In this thesis, we study a numerical tool named multi-mesh method within the framework of the adaptive finite element method. The aim of this method is to minimize the size of the linear system to get the optimal performance of simulations. Multi-mesh methods are typically used in multi-physics problems, where more than one component is involved in the system. During the discretization of the weak formulation of partial differential equations, a finite-dimensional space associated with an independently refined mesh is assigned to each component respectively. The usage of independently refined meshes leads less degrees of freedom from a global point of view. To our best knowledge, the first multi-mesh method was presented at the beginning of the 21st Century. Similar techniques were announced by different mathematics researchers afterwards. But, due to some common restrictions, this method is not widely used in the field of numerical simulations. On one hand, only the case of two-mesh is taken into scientists\' consideration. But more than two components are common in multi-physics problems. Each is, in principle, allowed to be defined on an independent mesh. Besides that, the multi-mesh methods presented so far omit the possibility that coefficient function spaces live on the different meshes from the trial and test function spaces. As a ubiquitous numerical tool, the multi-mesh method should comprise the above circumstances. On the other hand, users are accustomed to improving the performance by taking the advantage of parallel resources rather than running simulations with the multi-mesh approach on one single processor, so it would be a pity if such an efficient method was only available in sequential. The multi-mesh method is actually used within local assembling process, which should not be conflict with parallelization. In this thesis, we present a general multi-mesh method without the limitation of the number of meshes used in the system, and it can be applied to parallel environments as well. Chapter 1 introduces the background knowledge of the adaptive finite element method and the pioneering work, on which this thesis is based. Then, the main idea of the multi-mesh method is formally derived and the detailed implementation is discussed in Chapter 2 and 3. In Chapter 4, applications, e.g. the multi-phase flow problem and the dendritic growth, are shown to prove that our method is superior in contrast to the standard single-mesh finite element method in terms of performance, while accuracy is not reduced.

Background. In this thesis a novel method of skinning a mesh utilizing Nvidia’sTuring Mesh Shader pipeline is presented. Skinning a mesh is often performed with a Vertex Shader or a Compute Shader. By leveraging the strengths of the new pipeline it may be possible to further optimize the skinning process and increase performance, especially for more complex meshes. Objectives. The aim is to determine if the novel method is a suitable replacement for existing skinning implementations. The key metrics being studied is the total GPU frame time of the novel implementation in relation to the rest, and its total memory usage. Methods. Beyond the pre-existing implementations such as Vertex Shader skinning and Compute Shader skinning, two new methods using Mesh Shaders are implemented. The first implementation being a naive method that simply divides the mesh into meshlets and skins each meshlet in isolation. The proposed novel common influences method instead takes the skinning data, such as the joint influences of each vertex, into account when generating meshlets. The intention is to produce meshlets where all vertices are influenced by the same joints, allowing for information to be moved from a per vertex basis to a per meshlet basis. Allowing for fewer fetches to occur in the shader at run-time and potentially better performance. Results. The results indicate that utilizing Mesh Shaders results in approximately identical performance compared to Vertex Shader skinning, (which was observed to be the fastest of the previous implementations) with the novel implementation being marginally slower due to the increased number of meshlets generated. Mesh Shading has the potential to be faster if optimizations unique to the new shaders are employed. Despite producing more meshlets, the novel implementation is not significantly slower and is faster at processing individual meshlets compared to the naive approach. The novel Common Influences implementation spends between 15-22% less time processing each meshlet at run-time compared to the naive solution. Conclusions. Ultimately the unique capabilities of Mesh Shaders allow for potential performance increases to be had. The proposed novel Common Influences method shows promise due to it being faster on a per meshlet basis, but more work must be done in order to reduce the number of meshlets generated. The Mesh Shading pipeline is as of writing very new and there is a lot of potential for future work to further enhance and optimize the work presented in this thesis. More work must be done in order to make the meshlet generation more efficient so that the run-time workload is reduced as much as possible. / Bakgrund. I denna avhandling presenteras en ny metod för att deformera en modell med hjälp av den nya Mesh Shader funktionaliteten som är tillgänglig i Nvidias nya Turing arkitektur. Deformering av modeller utförs just nu oftast med så kallade Vertex eller Compute Shaders. Genom att nyttja styrkan hos den nya arkitekturen så kan det vara möjligt att ytterligare optimera deformeringsprocessen och på så sätt öka prestandan. Speciellt i samband där mer komplexa modeller används. Syfte. Syftet är att avgöra om den nya metoden är en lämplig ersättning av de nuvarande implementationerna. De viktigaste aspekterna som studeras är den totala GPU-exekveringstiden per bild som renderas av den nya metoden i förhållande till resterande, samt dess totala minnesanvändning. Metod. Utöver de befintliga implementeringarna, såsom Vertex Shader deformering och Compute Shader deformering, implementeras två nya metoder som använder Mesh Shaders. Den första implementeringen är en naiv metod som helt enkelt delar modellen i mindre delar, så kallade meshlets och deformerar varje meshlet i isolering. Den föreslagna nya common influences metoden tar i stället hänsyn till deformeringsdatan som tillhör modellen, såsom de gemensamma inverkningarna av varje vertex, vid generering av meshlets.  Avsikten är att producera meshlets där alla vertriser påverkas av samma leder i modellens skelett, vilket gör det möjligt att flytta informationen från en per vertris basis till en per meshlet basis. Detta tillåter att färre hämtningar sker på grafikkortet vid körning och vilket kan potentiellt ge bättre prestanda. Resultat. Resultaten indikerar att utnyttjandet av Mesh Shaders resulterar i ungefär samma prestanda jämfört med Vertex Shader deformering, (som observerades vara den snabbaste av de existerande implementationerna) samt att den orginella implementationen är marginellt långsammare på grund av ett högre antal meshlets genereras. Mesh Shading har potential till att bli snabbare om optimeringar somär unika till den nya arkitekturen används. Trots att man producerar fler meshlets,är den nya metoden inte markant långsammare och är snabbare med att bearbeta meshlets individuellt jämfört med den naiva implementationen. Den orginella implementationen spenderar mellan 15-22% mindre tid per meshlet vid körtid jämfört med den naiva lösningen. Slutsatser. I slutändan så erbjuder Mesh Shaders unika nya möjligheter till optimeringar som kan leda till potentiellt bättre prestanda. Den föreslagna nya Common Influences-metoden är lovande på grund av att den är snabbare per meshlet, men mer arbete måste utföras för att minska antalet genererade meshlets. Mash Shaders och Turing arkitekturen är vid skrivande stund fortfarande väldigt nya och det finns mycket potential för framtida arbeten att yterrligare förbättra och optimera det arbete som presenteras i denna avhandling. Mer arbete måste utföras för att göra meshletgenereringen effektivare så att arbetet som måste utföras under körtid minskas så mycket som möjligt.

