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in subjects: "Boundary-Value Problems"

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Precise Closed-Form Solutions of Some Mixed Boundary Value Problems of Plane Elasticity

Precise solutions are given for the problem of the semi-infinite strip extending from x=0 to x=infinity, stress-free along the edges y= +-1, when the edge x=0 is subject (a) to a quadratic sheer displacement and zero normal stress, (b) to a cubic normal displacement and zero sheer stress. These are the two simplest (non-trivial) end problems of the semi-infinite strip, antisymmetric in y, that may be formulated. The corresponding symmetric problems (a) linear seer displacement and zero normal s… more

Date: 1954

Creator: Horvay, Gabriel, 1908- & Born, J. B.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Progress Report on the Mach Reflection Calculation

"Mathematical methods are being developed for calculations in fluid dynamics. The work to date on the Mach reflection calculation is summarized. In the flow, there are two curved shocks, a slip surface, a plane shock, and rigid walls. The desired solution of the fluid-dynamics equations is stationary in similarity variables; approximate initial data are therefore assumed, with the expectation that the flow will settle down to the desired one asymptotically. The Eulerian equations for the smooth… more

Date: unknown

Creator: Richtmyer, Robert D.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

A Finite Difference Scheme for the Neumann and the Dirichlet Problem

"A specific feature of the finite difference scheme proposed is that in it the boundary condition and the differential equation are treated simultaneously. The scheme results from a variational principle of the original differential equation problem, simply by using the Ritz method employing piecewise linear approximation functions. Thus a rather uniform treatment of boundary condition and differential equation will result. The coefficients of the substitute boundary condition will be given as … more

Date: unknown

Creator: Friedrichs, K. O.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Stability for inhomogeneous difference schemes

Abstract. The Equivalence Theorem of P. Lax is extended to difference schemes for initial-value problems for linear inhomogeneous PDE with linear inhomogeneous boundary values and for boundary-value problems.

Date: July 13, 1960

Creator: Seidman, Thomas I.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Propagation Characteristics of Capillary Ripples, I. The Theory of Velocity Dispersion and Amplitude Attenuation of Plane Capillary Waves on Viscoelastic Films

From abstract: "The boundary value problem for velocity of propagation and attenuation of capillary ripples over viscoelastic surface films is set up and solved from the viewpoint of continuum hydrodynamics. Both soluble and insoluble films are treated. Successive approximation methods are used to derive explicit formulae for velocity of propagation and amplitude attenuation; formulae for these quantities accurate to second order are given for slightly viscoelastic and highly viscoelastic films… more

Date: January 4, 1963

Creator: Hansen, Robert S. & Mann, J. Adin, Jr.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

The Effect of Gaps on Pile Reactivity

From abstract: "The variation of the reactivity of a pile as a function of width of a transverse gap is obtained. The method involves first finding the boundary condition satisfied by the flux at the gap face. This, in principle, provides enough information for a complete solution of the pile equations. A method for calculating the reactivity change is presented. The calculated reactivity is compared with experiment and a brief discussion of the validity of the approximations is given."

Date: July 14, 1952

Creator: Tamor, S. & Ergen, W. K.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Mechanical behavior of materials and structural elements at elevated temperatures. Progress report, June 1, 1976--May 31, 1977

The analytical research performed includes solutions of boundary value problems for several structural elements using Hart's constitutive relations with and without the presence of anelastic strains. Research is in progress on the use of boundary-integral equation methods to solve inelastic deformation problems for planar bodies. The design and fabrication of a creep testing facility with auxilliary force, temperature and displacement transducers and data acquisition system is complete and cree… more

Date: May 1, 1977

Creator: Lance, R. H. & Mukherjee, S.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Recent developments in modeling groundwater systems

This paper reviews the developments in the mathematical modeling of groundwater systems over the past decde. The first part of the paper is devoted to a description of the physics of the different types of problems that are of interest in hydrogeology and a statement of the related initial-boundary-value problems. The various numerical techniques that have been employed to solve the governing equations are discussed in the second part. In the third section a few typical case histories are prese… more

Date: May 20, 1977

Creator: Narasimhan, T. N. & Witherspoon, P. A.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

INGEN: a general purpose mesh generator for finite element codes

INGEN is a general purpose mesh generator for two- and three-dimensional finite-element codes. The basic parts of the code are surface and three-dimensional region generators that are linear-blending interpolation formulas. These generators are based on an i, j, k index scheme which is used to number nodal points, construct elements, and develop displacement and traction boundary conditions. 12 figures, 2 tables.

Date: January 1, 1977

Creator: Cook, W. A.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Sweeping Algorithms for Five-Point Stencils and Banded Matrices

We record MATLAB experiments implementing the sweeping algorithms we proposed recently to solve five-point stencils arising from the discretization of partial differential equations, notably the Ginzburg-Landau equations from the theory of superconductivity. Algorithms tested include two-direction, multistage, and partial sweeping.

Date: June 1, 1992

Creator: Kwong, Man Kam

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Well posed boundary value problem in transonic gas dynamics. [Tricomi equation]

A boundary-value problem for the Tricomi equation is studied in connection with transonic gas dynamics. The transformed equation ..delta..u + (1/3 Y) u/sub Y/ = 0 in canonical coordinates is considered in the complex domain of two independent complex variables. A boundary-value problem is then set by prescribing the real part of the solution on the boundary of the real unit circle. The Dirichlet problem in the upper unit semicircle with vanishing values of the solution at Y = 0 is solved explic… more

Date: February 1, 1978

Creator: Sanz, J M

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Computation and graphics in mathematical research

This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.

