A prestudy indicated superior accuracy and convergence properties of apseudo-spectral method compared to a spline-based method implemented byCòrdoba et al. in 2005 when solving the α-patches problem. In this thesis wefurther investigate the numerical properties of the pseudo-spectral method and makeit more robust by implementing the Nonequispaced Fast Fourier Transform. Wepresent a more detailed overview and analysis of the pseudo-spectral method and theα-patches problem in general and conclude that the pseudo-spectral method issuperior in regards to accuracy in periodic settings.

In this thesis, parabolic-pseudoparabolic equations are derived coupling chemical reactions, diffusion, flow and mechanics in a heterogeneous medium using the framework of mixture theory. The weak solvability in 1-D of the obtained models is studied. Furthermore, it is numerically illustrated that approximate solutions according to the Rothe method exhibit expected realistic behaviour. For a simpler model formulation, the periodic homogenization in higher space dimensions is performed. / <p>Research is funded by the Netherlands Organisation of Scientific Research (NWO) with MPE-grant 657.000.004, and a research stay at Karlstads Universitet is funded by NWO cluster Nonlinear Dynamics in Natural Systems (NDNS+).</p>

This thesis explores and explains a method using discrete curvature as a feature to find regions of vertices that can be classified as being likely to indicate the presence of an underlying tumor on a kidney surface mesh. Vertices are tagged based on curvature type and mathematical morphology is used to form regions on the mesh. The size and location of the tumor is approximated by fitting a sphere to this region. The method is intended to be employed in noninvasive radiotherapy with a dynamic soft tissue model. It could also provide an alternative to volumetric methods used to segment tumors. A validation is made using the images from which the kidney mesh was constructed, the tumor is visible as a comparison to the method result. The dynamic kidney model is validated using the Hausdorff distance and it is explained how this can be computed in an effective way using bounding volume hierarchies. Both the tumor finding method and the dynamic model show promising results since they lie within the limit used by practitioners during therapy.

The goal of this project was to create a web-based, crowd-sourced, correlational database, that easily allowed users to submit objects and receive correlated objects as results. The webservice was created in the web development languages of HTML, CSS, PHP and Javscript, with MySQL to handle the database. Simultaneous development was kept in check with the aid of the source code management system GIT. Upon completion, the service contained several HTML-views, the ability to add and rate objects, a per-object dedicated page with information parsed from Wikipedia.org, and a view with objects ranked in accordance to the preferences specific to the current user. Roughly a month after the beginning of development, the website was publicly launched and promoted in order to collect data, and improvements were added to the website as needed. Two weeks after the public launch, the collected data was measured and analyzed. The algorithm proved effective and scalable, especially with the introduction of tags and simultaneous computation of object features.

The aim for this thesis is to develop a foundation for a compression system for animated mesh sequences, specifically under dynamic change of mesh geometry and topology. Compression of mesh sequences is of special interest in the game industry and this particular thesis is a part of an ongoing series of projects at EA DICE. One of the primary challenges when creating a mesh compression system is creating a matching bijective subset of the mesh surfaces between two subsequent frames in the animation to guide remeshing of the sequence. This thesis describes a method for producing a bijective set of matching mesh patches between two meshes along with an error metric that captures the quality of the matching in terms of shape similarity and distortion. Theory of mathematical topology and tensor algebra used in methods for high performance scientific digital 3D-image recognition are here adopted to extract similar local features between meshes. Techniques for creating parametrizations of mesh patches are combined with techniques for matching point clouds and deforming mesh geometry under energy minimization in order to produce a matching set of patches. The presented algorithm successfully creates bijective sets of matched patches for subsequent meshes in a sequence as well as measures the error for the matchings. Results show an average matching set size of approximately 25% of the mesh areas over a sequence of meshes. This suggests that the data size of such a sequence could potentially be reduced by 25%.

