In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical imagery, object tracking etc. The model is a way of finding a partition of an image by using a piecewise smooth representation of the image. Unfortunately numerical procedures for minimizing the Mumford-Shah functional have some difficulties because the problem is non convex and it has numerous local minima, so approximate approaches have been proposed. Two such methods are the Ambrosio-Tortorelli approximation and the Chan-Vese active contour method. Ambrosio and Tortorelli have developed a practical numerical implementation of the Mumford-Shah model which based on an elliptic approximation of the original functional. The Chan-Vese model is a piecewise constant generalization of the Mumford-Shah functional and it is based on level set formulation. Another widely used image segmentation technique is the &ldquo / Active Contours (Snakes)&rdquo / model and it is correlated with the Chan-Vese model. In this study, all these approaches have been examined in detail. Mathematical and numerical analysis of these models are studied and some experiments are performed to compare their performance.

In this thesis, we discuss the implementation of a low latency decoding algorithm for turbo codes and repeat accumulate codes and compare the implementation results in terms of maximum available clock speed, resource consumption, error correction performance, and the data (information bit) rate. In order to decrease the latency a parallelized decoder structure is introduced for these mentioned codes and the results are obtained by implementing the decoders on a field programmable gate array. The memory collision problem is avoided by using collision-free interleavers. Through a proposed quantization scheme and normalization approximations, computational issues are handled for overcoming the overflow and underflow issues in a fixed point arithmetic. Also, the effect of different implementation styles are observed.

A three-phase numerical study was undertaken to address some design issues related with special truss moment frames (STMFs). In the first phase, the design approaches for distribution of shear strength among stories were examined. Multistory STMFs sized based on elastic and inelastic behavior were evaluated from a performance point of view. A set of time history analysis was conducted to investigate performance parameters such as the interstory drift ratio and the plastic rotation at chord member ends. The results of the analysis reveal that the maximum interstory drifts are not significantly influenced by the adopted design philosophy while considerable differences are observed for plastic rotations. In the second phase, the expected shear strength at vierendeel openings was studied through three dimensional finite element modeling. The results from finite element analysis reveal that the expected shear strength formulation presented in the AISC Seismic Provisions for Structural Steel Buildings is overly conservative. Based on the analysis results, an expected shear strength formula was developed and is presented herein. In the third phase, the effects of the load share and slenderness of X-diagonals in the special segment on the performance of the system were evaluated. Lateral drift, curvature at chord member ends, axial strain at X-diagonals and base shear were the investigated parameters obtained from a set of time history analysis. The results illustrate that as the load share of X-diagonals increases, the deformations decreases. Moreover, the slenderness of X-diagonals is not significantly effective on the system performance.

Conformal map has application in a lot of areas of science, e.g., fluid flow, heat conduction, solidification, electromagnetic, etc. Especially conformal map applied to elasticity theory can provide most simple and useful solution. But finding of conformal map for custom domain is not trivial problem. We used a numerical method for building a conformal map to solve torsion problem. In addition it was considered an infinite system method to solve the same problem. Results are compared.

The aim of this study is to construct a numerical reservoir model for Bal&ccedil / ova geothermal field, which is located in the izmir bay area of the Aegean coast. A commercial numerical simulation program, TOUGH2 was utilized with a graphical interface, PETRASIM to model the Bal&ccedil / ova geothermal field. Natural state modeling of the field was carried out based on the conceptual model of the field, then history matching of production &ndash / injection practices of the field was established for the period of 1996 &ndash / 2008. The final stage of modeling was the future performance prediction of the field by using three different Scenarios. In Scenario-1, production and injection rates in year 2008 were repeated for 20 years. In Scenario-2, production and injection rates in year 2008 were repeated for the first 3 years, then they were increased at every 3 years. In Scenario-3, a new well (BT-1) that is assumed to be drilled to 1000 m depth is added for injecting some portion of water that was injected through BD-8 well. In that scenario, similar to Scenario-2, production and injection rates in year 2008 were repeated during the first 3 years, and then the rates of these wells (except the new well) were increased every three years. Analysis of the results indicated that in Scenario-2, compared to Scenario-1, both the temperatures of deep wells located at the eastern portion of the field (BD-6, BD-2, BD-14, BD-9, BD-11, BD-12) and the temperatures of deep wells located at the western portion (BD-4, BD-15, BD-7, BD-5) decreased more. In Scenario-3, compared to Scenario-1, the deep wells located at the eastern side experienced less temperature drops while the deep wells located at the western side experienced higher temperature drops. Such temperature differences were not encountered in shallow wells. No significant changes in bottom hole pressures of deep wells occurred in all three scenarios. On the other hand, shallow wells, especially B-10 and B-5, responded to Scenario-2 and Scenario-3 as decrease in bottom hole pressures.

