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Fast methods for static Hamilton-Jacobi Partial Differential Equations

Description: The authors develop a family of fast methods approximating the solution to a wide class of static Hamilton-Jacobi partial differential equations. These partial differential equations are considered in the context of control-theoretic and front-propagation problems. In general, to produce a numerical solution to such a problem, one has to solve a large system of coupled non-linear discretized equations. The techniques use partial information about the characteristic directions to de-couple the s… more
Date: May 1, 2001
Creator: Vladimirsky, Alexander Boris
Partner: UNT Libraries Government Documents Department
open access

The Development and Application of Reactive Transport Modeling Techniques to Study Radionuclide Migration at Yucca Mountain, NV

Description: Yucca Mountain, Nevada has been chosen as a possible site for the first high level radioactive waste repository in the United States. As part of the site investigation studies, we need to make scientifically rigorous estimations of radionuclide migration in the event of a repository breach. Performance assessment models used to make these estimations are computationally intensive. We have developed two reactive transport modeling techniques to simulate radionuclide transport at Yucca Mountain: … more
Date: September 1, 1999
Creator: Viswanathan, Hari Selvi
Partner: UNT Libraries Government Documents Department
open access

Development and application of the quasi-potential transformation

Description: The quasi-potential transformation, based on the Kirchhoff transformation, reduces the equations governing mass-transfer in a steady-state, nonconvective electrolytic system into two independent parts. The geometry-specific part involves the solution of Laplace`s equation subject to the relevant boundary conditions. The system-specific part involves the solution of a set of coupled first-order, nonlinear, ordinary differential equations. We develop a theoretical basis for the quasi-potential tr… more
Date: August 1, 1992
Creator: Pillay, B.
Partner: UNT Libraries Government Documents Department
open access

An adaptive level set method

Description: This thesis describes a new method for the numerical solution of partial differential equations of the parabolic type on an adaptively refined mesh in two or more spatial dimensions. The method is motivated and developed in the context of the level set formulation for the curvature dependent propagation of surfaces in three dimensions. In that setting, it realizes the multiple advantages of decreased computational effort, localized accuracy enhancement, and compatibility with problems containin… more
Date: December 1, 1995
Creator: Milne, R. B.
Partner: UNT Libraries Government Documents Department
open access

Multigrid methods with applications to reservoir simulation

Description: Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more t… more
Date: May 1, 1994
Creator: Xiao, Shengyou
Partner: UNT Libraries Government Documents Department
open access

Efficient biased random bit generation for parallel processing

Description: A lattice gas automaton was implemented on a massively parallel machine (the BBN TC2000) and a vector supercomputer (the CRAY C90). The automaton models Burgers equation {rho}t + {rho}{rho}{sub x} = {nu}{rho}{sub xx} in 1 dimension. The lattice gas evolves by advecting and colliding pseudo-particles on a 1-dimensional, periodic grid. The specific rules for colliding particles are stochastic in nature and require the generation of many billions of random numbers to create the random bits necessa… more
Date: September 28, 1994
Creator: Slone, D.M.
Partner: UNT Libraries Government Documents Department
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