This thesis summarizes interrelated simulation studies of three different physical phenomena. The three topics are: simulation of work hardening of materials using dislocation dynamics, investigation of anomalous diffusion in supercooled liquids using molecular dynamics,and kinetic Monte-Carlo simulation of annealing of radiation damaged materials. All three topics require special algorithms in order to enable physically relevant simulations. The author's contributionconsists of development, implementation, and optimization of these algorithms, as well as interpretation of simulation results. / QC 20100805

In high frequency computational electromagnetics, rigorous numerical methods be come unrealistic tools due to computational demand increasing with the frequency. Instead approximations to the solutions of the Maxwell equations can be employed to evaluate th electromagnetic fields. In this thesis, we present the implementations of three high frequency approximat methods. The first two, namely the Geometrical Theory of Diffraction (GTD) and th Physical Optics (PO), are commonly used approximations. The third is a new invention that will be referred to as the Surface Current Extraction-Extrapolation (SCEE). Specifically, the GTD solver is a flexible and modular software package which use Non-Uniform Rational B-spline (NURBS) surfaces to model complex geometries. The PO solver is based on a triangular description of the surfaces and includes fas shadowing by ray tracing as well as contribution from edges to the scattered fields. GTD ray tracing was combined with the PO solver by a well thought-out software architecture Both implementations are now part of the GEMS software suite, the General ElectroMag netic Solvers, which incorporates state-of-the-art numerical methods. During validations both GTD and PO techniques turned out not to be accurate enough to meet the indus trial standards, thus creating the need for a new fast approximate method providing bette control of the approximations. In the SCEE approach, we construct high frequency approximate surface currents ex trapolated from rigourous Method of Moments (MoM) models at lower frequency. T do so, the low frequency currents are projected onto special basis vectors defined on th surface relative to the direction of the incident magnetic field. In such configuration, w observe that each component displays systematic spatial patterns evolving over frequenc in close correlation with the incident magnetic field, thus allowing us to formulate a fre quency model for each component. This new approach is fast, provides good control of th error and represents a platform for future development of high frequency approximations. As an application, we have used these tools to analyse the radar detectability of a new marine distress signaling device. The device, called "Rescue-Wing", works as an inflatabl radar reflector designed to provide a strong radar echo useful for detection and positionin during rescue operations of persons missing at sea. / QC 20101004

In this work we consider the nonlinear case of Black-Scholes equation and apply it to American options. Also, method of Liao and Khaliq of high order was applied to nonlinear Black-Scholes equation in case of American options. Here, we use this method oh fourth order in time and space to raise American option price accuracy.

In this report, we show how to implement direct ray tracing of B´ezier surfaces on graphics processing units (GPUs), in particular bicubic rectangular Bézier surfaces and nonparametric cubic Bézier triangles. We use Newton’s method for the rectangular case and show how to use this method to find the ray-surface intersection. For Newton’s method to work we must build a spatial partitioning hierarchy around each surface patch, and in general, hierarchies are essential to speed up the process of ray tracing. We have chosen to use bounding box hierarchies and show how to implement stackless traversal of such a structure on a GPU. For the nonparametric triangular case, we show how to find the wanted intersection by simply solving a cubic polynomial. Because of the limited precision of current GPUs, we also propose a numerical approach to solve the problem, using a one-dimensional Newton search.

The MUSCL-Hancock finite volume method with different slope limiters has been analyzed in the context of a fast transient flow problem. A derivation and analysis of the axial forces inside a pipe system due to a flow transient is also performed.  The following slope limiters were implemented and compared: MC, van Leer, van Albada, Minmod and Superbee. The comparison was based on the method's ability to calculate the forces due to a flow transient inside a pipe system. The tests and comparisons in this thesis show that the MC, van Leer, van Albada and Minmod limiters behave very much the same for the flow transient problem. If one would rank these four limiters with respect to the numerical error, the order would be the one presented above, the MC limiter being the most accurate. The error the four limiters produce is mainly of diffusive nature and it is just the magnitude of the diffusion that seems to differ between the methods. One should also note that the workload rank of the four limiters is the same as the order presented above. The MC limiter being the least efficient of the four and the Minmod limiter the most efficient. In most of the tests performed the Superbee limiter display a rather negative unpredictable behavior. For some relatively simple cases this particular approach shows big difficulties maintaining the dynamical properties of the force. However, the upside of the Superbee limiter is its remarkable ability to maintain the maximum value of the forces present in the pipe system, preventing underestimation of the maximum magnitude of the force.

No description available.

