiques comme le glaucome sont souvent des maladies tardives, évolutives et incurables. Malgré les progrès récents de la recherche clinique, de nombreuses questions relatives à l’étiologie de ces troubles et à leur physiopathologie restent ouvertes. De plus, les données sur les tissus postérieurs oculaires sont difficiles à estimer de façon non invasive et leur interprétation clinique demeure difficile en raison de l’interaction entre de multiples facteurs qui ne peuvent pas être facilement isolés. L’utilisation récente de modèles mathématiques pour des problèmes biomédicaux a permis de révéler des mécanismes complexes de la physiologie humaine. Dans ce contexte très enthousiasmant, notre contribution est consacrée à la conception d’un modèle mathématique et computationnel couplant l’hémodynamique et la biomécanique de l’oeil humain. Dans le cadre de cette thèse, nous avons mis au point un modèle spécifique au patient appelé simulateur virtuel de mathématiques oculaires (OMVS), capable de démêler les facteurs multi-échelles et multi-physiques dans un environnement accessible en utilisant des modèles mathématiques et des méthodes numériques avancés et innovants. De plus, le cadre proposé peut servir comme méthode complémentaire pour l’analyse et la visualisation des données pour la recherche clinique et expérimentale, et comme outil de formation pour la recherche pédagogique.

Optic neuropathies such as glaucoma are often late-onset, progressive and incurable diseases. Despite the recent progress in clinical research, there are still numerous open questions regarding the etiology of these disorders and their pathophysiology. Furthermore, data on ocular posterior tissues are difficult to estimate noninvasively and their clinical interpretation remains challenging due to the interaction among multiple factors that are not easily isolated. The recent use of mathematical models applied to biomedical problems has helped unveiling complex mechanisms of the human physiology. In this very compelling context, our contribution is devoted to designing a mathematical and computational model coupling tissue perfusion and biomechanics within the human eye. In this thesis we have developed a patient-specific Ocular Mathematical Virtual Simulator (OMVS), which is able to disentangle multiscale and multiphysics factors in a accessible environment by employing advanced and innovative mathematical models and numerical methods. Moreover, the proposed framework may serve as a complementary method for data analysis and visualization for clinical and experimental research, and a training application for educational purposes.

Advisors/Committee Members: Prud'homme, Christophe (thesis director), Guidoboni, Giovanna (thesis director).

Subjects/Keywords: Modélisation d’écoulements biologiques; Multi-échelle; Multiphysique; Decomposition d'opérateur; Couplage 3d-0d; Méthode de Galerkin discontinue hybridisable; Biomécanique oculaire; Hémodynamique oculaire; Simulation virtuelle; Calcul haute performance; Analyse de sensibilité; Multiscale; Hybridizable Discontinuous Galerkin method; Ocular biomechanics; Ocular hemodynamics; Virtual simulator; Higperformance computing; Sensitivity analysis; 3d-0d coupling; Operator splitting; Multiphysics; 511.8; 571.43

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

APA (6^th Edition):

Sala, L. (2019). Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2019STRAD021

Chicago Manual of Style (16^th Edition):

Sala, Lorenzo. “Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions.” 2019. Doctoral Dissertation, Université de Strasbourg. Accessed February 28, 2021. http://www.theses.fr/2019STRAD021.

MLA Handbook (7^th Edition):

Sala, Lorenzo. “Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions.” 2019. Web. 28 Feb 2021.

Vancouver:

Sala L. Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2019. [cited 2021 Feb 28]. Available from: http://www.theses.fr/2019STRAD021.

Council of Science Editors:

Sala L. Modélisation mathématique et simulation de flux sanguins oculaires et leur interactions : Mathematical modelling and simulation of ocular blood flows and their interactions. [Doctoral Dissertation]. Université de Strasbourg; 2019. Available from: http://www.theses.fr/2019STRAD021

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Open Access Theses and Dissertations