To predict fluid properties and interactions is an important task for the industry. It is plagued, however, by being close to impossible to predict analytically. Hence, it is customary to turn to numerical solutions. This in itself comes with many different methods and approaches suitable for different needs. This work focuses on two methods: Tip Vortex Index (TVI) and Diffused Vortex Hydrodynamics (DVH). TVI is a method to predict when a marine propeller will experience cavitation of tip vortices and is based on calculations from a Boundary Element Method (BEM). DVH is a particle method for simulating the circulation of a fluid in two dimensions and three dimensions. The aim is to investigate an implemented TVI model based on MPUF-3A for different marine propeller series, with different sub-designs for a total of 28 unique propellers, and implement the DVH method and test it for 3 different bodies. The results of this thesis show that the implemented TVI model is non-functional for the 28 different propellers, but the DVH method is successfully implemented and able to handle 2 different bodies. / Att förutspå fluid egenskaper och interaktioner är en viktig uppgift för industrin. Det plågas dock av att vara näst intil omöjligt att förutspå analytiskt. Det är därför vanligt att vända sig till numeriska lösningar. Detta kommer i sig med många olika metoder och tillvägagångssätt som passar olika behov. Detta arbete fokuserar på två metoder: Tip Vortex Index (TVI) och Diffused Vortex Hydrodynamics (DVH). TVI är en metod för att förutsäga när en marin propeller kommer att uppleva kavitation av spetsvirvlar och baseras på beräkningar från en Boundary Element Method (BEM). DVH är en partikelmetod för att simulera cirkulationen i fluid i två dimensioner och tre dimensioner. Syftet är att undersöka en implementerad TVI-modell baserad på MPUF-3A för olika marina propellerserier, med olika underdesigner, för totalt 28 unika propellrar, och implementera DVH-metoden och testa den för 3 olika kroppar. Resultaten av denna avhandling visar att den implementerade TVI-modellen är icke-funktionell för de 28 olika propellrarna, men DVH-metoden är framgångsrikt implementerad och kan hantera 2 olika kroppar

Heart disease is the leading cause of death in the world. Therefore, numerous studies are undertaken to identify indicators which can be applied to discover cardiac dysfunctions at an early age. Among others, the fluid dynamics of the blood flow (hemodymanics) is considered to contain relevant information related to abnormal performance of the heart.This thesis presents a robust framework for numerical simulation of the fluid dynamics of the blood flow in the left ventricle of a human heart and the fluid-structure interaction of the blood and the aortic leaflets.We first describe a patient-specific model for simulating the intraventricular blood flow. The motion of the endocardial wall is extracted from data acquired with medical imaging and we use the incompressible Navier-Stokes equations to model the hemodynamics within the chamber. We set boundary conditions to model the opening and closing of the mitral and aortic valves respectively, and we apply a stabilized Arbitrary Lagrangian-Eulerian (ALE) space-time finite element method to simulate the blood flow. Even though it is difficult to collect in-vivo data for validation, the available data and results from other simulation models indicate that our approach possesses the potential and capability to provide relevant information about the intraventricular blood flow.To further demonstrate the robustness and clinical feasibility of our model, a semi-automatic pathway from 4D cardiac ultrasound imaging to patient-specific simulation of the blood flow in the left ventricle is developed. The outcome is promising and further simulations and analysis of large data sets are planned.In order to enhance our solver by introducing additional features, the fluid solver is extended by embedding different geometrical prototypes of both a native and a mechanical aortic valve in the outflow area of the left ventricle.Both, the contact as well as the fluid-structure interaction, are modeled as a unified continuum problem using conservation laws for mass and momentum. To use this ansatz for simulating the valvular dynamics is unique and has the expedient properties that the whole problem can be described with partial different equations and the same numerical methods for discretization are applicable.All algorithms are implemented in the high performance computing branch of Unicorn, which is part of the open source software framework FEniCS-HPC. The strong advantage of implementing the solvers in an open source software is the accessibility and reproducibility of the results which enhance the prospects of developing a method with clinical relevance. / <p>QC 20171006</p>

