An immersed interface method and an immersed finite element method for solving linear elasticity problems with two phases separated by an interface have been developed in this thesis. For the problem of interest, the underlying elasticity modulus is a constant in each phase but vary from phase to phase. The basic goal here is to design an efficient numerical method using a fixed Cartesian grid. The application of such a method to problems with moving interfaces driving by stresses has a great advantage: no re-meshing is needed. A local optimization strategy is employed to determine the finite difference equations at grid points near or on the interface. The bi-conjugate gradient method and the GMRES with preconditioning are both implemented to solve the resulting linear systems of equations and compared. The level set method is used to represent the interface. Numerical results are presented to show that the immersed interface method is second-order accurate.

Climate change may cause epidemic threats as species spreading human diseases invades previously unpopulated areas. A species can establish in new areas if they fulfills an invasion criterion. Two common invasion criteria are the long-term exponential growth-rate, r, and the basic reproduction number, R0, that measures the population's exponential growth in time and growth between generations respectively. Previous work have determined the long-term exponential growth-rate of the mosquito Aedes aegypti, a vector spreading dengue, zika and yellow fever, in Europe. However, in epidemiology r is rarely used as invasion criterion, which makes their results difficult to communicate and interpret. A more commonly used invasion criterion is the basic reproduction number R0. From this number, public health receives information about high-risk areas where they can vaccinate the population and prevent the mosquitoes from establishing by reducing breeding habitats. Here we extend the previous work by developing a method to calculate R0 for Aedes aegypti and verify it by the results from previous studies. Using R0 as invasion criterion we then predict the global distribution of Aedes aegypti during different climate change scenarios in the 21st century. One related to high emissions of greenhouse gases, RCP8.5, and one to low emissions, RCP2.6. We predict that the distribution of Aedes aegypti will expand towards higher latitudes at great speed during the 21st century assuming the high emission scenario RCP8.5. Assuming the low emission scenario RCP2.6, the distribution will not reach higher latitudes at the end of the 21st century. In Europe, the distribution covered 1.8 % in the beginning of the 20th century and at the end of the 21st century the distribution will cover 10 % assuming RCP8.5 and 2.0 % assuming RCP2.6. This work underscores the importance of reducing global warming and to take other preventive actions to avoid major epidemic outbreaks. Since we also provide instructions and software to calculate both r and R0 for stage-structured models in periodic environments, we anticipate that this work will support more studies of this kind to better understand the epidemic threats from climate change.

This thesis focuses on investigating the usage of statistical models for estimating fuel consumption of heavy duty vehicles. Several statistical models are assessed, along with machine learning using artificial neural networks. Data recorded by sensors on board trucks in the EU describe the operational usage of the vehicle. The usage of this data for estimating the fuel consumption is assessed, and several variables originating from the operational data is modelled and tested as possible input parameters. The estimation model for real world fuel consumption uses 8 parameters describing the operational usage of the vehicles, and 8 parameters describing the vehicles themselves. The operational parameters describe the average speed, topography, variation of speed, idling, and more. This model has an average relative error of 5.75%, with a prediction error less than 11.14% for 95% of all tested vehicles. When only vehicle parameters are considered, it is possible to make predictions with an average relative error of 9.30%, with a prediction error less than 19.50% for 95% of all tested vehicles. Furthermore, a computer software called Vehicle Energy Consumption Calculation tool(VECTO) must be used to simulate the fuel consumption for all heavy duty vehicles, according to legislation by the EU. Running VECTO is a slow process, and this thesis also investigates how well statistical models can be used to quickly estimate the VECTO fuel consumption. The model estimates VECTO fuel consumption with an average relative error of 0.32%and with a prediction error less than 0.65% for 95% of all tested vehicles. / Denna rapport fokuserar på att undersöka användningen av statistiska mod-eller för att uppskatta bränsleförbrukningen hos tunga fordon. Flera statistiska modeller utvärderas, tillsammans med maskinlärning med artificiella neurala nätverk. Data som registreras av sensorer ombord på Scania-lastbilar i EU beskriver fordonets drift. Användningen av dessa data för att uppskatta bränsleförbrukningen undersöks och flera variabler som kommer från operativa data modelleras och testas som möjliga in-parametrar. Uppskattningsmodellen för den verkliga bränsleförbrukningen använder 8 parametrar som beskriver användningen av fordonet och 8 parametrar som beskriver själva fordonet. Bland annat beskrivs medelhastighet, topografi, hastighetsvariation, andel tomgång. Denna modell har ett genomsnittligt relativfel på 5.75 %, med ett skattningsfel mindre än 11.14% för 95% av de de fordon som testats. Om endast fordonsparametrar beaktas som in-parametrar är det möjligt att göra skattningar med ett genomsnittligt relativfel på 9.30 %, med ett skattningsfel mindre än 19.50% för 95% av de de fordon som testats. Ett datorprogram kallat VECTO måste användas för att simulera bränsleförbrukningen för alla tunga fordon enligt EU-lagstiftning. Att köra VECTO är en tidskrävande process, och denna rapport undersöker också hur väl statistiska modeller kan användas för att snabbt uppskatta VECTO-bränsleförbrukningen. Modellen uppskattar VECTO-bränsleförbrukningen med ett genomsnittligt relativfel på 0.32% och med ett skattningsfel mindre än 0.65% för 95% av de de fordon som testats.

