The objective of this thesis is to develop a more efficient solver for a large system of linear equations arising from finite element discretization on unstructured tetrahedral meshes for a scalar elliptic partial differential equation of second order for pressure in a commercial computational fluid dynamics (CFD) simulation. Segregated solution methods (or pressure correction type methods) are a widely used approach to obtain solutions of Navier-Stokes equations during numerical simulation by many commercial CFD codes. At each time step, these simulations usually require the approximate solution of a series of scalar equations for velocity, pressure and temperature. Even if the simulation does not require high-accuracy approximations, the large systems of linear equations for pressure may not be efficiently solved. The matrices of these systems of linear equations of real-life industry problems often strongly violate weak diagonal dominance and the numerical simulation often requires solutions of very large systems with over a few hundred thousands degrees of freedom. These conditions produce very ill-conditioned systems of linear equations. Therefore, it is very difficult to solve such systems of linear equations efficiently using most currently available common iterative solvers. A survey of solvers for systems of linear equations was undertaken to determine the preferred solution methodology. An algebraic multigrid preconditioned conjugate gradient (AMGPCG) method solver was chosen for these problems. This solver uses the algebraic multigrid (AMG) cycle as a preconditioner for the conjugate gradient (CG) method. The disadvantages of the conventional AMG method are an expensive setup time and large memory requirements, particularly for three dimensional problems. The disadvantage of an expensive setup time needs to be overcome because the simulation usually requires only low-accuracy approximations for pressure. Also it is important to overcome the disadvantage of the large memory requirements for use in commercial software. In this work, an efficient AMGPCG solver is developed by overcoming the disadvantages of the conventional AMG method. The robustness of AMGPCG is shown theoretically so that the solver is always convergent. Optimum or close to optimum rates of convergence behavior for the solver are shown numerically so that the number of necessary iterations to obtain the estimated solution is approximately independent of mesh resolution. Furthermore, numerical experiments of solving pressure for some industry problems were carried out and compared with other efficient solvers including a fast commercial AMGPCG solver (SAMG, release 20b1). It was found that the developed AMGPCG solver was the fastest among these solvers for solving these problems and its algorithm has been numerically proven to be efficient. In addition, the memory requirement is at an acceptable level for commercial CFD codes.

In this paper we carry out fully Bayesian analysis of the general heterogeneity model, which is a mixture of random effects model, and its special cases, the random coefficient model and the latent class model. Our application comes from Conjoint analysis and we are especially interested in what is gained by the general heterogeneity model in comparison to the other two when modeling consumers' heterogeneous preferences. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaf 104). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaf 104). Also available on the Internet.

Integral equations arise in many scienti c and engineering problems. A large class of initial and boundary value problems can be converted to Volterra or Fredholm integral equations. The potential theory contributed more than any eld to give rise to integral equations. Integral equations also has signi cant application in mathematical physics models, such as di rac- tion problems, scattering in quantum mechanics, conformal mapping and water waves. The Volterra's population growth model, biological species living together, propagation of stocked sh in a new lake, the heat transfer and the heat radiation are among many areas that are described by integral equations. For limited applicability of analytical techniques, the numer- ical solvers often are the only viable alternative. General computational techniques of solving integral equation involve discretization and generates equivalent system of linear equations. In most of the cases the discretization produces dense matrix. Multigrid methods are widely used to solve partial di erential equation. We discuss the multigrid algorithms to solve integral equations and propose usages of distributive relaxation and the Kaczmarz method. / Department of Mathematical Sciences

The purpose of this thesis was to design controllers by using H1 and &sup1 / control strategies in order to suppress the free and forced vibrations of smart structures. The smart structures analyzed in this study were the smart beam and the smart &macr / n. They were aluminum passive structures with surface bonded PZT (Lead-Zirconate-Titanate) patches. The structures were considered in clamped-free con&macr / guration. The &macr / rst part of this study focused on the identi&macr / cation of nominal system models of the smart structures from the experimental data. For the experimentally identi&macr / ed models the robust controllers were designed by using H1 and &sup1 / -synthesis strategies. In the second part, the controller implementation was carried out for the suppression of free and forced vibrations of the smart structures. Within the framework of this study, a Smart Structures Laboratory was established in the Aerospace Engineering Department of METU. The controller implementations were carried out by considering two di&reg / erent experimental set-ups. In the &macr / rst set-up the controller designs were based on the strain measurements. In the second approach, the displacement measurements, which were acquired through laser displacement sensor, were considered in the controller design. The &macr / rst two &deg / exural modes of the smart beam were successfully controlled by using H1 method. The vibrations of the &macr / rst two &deg / exural and &macr / rst torsional modes of the smart &macr / n were suppressed through the &sup1 / -synthesis. Satisfactory attenuation levels were achieved for both strain measurement and displacement measurement applications.

Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 19, 2008) Includes bibliographical references.

Diss. (sammanfattning) Umeå : Sveriges lantbruksuniv. / Härtill 4 uppsatser.

Thesis (Ph.D.)--University of Delaware, 2008. / Principal faculty advisor: Tobin A. Driscoll, Dept. of Mathematical Sciences. Includes bibliographical references.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv., 2008. / Härtill 5 uppsatser.