This thesis is devoted to the analysis and optimization of pacing strategies in cross-country skiing and time-trial road cycling. In locomotive sports, it is well known that variable pacing strategies using changes in the distribution of power output are beneficial when external forces vary along the way. However, there is a lack of research that more in detail investigates the magnitude of power output alteration necessary to optimize performance.A numerical program has been developed in the MATLAB software to simulate cross-country skiing and time-trial road cycling, as well as pacing strategy optimization in these two locomotive sports. The simulations in this thesis are performed by solving equations of motion, where all the main forces acting on the athlete are considered. The motion equations also depend on the course profile, which is expressed as a connected chain of cubical splines.The simulation process is linked to an optimization routine called the Method of Moving Asymptotes (MMA), which strives to minimize the finishing time while altering the power output along the course. To mimic the human energetic system, the optimization is restricted by behavioural and side constraints.Simple constraints like maximum average power output are used for cross-country skiing in Papers I and II. In Paper III a more sophisticated and realistic constraint is used for the power output in time-trial road cycling. It is named the concept of critical power for intermittent exercise and combines the aerobic and anaerobic contributions to power output.In conclusion, this thesis has demonstrated the feasibility of using numerical simulation and optimization in order to optimize pacing strategies in two locomotive sports. The results are clearly showing that these optimized pacing strategies are more beneficial to performance than an even distribution of power output. / Denna avhandling är dedikerad att analysera och optimera farthållningsstrategier i längdskidåkning och tempocykling på landsväg. I idrotter som bygger på kontinuerlig framåtdrivning är det väl känt att farthållningsstrategier med variabel effekt är fördelaktiga om de yttre krafterna varierar längs banan. Ändå saknas forskning som mer i detalj utreder hur mycket effekten ska variera för att optimera prestationen.Ett numeriskt program har utvecklats i programvaran MATLAB för att simulera längdskidåkning och tempocykling samt optimera farthållningsstrategin i dessa idrotter. Simuleringarna använder sig av rörelseekvationer som består av de huvudsakliga krafter som verkar på idrottsutövaren under färd. Rörelseekvationerna påverkas också av banprofilen, som är uppbyggd av en sammankopplad kedja av tredjegradspolynom.Simuleringsprogrammet är kopplat till en optimeringsalgoritm med namnet Method of Moving Asyptotes (MMA), som strävar efter att minimera tiden mellan start och mål genom att ändra effekten längs med banan. Optimeringen begränsas av bivillkor i ett försök att efterlikna den mänskliga kroppens fysiologiska begränsningar.Enkla begränsningar såsom maximal medeleffekt används för längdskidåkningen i artikel I och II. I artikel III används mer sofistikerade och realistiska bivillkor för att begränsa uteffekten vid landsvägscykling. Här används modellen för kritisk effekt vid intervallträning, som kombinerar aerobt och anaerobt arbete.Sammanfattningsvis har denna avhandling visat på möjligheterna med att använda numerisk simulering och optimering för att optimera farthållningsstrategin i två idrotter. Resultaten visar tydligt att dessa optimerade farthållningsstrategier med varierande effekt är mer fördelaktiga för prestationen jämfört med en farthållningsstrategi med helt jämn effektfördelning.

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. / QC 20110627

Syfte med examensarbetet har varit att upprätta en grundvattenmodell överEnköpingsåsen med hjälp av programvaran MODFLOW för att därefter försöka skattagrundvattenmagasinets parametrar. Parameterskattningen utfördes med detmodelloberoende programmet PEST. Parallellt med detta gjordes även enpumptestutvärdering av dessa parametrar där typkurvor passades till en tidigare utfördprovpumpning av akviferen. Därefter jämfördes dessa båda metoder. Vidare utfördesäven en känslighetsanalys av grundvattenmodellen i MODFLOW för att försökalokalisera nya undersökningsplatser.Grundvattenmodellen uppfördes över Enköpingsåsen i och kring Enköping. Där är åsenlokaliserad i nord sydlig riktning och strax söder om Enköpings centrala delar korsasåsen av Enköpingsån. Det råder osäkerhet angående grundvattenmagasinetsvattenbalans och var åsen får sitt tillskott av vatten ifrån. Enköpingsåsen fungerar somhuvudvattentäkt i Enköpings stad vilket gör att detta har ansetts viktigt att utreda.Grundvattenmodellen byggdes upp genom att främst använda redan insamlad data frångeotekniska, geofysiska och hydrogeologiska undersökningar utförda i området samtdata från SGU och SMHI. Därifrån togs data om områdets uppbyggnad och struktursamt dess yttre betingelser som till exempel nederbörd och Mälarens vattenstånd för attskapa en numerisk modell i MODFLOW.Resultaten visar på ett överensstämmande resultat mellan parameterskattningen gjord iMODFLOW och pumptestutvärderingen. Vidare tyder resultaten i MODFLOW på attde största osäkerheterna i modellen ligger kring Enköpingsån och är då beroende av omvattnet tillförs från grundvattenmagasinets laterala delar eller från Enköpingsån.Känslighetsanalysen tyder även på att för ytterligare undersökningar av åsenshydrogeologiska betingelser bör fokus ligga på förhållandena i Enköpingsåns sedimentoch dess genomsläpplighet. / The purpose of this thesis is to establish a groundwater model of the Enköping eskerusing MODFLOW simulation and then estimate groundwater parameters with themodel-independent program PEST. In parallel, a pump test evaluation of theseparameters where type curves are fitted to a previously performed pump test of theaquifer is done to estimate the aquifer parameters. Eventually, these two methods arecompared. Furthermore, a sensitivity analysis of the groundwater model is performed totry to locate additional measurement points.The groundwater model was built for the Enköping esker in and around Enköping. Theesker is located in the north-south direction and just south of Enköpings central partswhere Enköpingsån crosses the esker. There is uncertainty regarding the water balanceof the aquifer and where the esker recharges its water from. Enköping esker serves asthe main water source in Enköping city and this is why it is considered important toinvestigate.The groundwater model was constructed primarily by using already collected data fromgeotechnical, geophysical and hydrogeological studies conducted in the area as well asdata from the SGU and SMHI. The data on the area's composition and structure as wellas its external conditions is taken to create a numerical model in MODFLOW.The results show consistent outcomes between parameter estimates made withMODFLOW/PEST and the pump test evaluation.The results made with MODFLOW makes it possible to do further analysis. Resultsshow large model uncertainties around Enköpingsån and the esker is dependent onwater supplied from either the groundwater aquifer’s lateral parts or Enköpingsån. Thesensitivity analysis also suggests that further studies of the hydrogeological conditionsshould be concentrated to Enköpingsån’s sediments and its water penetration capacity.