Date: August 13, 1992

Creator: Hoffman, D. A. & Spruck, J.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

On Multigrid for Overlapping Grids

The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other im… more

Date: January 13, 2004

Creator: Henshaw, W

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Mathematics and Statistics Research Department progress report for period ending June 30, 1977. [ORNL]

Brief descriptions are given of work done in mathematical and statistical research (moving-boundary problems; numerical analysis; continuum mechanics; matrices and other operators; experiment design; statistical testing; multivariate, multipopulation classification; statistical estimation) and statistical and mathematical collaboration (analytical chemistry, biological research, chemistry and physics research, energy research, engineering technology research, environmental sciences research, he… more

Date: September 1, 1977

Creator: Lever, W. E.; Shepherd, D. E.; Ward, R. C. & Wilson, D. G. (comps.)

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Asymptotic analysis: Working note {number_sign}3, boundary layers

In this chapter the authors discuss the asymptotic approximation of functions that display boundary-layer behavior. The purpose here is to introduce the basic concepts underlying the phenomenon, to illustrate its importance, and to describe some of the fundamental tools available for its analysis. To achieve their purpose in the clearest way possible, the authors will work with functions that are assumed to be given explicitly -- that is, functions f : (0,{epsilon}{sub 0}) {yields} X whose expr… more

Date: September 1, 1993

Creator: Garbey, M. & Kaper, H. G.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Sound velocity estimation: A system theoretic approach

A system-theoretic approach is proposed to investigate the feasibility of reconstructing a sound velocity profile (SVP) from acoustical hydrophone measurements. This problem is based on a state-space representation of the normal-mode propagation model. It is shown that this representation can be utilized to investigate the so-called observability of the SVP from noisy measurement data. A model-based processor is developed to extract this information and it is shown that even in cases where limi… more

Date: July 30, 1993

Creator: Candy, J. V. & Sullivan, E. J.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Hypersingular integrals at a corner

For a smooth boundary, hypersingular integrals can be defined as a limit from the interior, the approach direction being taken, for convenience, normal to the surface. At a boundary corner, the limit process, with a necessarily non-normal approach direction, provides a valid definition of the hypersingular equation, as long as the direction is employed for all integrations. The terms which are potentially singular in the limit are shown to cancel, provided the function approximations at the cor… more

Date: March 25, 1993

Creator: Gray, L. J. & Manne, L. L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Dynamic Response of a Transducer Mounted at One End of an Acoustical Cavity Which Is Subjected to a Specified Pressure at the Open End of the Cavity

The purpose of this report is to develop a mathematical model for a pressure transducer mounted in a fluid filled cavity (a system) and examine the pressure ``measurement`` error of the cavity and transducer by computing the dynamic response (output pressure) of the system to a specified pressure time history (input pressure). The ``measurement`` error is determined by comparing the calculated output pressure to the specified input pressure. The dynamic response of a transducer mounted at one e… more

Date: November 1, 1994

Creator: Benedetti, G. A. & Benson, J. Z.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Stable Parallel Elimination for Boundary Valve ODEs

A parallelizable and vectorizable algorithm for solving linear algebraic systems arising from two-point boundary value ODEs is described. The method is equivalent to Gaussian elimination, with row partial pivoting, applied to a certain row- and column-reordered version of the usual almost block-diagonal coefficient matrix. Analytical and numerical evidence is presented to show that the algorithm is stable. Results from implementation on a shared-memory multiprocessor and a vector processor are … more

Date: April 1, 1991

Creator: Wright, S. J.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Optimal control design that accounts for model mismatch errors

A new technique is presented in this paper that reduces the complexity of state differential equations while accounting for modeling assumptions. The mismatch controls are defined as the differences between the model equations and the true state equations. The performance index of the optimal control problem is formulated with a set of tuning parameters that are user-selected to tune the control solution in order to achieve the best results. Computer simulations demonstrate that the tuned contr… more

Date: February 1, 1995

Creator: Kim, T. J. & Hull, D. G.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Large spatial, temporal, and algorithmic adaptivity for implicit nonlinear finite element analysis

The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis has been the subject of much research in recent years. Robust algorithms are needed to handle the complex nonlinearities that arise in many implicit finite element applications such as metalforming process simulation. The authors experience indicates that robustness can best be achieved through adaptive solution strategies. In the course of their research, thi… more

Date: July 30, 1992

Creator: Engelmann, B. E. & Whirley, R. G.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Numerical solution of a tunneling equation

A numerical method is presented to solve mode conversion equations resulting from the use of radio frequency (rf) waves to heat plasmas. The solutions of the mode conversion equations contain exponentially growing modes, and ordinary numerical techniques give large errors. To avoid the unphysical growing modes, a set of boundary conditions are found, that eliminate the unphysical modes. The mode conversion equations are then solved with the boundary conditions as a standard two-point boundary v… more

Date: April 1, 1994

Creator: Wang, C. Y.; Carter, M. D.; Batchelor, D. B. & Jaeger, E. F.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992

Date: August 13, 1992

Creator: Hoffman, D. A. & Spruck, J.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Improved approximations applied to the S{sub N} even-parity equation

We have developed various finite element differencing schemes by applying lumping techniques in neutron streaming and removal terms of the S{sub N} even-parity transport equation in two-dimensional x-y geometry. We have derived an analytical form of the even-parity reflective boundary condition, which along with the vacuum boundary condition can be applied directly to solve second-order even-parity boundary value problems. We have also developed a new simplified even-parity equation that is muc… more

Date: July 1, 1993

Creator: Noh, Taewan, Miller, W. F. Jr. & Morel, J. E.

Item Type: Article

Partner: UNT Libraries Government Documents Department