| 1. |
- Nguyen, Van Dang, 1985-
(författare)
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High Performance Finite Element Methods with Application to Simulation of Vertical Axis Wind Turbines and Diffusion MRI
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Finite element methods have been developed over decades, and together with the growth of computer power, they become more and more important in dealing with large-scale simulations in science and industry.The objective of this thesis is to develop high-performance finite element methods, with two concrete applications: computational fluid dynamics (CFD) with simulation of turbulent flow past a vertical axis wind turbine (VAWT), and computational diffusion magnetic resonance imaging (CDMRI). The thesis presents contributions in the form of both new numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS/FEniCS-HPC platform. More specifically, we have four main contributions through the thesis work.First, we develop a DFS-ALE method which combines the Direct finite element simulation method (DFS) with the Arbitrary Lagrangian-Eulerian method (ALE) to solve the Navier-Stokes equations for a rotating turbine. This method is enhanced with dual-based a posteriori error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data with a good agreement.Second, we propose a partition of unity finite element method to tackle interface problems. In CFD, it allows for imposing slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. In CDMRI, it helps to overcome the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues and allows for efficient solutions of the Bloch-Torrey equation in heterogeneous domains. The method facilitates a straightforward implementation on the FEniCS/ FEniCS-HPC platform. The method is validated against reference solutions, and the implementation shows a strong parallel scalability.Third, we propose a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The method helps to significantly reduce the required simulation time, computer memory, and difficulties associated with mesh generation, while maintaining the accuracy. Thus, it opens the possibility to simulate complicated structures at a low cost, for a better understanding of diffusion MRI in the brain.Finally, we propose an efficient portable simulation framework that integrates recent advanced techniques in both mathematics and computer science to enable the users to perform simulations with the Cloud computing technology. The simulation framework consists of Python, IPython and C++ solvers working either on a web browser with Google Colaboratory notebooks or on the Google Cloud Platform with MPI parallelization.
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| 2. |
- Degirmenci, Niyazi Cem, 1982-
(författare)
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Adaptive Finite Element Methods for Fluid Structure Interaction Problems with Applications to Human Phonation
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work presents a unified framework for numerical solution of Fluid Structure Interaction (FSI) and acoustics problems with focus on human phonation. The Finite Element Method is employed for numerical investigation of partial differential equations that model conservation of momentum and mass. Since the resulting system of equations is very large, an efficient open source high performance implementation is constructed and provided. In order to gain accuracy for the numerical solutions, an adaptive mesh refinement strategy is employed which reduces the computational cost in comparison to a uniform refinement. Adaptive refinement of the mesh relies on computable error indicators which appear as a combination of a computable residual and the solution of a so-called dual problem acting as weights on computed residuals. The first main achievement of this thesis is to apply this strategy to numerical simulations of a benchmark problem for FSI. This FSI model is further extended for contact handling and applied to a realistic vocal folds geometry where the glottic wave formation was captured in the numerical simulations. This is the second achievement in the presented work. The FSI model is further coupled to an acoustics model through an acoustic analogy, for vocal folds with flow induced oscillations for a domain constructed to create the vowel /i/. The comparisons of the obtained pressure signal at specified points with respect to results from literature for the same vowel is reported, which is the final main result presented.
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| 3. |
- Hoffman, Tove
(författare)
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Dispersal of ticks and their microorganisms by African-Western Palaearctic migratory birds
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In Europe, tick-borne diseases are the most widespread and common vector-borne diseases and their geographical distribution is increasing. The dispersal of ticks depends on the movements of their vertebrate hosts. Avian hosts are more likely to be involved in long-distance range expansion of ticks due to their migration pattern. Billions of birds in the African-Palaearctic migration system migrate biannually between breeding grounds in the Palaearctic and wintering grounds in Africa and thereby create natural links between Africa, Europe, and Asia. In this thesis the dispersal of ticks and their microorganisms by northbound migratory birds utilizing flyways in the African-Western Palaearctic region has been investigated and the association between bird ecology and tick taxon addressed. The results suggest that long-distance migratory birds with wintering regions in Africa are involved in northward dispersal of the tick species Hyalomma rufipes, a known vector or Crimean-Congo hemorrhagic fever virus, and that birds with an open or wetland habitat have more H. rufipes in comparison to birds with a winter habitat comprising forest and shrubs. The results also suggest a role for birds in the ecology of Alkhurma hemorrhagic fever virus, a hemorrhagic flavivirus, and a potential mechanism for dispersal of the virus to new regions, including Europe and Asia Minor. The results did not provide evidence for immature ticks of the Hyalomma marginatum complex and birds having a major role in the ecology and northward dispersal of tick-borne Anaplasma phagocytophilum, a zoonotic bacterium causing febrile illness in humans and domestic animals. However, the results give support to the idea of a divergent enzootic cycle of A. phagocytophilum involving birds as hosts. Finally, the results of this thesis suggest that H. rufipes do not serve as vectors or contribute to the transmission of the tularemia-causing bacterium Francisella tularensis and that migratory birds do not contribute to northward dispersal of F. tularensis-infected ticks. However, the results suggest that migratory birds contribute to northward dispersal of H. rufipes carrying both Francisella and spotted fever group Rickettsia species, including Francisella-like endosymbionts and Rickettsia aeschlimannii. In conclusion, this thesis helps to clarify the knowledge about the dispersal of ticks and the microorganisms they carry by northbound migrating birds in the African-Western Palaearctic region. Furthermore, it highlights the need of establishing surveillance programs for monitoring the risk of introduction and establishment of important exotic tick species, such as H. rufipes, and tick-borne pathogens in the Western Palaearctic.