In this thesis we investigate how to optimize an algorithm that determines a scenario multiplier for a reverse stress test with a method where predefined scenarios are scaled. The scenarios are composed by different risk factors that represents market events. A reverse stress test is used for risk estimation and explains for what market condition a given portfolio will lose a particular amount. In this study we consider a reverse stress test where the goal is to find for what scenario a clearing house become insolvent, that is when the clearing house's loss is equal to its resource pool. The goal with this work is to find a more efficient algorithm than the current bisection algorithm for finding the scenario multiplier in the reverse stress test. The algorithms that were examined were one bracketing algorithm (the false-position algorithm) and two iterative algorithms (the Newton-Raphson and Halley's algorithms), which were implemented in MATLAB. A comparative study was made where the efficiency of the optimized algorithms were compared with the bisection algorithm. The algorithms were evaluated by comparing the running times and number of iterations needed to find the scenario multiplier in the reverse stress test. Other optimization strategies that were investigated were to reduce the number of scenarios in the predefined scenario matrix to decrease the running time and determine an appropriate initial multiplier to use in the iterative algorithms. The reduction of scenarios consisted of removing the scenarios that were multiples of other scenarios by comparing the risk factors in each scenario. We used Taylor approximation to simplify the loss function and thereby approximate an initial multiplier, which would reduce the manually input from the user. Furthermore, we investigated the running times and number of iterations needed to find the scenario multiplier when several initial multipliers were used in the iterative algorithms to increase the chance of finding a solution.   The result shows that both the Newton-Raphson algorithm and Halley's algorithm are more efficient and need less iterations to find the scenario multiplier than the current bisection algorithm. Halley's algorithm is the most efficient, which is on average 200-470% faster than the current algorithm depending on how many initial multipliers that are used (one, two or three), while the Newton-Raphson algorithm is on average 150-300% faster than the current algorithm. Furthermore, the result shows that the false-position algorithm is not efficient for this aim. The result from the reduction of scenarios shows that scenarios could be removed by this approach, where the real scenario obtained from performing a reverse stress test was never among the removed scenarios. Moreover, the initial multiplier approximation could be used when the scenario matrix contains a certain type of risk factors. Finally, this study shows that the current bisection algorithm can be optimized by the Newton-Raphson algorithm and Halley's algorithm.

Aircraft trailing vortices is an inevitable side effect when an aircraft generates lift. The vortices represent a danger for following aircraft and forces large spacing between landing and take off at airports. Detailed knowledge about the dynamics of aircraft trailing vortices is therefore needed to increase airport capacity and aviation safety. In this thesis, an accurate numerical simulation of aircraft trailing vortices is performed. The vortices undergo an expected instability phenomena followed by a reconnection process. The reconnection process is studied in detail. During the reconnection, theoretically described structures can be observed.

The numerical solution of chemical reactions described at the meso-scale is the topic of this thesis. This description, the master equation of chemical reactions, is an accurate model of reactions where stochastic effects are crucial for explaining certain effects observed in real life. In particular, this general equation is needed when studying processes inside living cells where other macro-scale models fail to reproduce the actual behavior of the system considered. The main contribution of the thesis is the numerical investigation of two different methods for obtaining numerical solutions of the master equation. The first method produces statistical quantities of the solution and is a generalization of a frequently used macro-scale description. It is shown that the method is efficient while still being able to preserve stochastic effects. By contrast, the other method obtains the full solution of the master equation and gains efficiency by an accurate representation of the state space. The thesis contains necessary background material as well as directions for intended future research. An important conclusion of the thesis is that, depending on the setup of the problem, methods of highly different character are needed.