Idag används ofta ett samband, framtaget av Hanafy och Emery (1980), för att uppskatta deformationer vid tunnelfronten då bergförstärkning ska installeras i närheten av tunnelfronten. Sambandet visar hur deformationerna i ett referensplan utvecklas som en funktion av tunnelfrontens avstånd till referensplanet. I det här examensarbetet studerades deformationsutvecklingen i en tunnel med syftet att utvärdera hur tunnelgeometri, bergtäckning, spänningsfält och bergkvalitet påverkar deformationsutvecklingen under framdriften. I examensarbetet studerades även bergförstärkning under framdriften med syftet att jämföra resultat när hänsyn tagits till sprutbetongens härdningstid relativt när full styvhet antagits direkt vid installation samt studera belastning i bergbultar. Studien visade att analysresultat och samband framtaget av Hanafy och Emery kan återskapas med FLAC3D. Kombination av förändrat spänningsfält, tunneltvärsnitt och/eller bergtäckning medförde att deformationsutvecklingen inte följde sambandet. Resultatet kunde generaliseras till alla fall skilt från ett hydrostatiskt spänningsfält. Baserat på studien rekommenderas att sambandet enbart bör användas när hydrostatiskt spänningsfält och elastiskt materialbeteende kan antas för att uppskatta deformationer i närheten av tunnelfronten. Tredimensionell modellering i närheten av tunnelfronten rekommenderas alltid utföras när spänningsfält ej kan antas hydrostatiskt. Detta för att på ett korrekt sätt uppskatta deformationer och spänningar kring tunneln. Simulering av bergförstärkning bör genomföras baserat på verklig uttagssekvens med projektspecifika indata för att belastningshistorik och deformationer ska kunna uppskattas och användas som grund för dimensionering. / Currently, a correlation developed by Hanafy and Emery (1980), is often used to estimate deformations at the tunnel face for projects where rock reinforcement is to be installed near the tunnel face. It shows how deformations at a reference plane develops as a function of the distance to the tunnel face. In this thesis, the displacements was studied in order to investigate how tunnel geometry, rock coverage, stresses and rock quality affected the accumulation of displacements in a tunnel during excavation. Studies of rock reinforcement were conducted with purpose to compare results from simulations when the shotcrete hardening process had been considered and when maximum stiffness was assumed directly at installation. Load in bolts was also studied. The study showed that elastic analyses with FLAC3D can recreate analysis results and correlation developed by Hanafy and Emery. Combinations of changed stress field, tunnel geometry and/or rock cover resulted in three-dimensional effects which gave a different displacement ratio compared to Hanafy and Emery. This could be generalised to all cases in which the stress field differed from a hydrostatic stress field. Based on the study it is recommended to only use the correlation for estimating displacements near a tunnel face when hydrostatic stress field and elastic material behaviour can be assumed. Three-dimensional modelling should always be carried out in cases where the stress field cannot be assumed hydrostatic in order to correctly estimate displacements and stresses around the tunnel in the vicinity of the tunnel face. Simulation of rock reinforcement should be carried out based on the actual excavation sequence that will take place. Simulations should be performed with project-specific input data so that load history and displacements can be estimated properly and used in design.