The present thesis treats the numerical simulation of immiscible incompressible two-phase flows with moving contact lines. The conventional Navier–Stokes equations combined with a no-slip boundary condition leads to a non-integrable stress singularity at the contact line. The singularity in the model can be avoided by allowing the contact line to slip. Implementing slip conditions in an accurate way is not straight-forward and different regularization techniques exist where ad-hoc procedures are common. This thesis presents the first steps in developing the macroscopic part of an accurate multiscale model for a moving contact line problem in two space dimensions. It is assumed that a micro model has been used to determine a relation between the contact angle and the contact line velocity. An intermediate region is introduced where an analytical expression for the velocity field exists, assuming the solid wall is perfectly flat. This expression is used to implement boundary conditions for the moving contact line, at the macroscopic scale, along a fictitious boundary located a small distance away from the physical boundary. Model problems where the shape of the interface is constant throughout the simulation are introduced. For these problems, experiments show that the errors in the resulting contact line velocities converge with the grid size h at a rate of convergence p ≈ 2. Further, an analytical expression for the velocity field in the intermediate region for the case with a curved solid wall is derived. The derivation is based on perturbation analysis. / eSSENCE

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During the last two decades, advances in molecular technology have facilitated the sequencing and analysis of ancient DNA recovered from archaeological finds, contributing to novel insights into human evolutionary history. As more ancient genetic information has become available, the need for specialized methods of analysis has also increased. In this thesis, we investigate statistical and computational models for analysis of genetic data, with a particular focus on the context of ancient DNA. The main focus is on imputation, or the inference of missing genotypes based on observed sequence data. We present results from a systematic evaluation of a common imputation pipeline on empirical ancient samples, and show that imputed data can constitute a realistic option for population-genetic analyses. We also discuss preliminary results from a simulation study comparing two methods of phasing and imputation, which suggest that the parametric Li and Stephens framework may be more robust to extremely low levels of sparsity than the parsimonious Browning and Browning model. An evaluation of methods to handle missing data in the application of PCA for dimensionality reduction of genotype data is also presented. We illustrate that non-overlapping sequence data can lead to artifacts in projected scores, and evaluate different methods for handling unobserved genotypes. In genomics, as in other fields of research, increasing sizes of data sets are placing larger demands on efficient data management and compute infrastructures. The last part of this thesis addresses the use of cloud resources for facilitating such analysis. We present two different cloud-based solutions, and exemplify them on applications from genomics. / eSSENCE

This thesis focuses on developing an appropriate stochastic model for temperature dynamics as a means of pricing weather derivative contracts based on temperature. There are various methods for pricing weather derivatives ranging from simple one like historical burn analysis, which does not involve modeling the underlying weather variable to complex ones that require Monte Carlo simulations to achieve explicit weather derivatives contract prices, particularly the daily average temperature (DAT) dynamics models. Among various DAT models, appropriate regime switching models are considered relative better than single regime models due to its ability to capture most of the temperature dynamics features caused by urbanization, deforestation, clear skies and changes of measurement station. A new proposed model for DAT dynamics, is a two regime switching models with heteroskedastic mean-reverting process in the base regime and Brownian motion with nonzero drift in the shifted regime. Before using the model for pricing temperature derivative contracts, we compare the performance of the model with a benchmark model proposed by Elias et al. (2014), interms of the HDDs, CDDs and CAT indices. Using ve data sets from dierent measurement locations in Sweden, the results shows that, a two regime switching models with heteroskedastic mean-reverting process gives relatively better results than the model given by Elias et al. We develop mathematical expressions for pricing futures and option contracts on HDDs, CDDs and CAT indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

Investigating the properties, explaining, and predicting the behaviour of a physical system described by a system (matrix) pencil often require the understanding of how canonical structure information of the system pencil may change, e.g., how eigenvalues coalesce or split apart, due to perturbations in the matrix pencil elements. Often these system pencils have different block-partitioning and / or symmetries. We study changes of the congruence canonical form of a complex skew-symmetric matrix pencil under small perturbations. The problem of computing the congruence canonical form is known to be ill-posed: both the canonical form and the reduction transformation depend discontinuously on the entries of a pencil. Thus it is important to know the canonical forms of all such pencils that are close to the investigated pencil. One way to investigate this problem is to construct the stratification of orbits and bundles of the pencils. To be precise, for any problem dimension we construct the closure hierarchy graph for congruence orbits or bundles. Each node (vertex) of the graph represents an orbit (or a bundle) and each edge represents the cover/closure relation. Such a relation means that there is a path from one node to another node if and only if a skew-symmetric matrix pencil corresponding to the first node can be transformed by an arbitrarily small perturbation to a skew-symmetric matrix pencil corresponding to the second node. From the graph it is straightforward to identify more degenerate and more generic nearby canonical structures. A necessary (but not sufficient) condition for one orbit being in the closure of another is that the first orbit has larger codimension than the second one. Therefore we compute the codimensions of the congruence orbits (or bundles). It is done via the solutions of an associated homogeneous system of matrix equations. The complete stratification is done by proving the relation between equivalence and congruence for the skew-symmetric matrix pencils. This relation allows us to use the known result about the stratifications of general matrix pencils (under strict equivalence) in order to stratify skew-symmetric matrix pencils under congruence. Matlab functions to work with skew-symmetric matrix pencils and a number of other types of symmetries for matrices and matrix pencils are developed and included in the Matrix Canonical Structure (MCS) Toolbox.

