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A three-level BDDC algorithm for Mortar discretizations

Description: In this paper, a three-level BDDC algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems. The mortar discretization is considered on geometrically non-conforming subdomain partitions. In two-level BDDC algorithms, the coarse problem needs to be solved exactly. However, its size will increase with the increase of the number of the subdomains. To overcome this limitation, the three-level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained. This is an extension of previous work, the three-level BDDC algorithms for standard finite element discretization. Estimates of the condition numbers are provided for the three-level BDDC method and numerical experiments are also discussed.
Date: December 9, 2007
Creator: Kim, H. & Tu, X.
Partner: UNT Libraries Government Documents Department

Existence and multiplicity of solutions for semilinear elliptic boundary value problems

Description: This thesis studies the existence, multiplicity, bifurcation and the stability of the solutions to semilinear elliptic boundary value problems. These problems are motivated both by the mathematical structure and the numerous applications in fluid mechanics chemical reactions, nuclear reactors, Riemannian geometry and elasticity theory. This study considers the problem for different classes of nonlinearities and obtain the existence and multiplicity of positive solutions.
Date: August 1992
Creator: Gadam, Sudhasree
Partner: UNT Libraries

Iterative Solution of Linear Boundary Value Problems

Description: The investigation is initially a continuation of Neuberger's work on linear boundary value problems. A very general iterative procedure for solution of these problems is described. The alternating-projection theorem of von Neumann is the mathematical starting point for this study. Later theorems demonstrate the validity of numerical approximation for Neuberger's method under certain conditions. A sampling of differential equations within the scope of our iterative method is given. The numerical evidence is that the procedure works well on neutral-state equations, for which no software is written now.
Date: August 1983
Creator: Walsh, John Breslin
Partner: UNT Libraries

Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds

Description: FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.
Date: June 1, 1999
Creator: Wiegmann, A.
Partner: UNT Libraries Government Documents Department

Ductile Fracture of Cracked Steel Plates

Description: A simple relationship between loading for crack initiation, or onset of ductile tear, and crack length is presented for center-cracked plates of mild steel. Formulation of the nonlinear boundary-value problem is based on incremental theory of plasticity for Prandtl-Reuss materials. Quasi-static solutions corresponding to a series of incremental loading conditions are obtained by the method of finite elements. Tests conducted on plates of two types of mild steel agree with numerical results.
Date: October 23, 2001
Creator: Yau, W.F.
Partner: UNT Libraries Government Documents Department

Multiple solutions for semilinear elliptic boundary value problems

Description: In this paper results concerning a semilinear elliptic boundary value problem are proven. This problem has five solutions when the range of the derivative of the nonlinearity ƒ includes the first two eigenvalues. The existence and multiplicity or radially symmetric solutions under suitable conditions on the nonlinearity when Ω is a ball in R^N.
Date: December 1991
Creator: Cossio, Jorge Ivan
Partner: UNT Libraries

Gabor Wave Packet Method to Solve Plasma Wave Equations

Description: A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach.
Date: June 18, 2003
Creator: Pletzer, A.; Phillips, C.K. & Smithe, D.N.
Partner: UNT Libraries Government Documents Department

BPERM version 3.0: A 2-D wakepotential/impedance code

Description: BPERM 3.0 is an improved version of a previous release. The main purpose of this version is to make it more user friendly. Following a simple 1-2-3 procedure, one obtains both text and graphical output of the wakepotential and impedance for a given geometry. The calculation is based on a boundary perturbation method, which is significantly faster than numerical simulations. It is accurate when the discontinuities are small. In particular, it works well for tapered structures. 5 refs., 3 figs.
Date: October 1, 1996
Creator: Barts, T. & Chou, W.
Partner: UNT Libraries Government Documents Department

Neighboring extremal optimal control design including model mismatch errors

Description: The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.
Date: November 1, 1994
Creator: Kim, T.J. & Hull, D.G.
Partner: UNT Libraries Government Documents Department

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

Description: This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Date: August 1, 1998
Creator: Attaway, S.W.; Laursen, T.A. & Zadoks, R.I.
Partner: UNT Libraries Government Documents Department

One-Dimensional Leakage-Flow Vibration Instabilities

Description: Simple boundary conditions, pressure losses, and channel geometries necessary for the unstable, rigid-body translational vibrations of the wall of one-dimensional leakage-flow channel are identified. General expressions for the flow damping and stiffness forces acting on the vibrating channel wall are derived and specific results are given for channels with wall friction, point pressure losses, sharp-edged constrictions, and diverging or converging widths. The minimum conditions necessary for dynamic and static (divergence) instability were found to be an upstream point pressure loss and a diverging channel width with a finite-length throat region, respectively.
Date: September 1987
Creator: Mulcahy, T. M.
Partner: UNT Libraries Government Documents Department

THI3D-1: A Computer Program for Steady-State Thermal-Hydraulic Multichannel Analysis

Description: THI3D-1 is an improved version of the THI3D computer program for steady-state, single-phase, thermal-hydraulic multichannel analysis. The program accounts for conservation of mass, energy, and momentum subject to pressure-drop boundary conditions, and leads to a nonlinear multipoint boundary-value problem. Turbulent interchange, radial thermal conduction, and forced flow due to wire wraps or grids between channels are explicitly taken into account. Temperature distributions in the coolant, cladding, fuel, and duct wall and the size of the central void of the oxide fuel after thermal restructuring are computed. Also included are program-input description and format, and a sample problem reflecting these improvements.
Date: July 1977
Creator: Sha, William T.; Schmitt, R. C. & Lin, E. I. H.
Partner: UNT Libraries Government Documents Department

Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems, Vol. 2: Singular Differential Equations

Description: Report on research and exchange of views among 24 mathematicians for investigations of the theory of singular Sturm-Liouville equations, the asymptotic analysis of the Titchmarsh-Weyl m(λ)-coefficient, and the qualitative theory of non-linear differential equations.
Date: September 1988
Creator: Kaper, H. G.; Kwong, Man Kam & Zettl, Anton
Partner: UNT Libraries Government Documents Department

Identification of the Permeability Field of Porous Medium from the Injection of Passive Tracer

Description: In this paper, a method was proposed which focused on the question, namely on how to invert data on arrival times at various (and numerous) points in the porous medium to map the permeability field. The method, elements of which were briefly described in (9), is based on a direct inversion of the data, as will be described below , rather than on the optimization of initial random (or partly constrained) guesses of the permeability field, to match the available data, as typically done in the analogous problem of pressure transients. The direct inversion is based on two conditions, that Darcy's law for single-phase flow in porous media is valid, and that dispersion of the concentration of the injected tracer is negligible. While the former is a well-accepted premise, the latter depends on injection and field conditions, and may not necessarily apply in all cases. Based on these conditions, we formulate a nonlinear boundary value problem, the coefficients of which depend on the experimental arrival time data.
Date: October 18, 1999
Creator: Zhan, Lang & Yortsos, Y.C.
Partner: UNT Libraries Government Documents Department

Uniqueness of Neumann-Tricomi problem in IR/sup 2/. Technical note BN-906. [Energy-integral method]

Description: Using a variation of the energy-integral method sufficient conditions for the uniqueness of the solution of the Neumann-Tricomi boundary value problem are obtained. A uniqueness theorem is given for a general function. 11 references. (JFP)
Date: April 1, 1979
Creator: Aziz, A.K. & Schneider, M.
Partner: UNT Libraries Government Documents Department

Construction of Superconvergent Discretizations with Differential-Difference Invariants

Description: To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations.
Date: August 12, 2005
Creator: Axford, R.A.
Partner: UNT Libraries Government Documents Department

Stress and flow in fractured porous media

Description: The purpose of the present study is to develop a method for simultaneous solution of stress and flow in a deformable fractured isotropic porous medium saturated with a single phase slightly compressible fluid. The system defined as such can be under the effect of body forces, boundary loads, initial stress, and influenced by some fluid pressure disturbance. The method involves application of the theory of elasticity for plane strain systems, Darcy's law for porous medium, and Biot's constitutive equations for the mixture of fluid and solid skeleton. The resulting initial boundary value problem is then numerically formulated into finite element equations using the calculus of variations. A computer program has been developed by modifying existing programs to consider interactions between fractures and porous medium when both flow and stress fields are coupled. The program is capable of handling problems in rock masses where fractures extend from one boundary to another, intersect each other, or are isolated in the porous medium. The fractures may have random orientations and the rock matrix can be permeable or impermeable. The region under investigation may be two dimensional or axially symmetric. Solutions can be obtained for either a steady-state flow field under static equilibrium or a non-steady flow field in conjunction with quasi-static equilibrium conditions.
Date: January 1, 1978
Creator: Ayatollahi, Mohammad Sadegh
Partner: UNT Libraries Government Documents Department

Conservation Laws for Coupled Hydro-mechanical Processes in Unsaturated Porous Media: Theory and Implementation

Description: We develop conservation laws for coupled hydro-mechanical processes in unsaturated porous media using three-phase continuum mixture theory. From the first law of thermodynamics, we identify energy-conjugate variables for constitutive modeling at macroscopic scale. Energy conjugate expressions identified relate a certain measure of effective stress to the deformation of the solid matrix, the degree of saturation to the matrix suction, the pressure in each constituent phase to the corresponding intrinsic volume change of this phase, and the seepage forces to the corresponding pressure gradients. We then develop strong and weak forms of boundary-value problems relevant for 3D finite element modeling of coupled hydro-mechanical processes in unsaturated porous media. The paper highlights a 3D numerical example illustrating the advances in the solution of large-scale coupled finite element systems, as well as the challenges in developing more predictive tools satisfying the basic conservation laws and the observed constitutive responses for unsaturated porous materials.
Date: February 19, 2010
Creator: Borja, R I & White, J A
Partner: UNT Libraries Government Documents Department

An overview of integration methods for hypersingular boundary integrals

Description: Several methods of analyzing the hypersignular gradient BIE have been developed recently. This paper is a review highlighting the numerous common aspects and several differences among the methods. Significant common aspects include (a) a regularization of constant and linear terms, (b) analysis of integration points near rather than on the surface, and (c) analysis of the neighborhood of the singular point rather than of individual elements. 26 refs.
Date: January 1, 1991
Creator: Lutz, E.; Ingraffea, A.R. (Cornell Univ., Ithaca, NY (United States)) & Gray, L.J. (Oak Ridge National Lab., TN (United States))
Partner: UNT Libraries Government Documents Department