Deep neural networks (DNNs) have successfully been applied across various data intensive applications ranging from computer vision, language modeling, bioinformatics and search engines. Hyper-parameters of a DNN are defined as parameters that remain fixed during model training and heavily influence the DNN performance. Hence, regardless of application, the design-phase of constructing a DNN model becomes critical. Framing the selection and tuning of hyper-parameters as an expensive black-box optimization (BBO) problem, obstacles encountered in manual by-hand tuning could be addressed by taking instead an automated algorithmic approach. In this work, the following BBO algorithms: Nelder-Mead Algorithm (NM), ParticleSwarm Optmization (PSO), Bayesian Optimization with Gaussian Processes (BO-GP) and Tree-structured Parzen Estimator (TPE), are evaluated side-by-side for two hyper-parameter optimization problem instances. These instances are: Problem 1, incorporating a convolutionalneural network and Problem 2, incorporating a recurrent neural network. A simple Random Search (RS) algorithm acting as a baseline for performance comparison is also included in the experiments. Results in this work show that the TPE algorithm achieves the overall highest performance with respect to mean solution quality, speed ofimprovement and with a comparatively low trial-to-trial variability for both Problem 1 and Problem 2. The NM, PSO and BO-GP algorithms are shown capable of outperforming the RS baseline for Problem 1, but fails to do so in Problem 2.

Compact Riemann surfaces of genus greater than 1 can be realized as quotient spaces of the hyperbolic plane by the action of Fuchsian groups. The Teichmüller space is the set of all complex structures of Riemann surfaces and the moduli space the set of conformal equivalence classes of Riemann surfaces. For genus greater than two the branch locus of the covering of the moduli space by the Teichmüller space can be identified wi the set of Riemann surfaces admitting non-trivial automorphisms. Here we give the orbifold structure of the branch locus of surfaces of genus 5 by studying the equisymmetric stratification of the branch locus. This gives the orbifold structure of the moduli space. We also show that the strata corresponding to surfaces with automorphisms of order 2 and 3 belong to the same connected component for every genus. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

This thesis deals with fast and efficient methods for electrostatic calculations with application in molecular dynamics simulations. The electrostatic calculations are often the most expensive part of MD simulations of charged particles. Therefore, fast and efficient algorithms are required to accelerate these calculations. In this thesis, two types of methods have been considered: FFT-based methods and fast multipole methods (FMM). The major part of this thesis deals with fast N.log(N) and spectrally accurate methods for accelerating the computation of pairwise interactions with arbitrary periodicity. These methods are based on the Ewald decomposition and have been previously introduced for triply and doubly periodic problems under the name of Spectral Ewald (SE) method. We extend the method for problems with singly periodic boundary conditions, in which one of three dimensions is periodic. By introducing an adaptive fast Fourier transform, we reduce the cost of upsampling in the non periodic directions and show that the total cost of computation is comparable with the triply periodic counterpart. Using an FFT-based technique for solving free-space harmonic problems, we are able to unify the treatment of zero and nonzero Fourier modes for the doubly and singly periodic problems. Applying the same technique, we extend the SE method for cases with free-space boundary conditions, i.e. without any periodicity. This thesis is also concerned with the fast multipole method (FMM) for electrostatic calculations. The FMM is very efficient for parallel processing but it introduces irregularities in the electrostatic potential and force, which can cause an energy drift in MD simulations. In this part of the thesis we introduce a regularized version of the FMM, useful for MD simulations, which approximately conserves energy over a long time period and even for low accuracy requirements. The method introduces a smooth transition over the boundary of boxes in the FMM tree and therefore it removes the discontinuity at the error level inherent in the FMM. / <p>QC 20171213</p>

District heating is today, in Sweden, the most common method used for heating buildings in cities. More than half of all the buildings, both commercial and residential, are heated using district heating. The load on the district heating networks are affected by, among other things, the time of the day and different external conditions, such as temperature differences. One has to be able to simulate the heat and pressure losses in the network in order to deliver the amount of heat demanded by the customers. Expansions of district heating networks and disrupted pipes also demand good simulations of the networks. To cope with this, energy companies use simulation software. These software need to contain numerical methods that provide accurate and stable results and at the same time be fast and efficient. At the moment there are available software packages that works but these have some limitations. Among other things you may need to divide the whole network into smaller loops or try to guess how the distribution of pressure and flow in the network looks like. The development in recent years makes it possible to use better and more efficient algorithms for these types of problems. The purpose of this report is therefore to introduce a better and more efficient method than that used in the current situation. This work is the first step in order to replace a current method used in a simulation software provided by Vitec energy. Therefore, we will in this report, stick to computing pressure and flow in the network. The method we will introduce in this report is called the gradient method and it is based on the Newton Raphson method. Unlike with older methods like Hardy Cross which is a relaxation method, you do not have to divide the network into loops. Instead you create a matrix representation of the network that is used in the computations. The idea is also that you should not need to make good initial guesses to get the method to converge quickly. We performed a number of test simulations in order to examine how the method performs. We tested how different initial guesses and how different sizes of the networks affected the number of iterations. The results shows that the model is capable of solving large networks within a reasonable number of iterations. The results also show that the initial guesses have little impact on the number of iterations. Changing the initial guess on the pressure does not affect the number at all but it turns out that changing the initial guess on the flow can affect the number of iterations a little, but not much.