The solution of the linear system of equations is one of the core aspects of Finite Element Analysis (FEA) software. Since large amount of arithmetic operations are required for the solution of the system obtained by FEA, the influence of the solution of linear equations on the performance of the software is very significant. In recent years, the increasing demand for performance in the game industry caused significant improvements on the performances of Graphical Processing Units (GPU). With their massive floating point operations capability, they became attractive sources of performance for the general purpose programmers. Because of this reason, GPUs are chosen as the target hardware to develop an efficient parallel direct solver for the solution of the linear equations obtained from FEA.

In this study, atmospheric and turbulent flow solutions are obtained using meteorological flowfield and topographical terrain data in high resolution. The terrain topology of interest, which may be obtained in various resolution levels, is accurately modeled using structured or unstructured grids depending on whether high-rise building models are present or not. Meteorological weather prediction software MM5, is used to provide accurate and unsteady boundary conditions for the solution domain. Unsteady turbulent flow solutions are carried out via FLUENT with the help of several User Defined Functions developed. Unsteady flow solutions over topographical terrain of METU campus are computed with 25m x 25m x 15m resolution using structured grids. These FLUENT solutions are compared with the MM5 solutions. Also, the accuracy of the boundary layer velocity profiles is assessed. Finally, effects of surface roughness model extracted from MM5 for the region of interest is investigated. In addition, unsteady flow solutions over METU campus are repeated in presence of high-rise building models using unstructured grids with resolution varying from 5 meters around buildings to 80 meters further away. The study shows that unsteady, turbulent flow solutions can be accurately obtained using low resolution atmospheric weather prediction models and high resolution Navier-Stokes solutions over topographical terrains.

Conventional coupling paradigms used nowadays to couple various physics components in reactor analysis problems can be inconsistent in their treatment of the nonlinear terms. This leads to usage of smaller time steps to maintain stability and accuracy requirements thereby increasing the computational time. These inconsistencies can be overcome using better approximations to the nonlinear operator in a time stepping strategy to regain the lost accuracy. This research aims at finding remedies that provide consistent coupling and time stepping strategies with good stability properties and higher orders of accuracy. Consistent coupling strategies, namely predictive and accelerated methods, were introduced for several reactor transient accident problems and the performance was analyzed for a 0-D and 1-D model. The results indicate that consistent approximations can be made to enhance the overall accuracy in conventional codes with such simple nonintrusive techniques. A detailed analysis of a monoblock coupling strategy using time adaptation was also implemented for several higher order Implicit Runge-Kutta (IRK) schemes. The conclusion from the results indicate that adaptive time stepping provided better accuracy and reliability in the solution fields than constant stepping methods even during discontinuities in the transients. Also, the computational and the total memory requirements for such schemes make them attractive alternatives to be used for conventional coupling codes.

Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches. These devices typically consist of a metallic membrane which is activated by a time-periodic electrostatic force and makes periodic contact with a contact pad. The increase in switch capacitance at contact causes the RF signal to be deflected and the switch thus closes. Membrane motion is damped by the surrounding gas, typically air or nitrogen. As the switch opens and closes, the flow transitions between the continuum and rarefied regimes. Furthermore, creep is a critical physical mechanism responsible for the failure in these devices, especially those operating at high RF power. Simultaneous and accurate modeling of all these different physics is required to understand the dynamical membrane response in these devices and to estimate device lifetime and to improve MEMS reliability. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this work, we develop a single unified finite volume method based numerical framework to study this multi-physics problem in RF MEMS. Our objective required us to develop structural solvers, fluid flow solvers, and electrostatic solvers using the finite volume method, and efficient mechanisms to couple these different solvers. A particular focus is the development of flow solvers which work efficiently across continuum and rarefied regimes. A number of novel contributions have been made in this process. Structural solvers based on a fully implicit finite volume method have been developed for the first time. Furthermore, strongly implicit fluid flow solvers have also been developed that are valid for both continuum and rarefied flow regimes and which show an order of magnitude speed-up over conventional algorithms on serial platforms. On parallel platforms, the solution techniques developed in this thesis are shown to be significantly more scalable than existing algorithms. The numerical methods developed are used to compute the static and dynamic response of MEMS. Our results indicate that our numerical framework can become a computationally efficient tool to model the dynamics of RF MEMS switches under electrostatic actuation and gas damping. / text

In the design of high-hydrogen content gas turbines for power generation, flashback of the turbulent flame by propagation through the low velocity boundary layers in the premixing region is an operationally dangerous event. The high reactivity of hydrogen combined with enhanced flammability lim- its (compared to natural gas) promotes flame propagation along low-speed boundary layers adjoining the combustion walls. This work focuses on the simulation of boundary layer flashback using large-eddy simulations (LES). A canonical channel configuration is studied to assess the capabilities of LES and determine the modeling requirements for boundary layer flashback simulations. To extend this work to complex geometries, a new reactive low-Mach number solver has been written in an unstructured code. / text

The performance of a horizontal axis marine current turbine is predicted by three numerical methods, vortex lattice method MPUF-3A, boundary element method PROPCAV and a commercial RANS solver FLUENT. The predictions are compared with the experimental measurements for the same turbine model. A fully unsteady wake alignment is utilized in order to model the realistic wake geometry of the turbine. A lifting line theory based method is developed to produce the optimum circulation distribution for turbines and propellers and a lifting line theory based database searching method is used to achieve the optimum circulation distribution for tidal turbines. A nonlinear optimization method (CAVOPT-3D) and another database-searching design method (CAVOPT-BASE) are utilized to design the blades of marine current turbines and marine propellers. A design procedure for the tidal turbine is proposed by using the developed methods successively. Finally, an interactive viscous/potential flow method is utilized to analyze the effect of nonuniform inflow on the performance of tidal turbines. / text

We have effectively identified and removed ground roll through a twostep process. The first step is to identify the major components of the ground roll through various methods including multiscale separation, directional or frequency filtering or by any other method that identifies the ground roll. Given this estimate for ground roll, the recorded signal is separated during the second step through a block-coordinate relaxation method that seeks the sparsest set for weighted curvelet coefficients of the ground roll and the sought-after reflectivity. The combination of these two methods allows us to separate out the ground roll signal while preserving the reflector information. Since our method is iterative, we have control of the separation process. We successfully tested our algorithm on a real data set with a complex ground roll and reflector structure.

