# Browsing by Subject "Iterative methods (Mathematics)"

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Item An explicit iterative method for solving finite element equations(Texas Tech University, 1981-08) Chou, Gee DavidShow more Not availableShow more Item Iterative approach to deformable membrane design(Texas Tech University, 2004-05) Nellore, Prashanth RShow more A continuous deformable membrane mirror can be fabricated using MEMS processes. It will have a highly reflective thin membrane, which is the mirror surface, and a number of actuators below it. The shape of the mirror surface is controlled by inducing an electrostatic force through applying a voltage between the mirror surface and the actuators. Small displacements of a membrane under tension are governed by Poisson's equation. The solutions of this equation determine the deflections in the vertical direction for different pressures applied at various surface points, due to various electrode positions. This thesis examines the influence of number, position, thickness of the electrodes and also the electrostatic pressure applied by each electrode on the surface of the mirror. A Matlab Graphical User Interface is designed that computes the deflections and uses iterative methods to optimize the voltages on the electrodes, their position and thickness. It produces a deformable membrane design that will match the surface of the mirror to that of a spherical mirror of known radius of curvature.Show more Item Nonlinear time axis for multiexponential fitting of luminescence decay times over several orders of magnitude(Texas Tech University, 1990-08) Kher, Alok R.Show more Not availableShow more Item Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.(2008-10-02T18:39:19Z) Nicely, Dywayne A.; Morgan, Ronald Benjamin, 1958-; Mathematics.; Baylor University. Dept. of Mathematics.Show more We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos.Show more Item Three-dimensional mortar finite element method for convection-diffusion equation with nonconforming meshes(Texas Tech University, 2003-08) McGee, Wayne MichaelShow more In the last decade, non-conforming domain decomposition methods such as the mortar finite element method have been shown to be reliable techniques for several engineering applications that often employ complex finite element design. With this technique, one can conveniently assemble local subcomponents into a global domain without matching the finite element nodes of each subcomponent at the common interface. We employ the mortar finite element formulation in conjunction with higher-order elements, where both mesh refinement and degree enhancement are combined to increase accuracy. The mortar finite element method has proven to be a good candidate for implementation in two dimensions. In this work, for the first time, we present computational results for the convergence of the mortar finite element technique in three dimensions for the convection-diffusion equation. Our numerical results demonstrate optimality for the resulting non-conforming method for various mesh and polynomial degree discretizations.Show more Item Well-posedness for the space-time monopole equation and Ward wave map(2008-05) Czubak, Magdalena, 1977-; Uhlenbeck, Karen K.Show more We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods.Show more