This dissertation presents a comprehensive and comparative progress in sequencing approaches of mixed-model just-in-time (JIT) sequencing problem together with discrete apportioment problem (DAP). The goal of JIT sequencing problem (JITSP) is to keep the rate of usage of parts as constant as possible along the assembly lines, and the goal of DAP is to divide a given integer number of delegates proportionally among the states or the parties according to their population or votes. Furthermore, the supply chain logistics problem is also reported in here with some real life applications.The single-level JITSP, known as the product rate variation problem (PRVP), is pseudo-polynomially solvable. The total PRVP minimizes sum deviation and the bottleneck PRVP minimizes the maximum deviation between the actual production and the ideal production. The assignment approach solves total PRVP whereas the perfect matching works for bottleneck PRVP solving the problem in pseudo-polynomial time. The multi-level JITSP, known as the output rate variation problem (ORVP), is NP-hard in most of the cases. However, some sequencing heuristics and dynamic programming are devised for near optimal solutions. And the pegging assumption reduces the ORVP into weighted case of PRVP. In this dissertation, the total PRVP with square and absolute deviations are considered and mean-based divisor methods are devised for the equitably efficient solution. The simultaneous dealing to the PRVP and DAP establishes the interlink between the production sequencing problem and integer seat allocating problem. The new upper bottlenecks are investigated and the problems are solved comparatively. The bottleneck PRVP instances for small deviations and cyclic sequences for total PRVP are shown to be optimal. The bicriterion sequencing is discussed with Pareto optimal solutions.The production sequencing problem is simultaneously dealt with supply chain logistics to balance overall supply chain system. The cross-docking supply chain logistics problem is formulated with a proposition to be solved. The real-world applications of JITSP and supply chain are listed and some open problems are pointed out as the closing of the dissertation.

Event-based models find frequent usage in fields such as computational physics and biology as they may contain both continuous and discrete state variables and may incorporate both deterministic and stochastic state transitions. If the state transitions are stochastic, computer-generated random numbers are used to obtain the model solution. This type of event-based computations is also known as Monte-Carlo simulation. In this thesis, I study different approaches to execute event-based computations on parallel computers. This ultimately allows users to retrieve their simulation results in a fraction of the original computation time. As system sizes grow continuously or models have to be simulated at longer time scales, this is a necessary approach for current computational tasks. More specifically, I propose several ways to asynchronously simulate such models on parallel shared-memory computers, for example using parallel discrete-event simulation or task-based computing. The particular event-based models studied herein find applications in systems biology, computational epidemiology and computational neuroscience. In the presented studies, the proposed methods allow for high efficiency of the parallel simulation, typically scaling well with the number of used computer cores. As the scaling typically depends on individual model properties, the studies also investigate which quantities have the greatest impact on the simulation performance. Finally, the presented studies include other insights into event-based computations, such as methods how to estimate parameter sensitivity in stochastic models and how to simulate models that include both deterministic and stochastic state transitions. / UPMARC

Radial basis function methods exhibit several very attractive properties such as a high order convergence of the approximated solution and flexibility to the domain geometry. However the method in its classical formulation becomes impractical for problems with relatively large numbers of degrees of freedom due to the ill-conditioning and dense structure of coefficient matrix. To overcome the latter issue we employ a localisation technique, namely a partition of unity method, while the former issue was previously addressed by several authors and was of less concern in this thesis. In this thesis we develop radial basis function partition of unity methods for partial differential equations arising in financial mathematics and glaciology. In the applications of financial mathematics we focus on pricing multi-asset equity and credit derivatives whose models involve several stochastic factors. We demonstrate that localised radial basis function methods are very effective and well-suited for financial applications thanks to the high order approximation properties that allow for the reduction of storage and computational requirements, which is crucial in multi-dimensional problems to cope with the curse of dimensionality. In the glaciology application we in the first place make use of the meshfree nature of the methods and their flexibility with respect to the irregular geometries of ice sheets and glaciers. Also, we exploit the fact that radial basis function methods are stated in strong form, which is advantageous for approximating velocity fields of non-Newtonian viscous liquids such as ice, since it allows to avoid a full coefficient matrix reassembly within the nonlinear iteration. In addition to the applied problems we develop a least squares radial basis function partition of unity method that is robust with respect to the node layout. The method allows for scaling to problem sizes of a few hundred thousand nodes without encountering the issue of large condition numbers of the coefficient matrix. This property is enabled by the possibility to control the coefficient matrix condition number by the rate of oversampling and the mode of refinement.