The most commonly used method for the time-domain Maxwell equations is the Finite-Difference Time-Domain method (FDTD). This is an explicit, second-order accurate method, which is used on a staggered Cartesian grid. The main drawback with the FDTD method is its inability to accurately model curved objects and small geometrical features. This is due to the Cartesian grid, which leads to a staircase approximation of the geometry and small details are not resolved at all. This thesis presents different ways to circumvent this drawback, but still take advantage of the benefits of the FDTD method. An approach to avoid staircasing errors but still retain the efficiency of the FDTD method is to use a hybrid grid. A few layers of unstructured cells are used close to curved objects and a Cartesian grid is used for the rest of the domain. For the choice of solver on the unstructured grid two different alternatives are compared: an explicit Finite-Volume Time-Domain (FVTD) solver and an implicit Finite-Element Time-Domain (FETD) solver. The hybrid solvers calculate the scattering from complex objects much more efficiently compared to using FDTD on highly resolved Cartesian grids. For the same accuracy in the solution roughly a factor of 10 in memory requirements and a factor of 20 in execution time are gained. The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this thesis a technique to generalize a well-known subcell model for thin wires, in order to take arbitrarily oriented wires in FETD and FDTD into account, is proposed. The method gives considerable modeling flexibility compared to earlier methods and is proven stable. The results show excellent consistency and very good accuracy on different antenna configurations. The recursive convolution method is often used to model frequency dispersive materials in FDTD. This method is used to enable modeling of such materials in the unstructured FVTD and FETD solvers. The stability of both solvers is analyzed and their accuracy is demonstrated by computing the radar cross section for homogeneous as well as layered spheres with frequency dependent permittivity.

Currently, the accurate prediction of the impact of an extreme wave on infrastructure located near shore is difficult to assess. There is a lack of established methods to accurately quantify these impacts. Extreme waves, such as tsunamis generate, through breaking, extremely powerful hydraulic bores that impact and significantly damage coastal structures and buildings located close to the shoreline. The damage induced by such hydraulic bores is often due to structural failure. Examples of devastating coastal disasters are the 2004 Indian Ocean Tsunami, 2005 Hurricane Katrina and most recently, the 2011 Tohoku Japan Tsunami. As a result, more advanced research is needed to estimate the magnitude of forces exerted on structures by such bores. This research presents results of a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is used to simulate the impact of extreme hydrodynamic forces on shore protection walls. Typically, fluids are modeled numerically based on a Lagrangian approach, an Eulerian approach or a combination of the two. Many of the common problems that arise from using more traditional techniques can be avoided through the use of SPH-based models. Such challenges include the model computational efficiency in terms of complexity of implementation. The SPH method allows water particles to be individually modeled, each with their own characteristics, which then accurately depicts the behavior and properties of the flow field. An open source code, known as SPHysics, was used to run the simulations presented in this thesis. Several cases analysed consist of hydraulic bores impacting a flat vertical wall as well as a sloping seawall. The analysis includes comparisons of the numerical results with published experimental data. The model is shown to accurately reproduce the formation of solitary waves as well as their propagation and breaking. The impacting bore profiles as well as the resulting pressures are also efficiently simulated using the model.

In this dissertation, we develop multiscale finite element methods and uncertainty quantification technique for Richards' equation, a mathematical model to describe fluid flow in unsaturated porous media. Both coarse-level and fine-level numerical computation techniques are presented. To develop an accurate coarse-scale numerical method, we need to construct an effective multiscale map that is able to capture the multiscale features of the large-scale solution without resolving the small scale details. With a careful choice of the coarse spaces for multiscale finite element methods, we can significantly reduce errors. We introduce several methods to construct coarse spaces for multiscale finite element methods. A coarse space based on local spectral problems is also presented. The construction of coarse spaces begins with an initial choice of multiscale basis functions supported in coarse regions. These basis functions are complemented using weighted local spectral eigenfunctions. These newly constructed basis functions can capture the small scale features of the solution within a coarse-grid block and give us an accurate coarse-scale solution. However, it is expensive to compute the local basis functions for each parameter value for a nonlinear equation. To overcome this difficulty, local reduced basis method is discussed, which provides smaller dimension spaces with which to compute the basis functions. Robust solution techniques for Richards' equation at a fine scale are discussed. We construct iterative solvers for Richards' equation, whose number of iterations is independent of the contrast. We employ two-level domain decomposition pre-conditioners to solve linear systems arising in approximation of problems with high contrast. We show that, by using the local spectral coarse space for the preconditioners, the number of iterations for these solvers is independent of the physical properties of the media. Several numerical experiments are given to support the theoretical results. Last, we present numerical methods for uncertainty quantification applications for Richards' equation. Numerical methods combined with stochastic solution techniques are proposed to sample conductivities of porous media given in integrated data. Our proposed algorithm is based on upscaling techniques and the Markov chain Monte Carlo method. Sampling results are presented to prove the efficiency and accuracy of our algorithm.