The understanding of flow problems, and finding their solution, has been important for most of human history, from the design of aqueducts to boats and airplanes. The use of physical miniature models and wind tunnels were, and still are, useful tools for design, but with the development of computers, an increasingly large part of the design process is assisted by computational fluid dynamics (CFD). Many industrial CFD codes have their origins in the 1980s and 1990s, when the low order finite volume method (FVM) was prevalent. Discontinuous Galerkin methods (DGM) have, since the turn of the century, been seen as the successor of these methods, since it is potentially of arbitrarily high order. In its lowest order form DGM is equivalent to FVM. However, many existing codes are not compatible with standard DGM and would need a complete rewrite to obtain the advantages of the higher order. This thesis shows how to extend existing vertex-centered and edge-based FVM codes to higher order, using a special kind of DGM discretization, which is different from the standard cell-centered type. Two model problems are examined to show the necessary data structures that need to be constructed, the order of accuracy for the method, and the use of an hp-adaptation scheme to resolve a developing shock. Then the method is further developed to solve the steady Euler equations, within the existing industrial Edge code, using acceleration techniques such as local time stepping and multigrid. With the ever increasing need for more efficient and accurate solvers and algorithms in CFD, the modified DGM presented in this thesis could be used to help and accelerate the adoption of high order methods in industry.

Accurate numerical simulation of time-dependent phenomena in many spatial dimensions is a challenging computational task apparent in a vast range of application areas, for instance quantum dynamics, financial mathematics, systems biology and plasma physics. Particularly problematic is that the number of unknowns in the governing equations (the number of grid points) grows exponentially with the number of spatial dimensions introduced, often referred to as the curse of dimensionality. This limits the range of problems that we can solve, since the computational effort and requirements on memory storage directly depend on the number of unknowns for which to solve the equations. In order to push the limit of tractable problems, we are developing an implementation framework, HAParaNDA, for high-dimensional PDE-problems. By using high-order accurate schemes and adaptive mesh refinement (AMR) in space, we aim at reducing the number of grid points used in the discretization, thereby enabling the solution of larger and higher-dimensional problems. Within the framework, we use structured grids for spatial discretization and a block-decomposition of the spatial domain for parallelization and load balancing. For integration in time, we use exponential integration, although the framework allows the flexibility of other integrators to be implemented as well. Exponential integrators using the Lanzcos or the Arnoldi algorithm has proven a succesful and efficient approach for large problems. Using a truncation of the Magnus expansion, we can attain high levels of accuracy in the solution. As an example application, we have implemented a solver for the time-dependent Schrödinger equation using this framework. We provide scaling results for small and medium sized clusters of multicore nodes, and show that the solver fulfills the expected rate of convergence. / eSSENCE / UPMARC

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Problems with time-evolving domains are frequently occurring in computationalfluid dynamics and many other fields of science and engineering.Unfitted methods, where the computational mesh does not conform to thegeometry, are of great interest for handling such problems, since they removethe burden of mesh generation. We work towards the goal of developingan unfitted solver for Navier-Stokes equations on time-evolving domainsby developing and presenting cut finite element (CutFEM) splitting methodsfor solving Navier-Stokes equations. These CutFEM splitting methodsuse Nitsche’s method for incorporating boundary conditions and employpatch-based ghost penalty stabilization of the cut elements to achieve stabilityand optimal order error estimates. Numerical benchmarks are used toverify the methods and implementations. The methods are tested against aproblem with known analytical solution, the Taylor-Green vortex, and alsocompared to the classical Deutsche Forschungsgemeinschaft (DFG) benchmarkproblem with channel flow around a cylinder. For both benchmarks,the methods was shown to be stable when satisfying the parabolic Courant–Friedrichs–Lewy (CFL) condition, and to produce optimal convergencerates.

Discrete-event models depict systems where a discrete state is repeatedly altered by instantaneous changes in time, the events of the model. Such models have gained popularity in fields such as Computational Systems Biology or Computational Epidemiology due to the high modeling flexibility and the possibility to easily combine stochastic and deterministic dynamics. However, the system size of modern discrete-event models is growing and/or they need to be simulated at long time periods. Thus, efficient simulation algorithms are required, as well as the possibility to harness the compute potential of modern multicore computers. Due to the sequential design of simulators, parallelization of discrete event simulations is not trivial. This thesis discusses event-based modeling and sensitivity analysis and also examines ways to increase the efficiency of discrete-event simulations and to scale models involving deterministic and stochastic spatial dynamics on a large number of processor cores. / UPMARC / eSSENCE