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| 4. |
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| 5. |
- Jonsson, Tobias, 1991-
(författare)
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Cut isogeometric methods on trimmed multipatch surfaces
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Partial differential equations (PDE) on surfaces appear in a variety of applications, such as image processing, modeling of lubrication, fluid flows, diffusion, and transport of surfactants. In some applications, surfaces are drawn and modeled by using CAD software, giving a very precise patchwise parametric description of the surface. This thesis deals with the development of methods for finding numerical solutions to PDE posed on such parametrically described multipatch surfaces. The thesis consists of an introduction and five papers.In the first paper, we develop a general framework for the Laplace-Beltrami operator on a patchwise parametric surface. Each patch map induces a Riemannian metric, which we utilize to compute quantities in the simpler reference domain. We use the cut finite element method together with Nitsche’s method to enforce continuity over the interfaces between patches.In the second paper, we extend the framework to be able to handle geometries that consist of an arrangement of surfaces, i.e., more than two per interface. By using a Kirchhoff's condition this method avoids defining any co-normal to each surface and can deal with sharp edges. This approach is shown to be equivalent to standard Nitsche interface method for flat geometries.In the third paper, we developed a cut finite element method for elliptic problems with corner singularities. The main idea is to use an appropriate radial map that grades the finite element mesh towards the corner that counter-acts the solution's singularity.In the fourth paper, we present a new robust isogeometric method for surfaces described by CAD patches with gaps or overlaps. The main approach here is to cover all interfaces with a three-dimensional mesh and then use a hybrid variable in a Nitsche-type formulation to transfer data over the gaps. Using this hybridized approach leads to a convenient and easy to implement method with no restriction on the number of coupled patches per interface.In the fifth paper, we present a routine to the multipatch isogeometric framework for dealing with singular maps. To exemplify this, we consider a specific type of singular parametrization which essentially maps a square onto a triangle. One part of the boundary of the square will be transformed into a single point and the metric tensor becomes singular as we approach this boundary. In this work we propose a regularization procedure which is based on eigenvalue decomposition of the metric tensor.
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| 6. |
- Nguyen, Van-Dang, 1985-
(författare)
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High-Performance Finite Element Methods : with Application to Simulation of Diffusion MRI and Vertical Axis Wind Turbines
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform.
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| 7. |
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| 8. |
- Jansson, Niclas
(författare)
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High performance adaptive finite element methods for turbulent fluid flow
- 2011
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Understanding the mechanics of turbulent fluid flow is of key importance for industry and society as for example in aerodynamics and aero-acoustics. The massive computational cost for resolving all turbulent scales in a realistic problem makes direct numerical simulation of the underlying Navier-Stokes equations impossible. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized where the mesh is adaptively resolved, based on a posteriori error control. These adaptive methods have been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method for modern parallel computer architectures. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallellization of local mesh refinement methods such as recursive longest edge bisection. We also address the load balance problem with the development of an a priori predictive dynamic load balancing method. Current results are encouraging with almost linear strong scaling to thousands of cores on several modern architectures.
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| 9. |
- Leoni, Massimiliano
(författare)
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Finite Element simulations: computations and applications to aerodynamics and biomedicine
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Partial Differential Equations describe a large number of phenomena of practical interest and their solution usually requires running huge simulations on supercomputing clusters. Especially when dealing with turbulent flows, the cost of such simulations, if approached naively, makes them unfeasible, requiring modelling intervention. This work is concerned with two main aspects in the field of Computational Sciences. On the one hand we explore new directions in turbulence modelling and simulation of turbulent flows; we use an adaptive Finite Element Method and an \emph{infinite Reynolds number} model to reduce the computational cost of otherwise intractable simulations, showing that we are able to perform time-dependent computations of turbulent flows at very high Reynolds numbers, considered the main challenge in modern aerodynamics. The other focus of this work is on biomedical applications. We develop a computational model for (Cardiac) Radiofrequency Ablation, a popular clinical procedure administered to treat a variety of conditions, including arrhythmia. Our model improves on the state of the art in several ways, most notably addressing the critical issue of accurately approximating the geometry of the configuration, which proves indispensable to correctly reproduce the physics of the phenomenon.
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| 10. |
- Nazarov, Murtazo, 1980-
(författare)
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Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows. The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D. To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity. The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation.
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