In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) matrices whereas all the other terms in the differential equations governing the flows are considered as nonhomogeneity. This is the main advantage of DRBEM to tackle the nonlinearities in the equations with considerably small computational cost. All the convective terms are evaluated by using the DRBEM coordinate matrix which is already computed in the formulation of nonlinear terms. The resulting systems of initial value problems with respect to time are solved with forward and central differences using relaxation parameters, and the fourth-order Runge-Kutta method. The numerical stability analysis is developed for the flow problems considered with respect to the choice of the time step, relaxation parameters and problem constants. The stability analysis is made through an eigenvalue decomposition of the final coefficient matrix in the DRBEM discretized system. It is found that the implicit central difference time integration scheme with relaxation parameter value close to one, and quite large time steps gives numerically stable solutions for all flow problems solved in the thesis. One-and-two-sided lid-driven cavity flow, natural and mixed convection flows in cavities, natural convection flow of nanofluids and micropolar fluids in enclosures are solved with several geometric configurations. The solutions are visualized in terms of streamlines, vorticity, microrotation, pressure contours, isotherms and flow vectors to simulate the flow behaviour.

To investigate the lateral load distribution of each pile in a pile group, the bending moment distribution along the pile and the lateral group displacements with respect to pile location in the group, pile spacing, pile diameter and soil stiffness three dimensional finite element analysis were performed on 4x4 pile groups in clay. Different Elatic Modulus values, pile spacings, pile diameters and lateral load levels used in this study. In the analysis PLAXIS 3D Foundation geotechnical finite element package was used. It is found that, lateral load distribution among the piles was mainly a function of row location in the group independent from pile spacing. For a given load the leading row piles carried the greatest load. However, the trailing row piles carried almost the same loads. For a given load, bending moment values of the leading row piles were greater than the trailing row piles. On the other hand, as the spacing increased group displacements and individual pile loads decreased under the same applied load. However, this behavior was seen more clearly in the first and the second row piles. For the third and the fourth row piles, pile spacing became a less significant factor affecting the load distribution. It is also found that, pile diameter and soil stiffness are not significant factors on lateral load distribution as row location and pile spacing.

Conduction based compact thermal modeling of DC/DC converters, which are electronic components commonly used in military applications, are investigated. Three carefully designed numerical case studies are carried out at component, board and system levels using ICEPAK software. Experiments are conducted to gather temperature data that can be used to study compact thermal models (CTMs) with different levels of simplification. In the first (component level) problem a series of conduction based CTMs are generated and used to study the thermal behavior of a Thin-Shrink Small Outline Package (TSSOP) type DC/DC converter under free convection conditions. In the second (board level) case study, CTM alternatives are produced and investigated for module type DC/DC converter components using a printed circuit board (PCB) of an electro-optic system. In the last case study, performance of the CTM alternatives generated for the first case are assessed at the system level using them on a PCB placed inside a realistic avionic box. v Detailed comparison of accuracy of simulations obtained using CTMs with various levels of simplification is made based on experimentally obtained temperature data. Effects of grid size and quality, choice of turbulence modeling and space discretization schemes on numerical solutions are discussed in detail. It is seen that simulations provide results that are in agreement with measurements when appropriate CTMs are used. It is also showed that remarkable reductions in modeling and simulation times can be achieved by the use of CTMs, especially in system level analysis.

In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis. Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear&#039 / s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.

In statistics, regression analysis is a technique, used to understand and model the relationship between a dependent variable and one or more independent variables. Multiple Adaptive Regression Spline (MARS) is a form of regression analysis. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models non-linearities and interactions. MARS is very important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. In our study, we analyzed Generalized Partial Linear Models (GPLMs), which are particular semiparametric models. GPLMs separate input variables into two parts and additively integrates classical linear models with nonlinear model part. In order to smooth this nonparametric part, we use Conic Multiple Adaptive Regression Spline (CMARS), which is a modified form of MARS. MARS is very benefical for high dimensional problems and does not require any particular class of relationship between the regressor variables and outcome variable of interest. This technique offers a great advantage for fitting nonlinear multivariate functions. Also, the contribution of the basis functions can be estimated by MARS, so that both the additive and interaction effects of the regressors are allowed to determine the dependent variable. There are two steps in the MARS algorithm: the forward and backward stepwise algorithms. In the first step, the model is constructed by adding basis functions until a maximum level of complexity is reached. Conversely, in the second step, the backward stepwise algorithm reduces the complexity by throwing the least significant basis functions from the model. In this thesis, we suggest not using backward stepwise algorithm, instead, we employ a Penalized Residual Sum of Squares (PRSS). We construct PRSS for MARS as a Tikhonov Regularization Problem. We treat this problem using continuous optimization techniques which we consider to become an important complementary technology and alternative to the concept of the backward stepwise algorithm. Especially, we apply the elegant framework of Conic Quadratic Programming (CQP) an area of convex optimization that is very well-structured, hereby, resembling linear programming and, therefore, permitting the use of interior point methods. At the end of this study, we compare CQP with Tikhonov Regularization problem for two different data sets, which are with and without interaction effects. Moreover, by using two another data sets, we make a comparison between CMARS and two other classification methods which are Infinite Kernel Learning (IKL) and Tikhonov Regularization whose results are obtained from the thesis, which is on progress.