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This paper gives an overview of the mathematical and practical tools that can be used in turbo-machinery RANS simulation to realize unstructured mesh adaptation. It first presents the concept of metric and recalls that the hessian of the physical flow properties can become, thanks to small modifications, both a metric and a upper bound of the P1 projection error. The resulting metric is then studied on a simple 2D case. In a second part, the industrial application of this concept is addressed and the tools used to overcome the turbo-machinery specificities are explained. Finally, some 2D and 3D results are presented.

Wireless mesh networks (WMN) is a new promising wireless technology which uses already available hardware and software components. This thesis proposes a routing algorithm for military applications. More specifically, a specialized scenario consisting of a network of flying Unmanned Aerial Vehicles (UAVs) executing reconnaissance missions is investigated. The proposed routing algorithm is hybrid in nature and uses both reactive and proactive routing characteristics to transmit information. Through simulations run on a specially built stand alone simulator, based on Java, packet overhead, delivery ratio and latency metrics were monitored with respect to varying number of nodes, node density and mobility. The results showed that the high overhead leads to high delivery ratio while latency tends to increase as the network grows larger. All the metrics revealed sensitivity in high mobility conditions.

Simulations were performed to evaluate solution adaptive meshing strategies for flows with vortices whose axes of rotation are parallel to the bulk fluid motion. Two configurations were investigated: a wing in a wind tunnel and a missile spinning at 30Hz and 60Hz at 0◦ angle of attack with canards deflected 15◦. Feature-based descriptors were used to identify regions of the flow near vortices that are candidate regions for adaptive meshing. Several different adaptive meshing techniques were evaluated. These techniques include refinement around the vortex core, refinement near the vortex extent surface, refinement inside the extent surface, refinement inside and near the extent surface, and mesh regeneration using the vortex extent surface as an embedded surface. Results for the wing case, compared to experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to accurately recreate physical characteristics and achieve an acceptable solution.

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Mobil datakonsumtion har drastiskt ökat de senaste åren vilket belastar de existerande kommunikationsnätverken. I och med den ökade belastningen av existerande infrastrukturer krävs det nya kommunikationslösningar. Detta har i sin tur skapat ett behov för dataavlastning på fasta nätverk, exempelvis Wi-Fi-nätverk. I denna studie undersöker vi genom simuleringar hur vi kan underhålla ett storskaligt och dynamiskt Bluetooth meshnätverk i en miljö likt Stortorget under Malmöfestivalen. Vi implementerar en nätverkstopologi för Bluetooth, scatternettopologin, i nätverkssimulatorn NS-3 och utför simuleringar där vi provocerar förändringar i topologin. Resultaten av våra simuleringar visar på att nätverket lyckas återhämta sig vid förändring i topologin, att scatternettopologin minst klarar av 240 dynamiska mobila noder samt att max 3 noder påverkas vid förändringar i topologin för simuleringar av upp till 240 noder. / Mobile data consumption has drastically increased in the recent years which stress theexisting communication networks. As an effect of the increased load a demand for newcommunication solutions has arisen, creating a need for data offloading onto fixed networks such as Wi-Fi. In this thesis, we aim to study how to maintain and reconstruct a large and dynamic Bluetooth mesh network in an environment such as Stortorget during Malmöfestivalen. We implement a network topology specific for Bluetooth, the scatternet topology, in the network simulator NS-3 and run simulations in which we provoke changes in the network topology. The result of our simulations shows that the network is able to heal itself when the topology changes, that the scatternet topology can manage up to 240 dynamic mobile nodes and that at most 3 nodes are affected when the topology changes during simulations of up to 240 nodes.