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Overture: An Object-Oriented Framework for Overlapping Grid Applications

Description: The Overture framework is an object-oriented environment for solving partial differential equations on over-lapping grids. We describe some of the tools in Overture that can be used to generate grids and solve partial differential equations (PDEs). Overture contains a collection of C++ classes that can be used to write PDE solvers either at a high level or at a lower level for efficiency. There are also a number of tools provided with Overture that can be used with no programming effort. These tools include capabilities to: repair computer-aided-design (CAD) geometries and build global surface triangulations; generate surface and volume grids with hyperbolic grid generation; generate composite overlapping grids; generate hybrid (unstructured) grids; and solve particular PDEs such as the incompressible and compressible Navier-Stokes equations.
Date: April 4, 2002
Creator: Henshaw, W. D.
Partner: UNT Libraries Government Documents Department

Control and Analysis of a Single-Link Flexible Beam with Experimental Verification

Description: The objective of this report is to ascertain the general conditions for the avoidance and reduction of residual vibration in a flexible manipulator. Conventional manipulators usually have a 1.5 to 2-m reach, and their associated dynamic models typically are composed of lumped parameter elements; the major compliance emanates from the, drive trains because of torsional loading effects. The energy storage of the drive system is predominantly potential energy because of the low inertia in the drive tram; thus simple spring models have been adequate. A long-reach manipulator with a large aspect ratio (length to diameter) is a fundamentally different problem. Energy storage for this type of manipulator is distributive by nature because of the potential energy resulting from bending and the kinetic energy due to deflection rates. Instead of ordinary differential equations, partial differential equations are required to describe this system, making the analysis more difficult. The general flexibility problem associated with a distributive dynamic system, with specific emphasis on flexible manipulator, will be addressed in this report. Furthermore, three control schemes will be discussed and demonstrated on, a single flexible manipulator to determine their general merits.
Date: January 1, 1992
Creator: Jansen, J.F.
Partner: UNT Libraries Government Documents Department

Overture: The grid classes

Description: Overture is a library containing classes for grids, overlapping grid generation and the discretization and solution of PDEs on overlapping grids. This document describes the Overture grid classes, including classes for single grids and classes for collections of grids.
Date: January 1, 1997
Creator: Brislawn, K.; Brown, D.; Chesshire, G. & Henshaw, W.
Partner: UNT Libraries Government Documents Department

Dynamics of the Ginzburg-Landau equations of superconductivity

Description: This article is concerned with the dynamical properties of solutions of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. It is shown that the TDGL equations define a dynamical process when the applied magnetic field varies with time, and a dynamical system when the applied magnetic field is stationary. The dynamical system describes the large-time asymptotic behavior: Every solution of the TDGL equations is attracted to a set of stationary solutions, which are divergence free. These results are obtained in the {open_quotes}{phi} = -{omega}({gradient}{center_dot}A){close_quotes} gauge, which reduces to the standard {close_quotes}{phi} = -{gradient}{center_dot}A{close_quotes} gauge if {omega} = 1 and to the zero-electric potential gauge if {omega} = 0; the treatment captures both in a unified framework. This gauge forces the London gauge, {gradient}{center_dot}A = 0, for any stationary solution of the TDGL equations.
Date: August 1997
Creator: Fleckinger-Pelle, J.; Kaper, H. G. & Takac, P.
Partner: UNT Libraries Government Documents Department

Dispersive water waves in one and two dimensions

Description: This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We derived and analyzed new shallow water equations for one-dimensional flows near the critical Froude number as well as related integrable systems of evolutionary nonlinear partial differential equations in one spatial dimension, while developing new directions for the mathematics underlying the integrability of these systems. In particular, we applied the spectrum generating equation method to create and study new integrable systems of nonlinear partial differential equations related to our integrable shallow water equations. We also investigated the solutions of these systems of equations on a periodic spatial domain by using methods from the complex algebraic geometry of Riemann surfaces. We developed certain aspects of the required mathematical tools in the course of this investigation, such as inverse scattering with degenerate potentials, asymptotic reduction of the angle representations, geometric singular perturbation theory, modulation theory and singularity tracking for completely integrable equations. We also studied equations that admit weak solutions, i.e., solutions with discontinuous derivatives in the form of comers or cusps, even though they are solutions of integrable models, a property that is often incorrectly assumed to imply smooth solution behavior. In related work, we derived new shallow water equations in two dimensions for an incompressible fluid with a free surface that is moving under the force of gravity. These equations provide an estimate of the long-time asymptotic effects of slowly varying bottom topography and weak hydrostatic imbalance on the vertically averaged horizontal velocity, and they describe the flow regime in which the Froude number is small -- much smaller even than the small aspect ratio of the shallow domain.
Date: August 1, 1997
Creator: Holm, D.D. & Camassa, R.A.
Partner: UNT Libraries Government Documents Department

Perturbation approach and the constant of motion for on-dimensional dynamical systems

Description: A perturbation technic is used to find the constant of motion of a one-dimensional autonomous system. The convergence of the method is discussed through some examples. In addition, the approach is extended to one-dimensional non-autonomous systems where some examples are given.
Date: November 1, 1991
Creator: Lopez, G.
Partner: UNT Libraries Government Documents Department

Numerical Methods for Stochastic Partial Differential Equations

Description: This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
Date: July 8, 1999
Creator: Sharp, D.H.; Habib, S. & Mineev, M.B.
Partner: UNT Libraries Government Documents Department

Final report: Stochastic partial differential equations applied to the predictability of complex multiscale phenomena

Description: The objectives of this research remain as stated in our proposal of November 1997. We report on progress in the quantification of uncertainty and prediction, with applications to flow in porous media and to shock wave physics. The main strength of this work is an innovative theory for the quantification of uncertainty based on models for solution errors in numerical simulations. We also emphasize a deep connection to application communities, including those in DOE Laboratories.
Date: August 30, 2001
Creator: Glimm, James; Deng, Yuefan; Lindquist, W. Brent & Tangerman, Folkert
Partner: UNT Libraries Government Documents Department

Using automatic differentiation for second-order matrix-free methods in PDE-constrained optimization.

Description: Classical methods of constrained optimization are often based on the assumptions that projection onto the constraint manifold is routine but accessing second-derivative information is not. Both assumptions need revision for the application of optimization to systems constrained by partial differential equations, in the contemporary limit of millions of state variables and in the parallel setting. Large-scale PDE solvers are complex pieces of software that exploit detailed knowledge of architecture and application and cannot easily be modified to fit the interface requirements of a blackbox optimizer. Furthermore, in view of the expense of PDE analyses, optimization methods not using second derivatives may require too many iterations to be practical. For general problems, automatic differentiation is likely to be the most convenient means of exploiting second derivatives. We delineate a role for automatic differentiation in matrix-free optimization formulations involving Newton's method, in which little more storage is required than that for the analysis code alone.
Date: November 20, 2000
Creator: Hovland, P. D.; Keyes, D. E.; McInnes, L. C. & Samyono, W.
Partner: UNT Libraries Government Documents Department

Overture: an objectoriented framework for solving partial differential equations on overlapping grids

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It merges geometry, grid generation, difference operators, boundary conditions, data-base access and graphics into an easy to use high level interface.
Date: September 22, 1998
Creator: Brown, D L; Henshaw, W D & Quinlan , D J
Partner: UNT Libraries Government Documents Department

Final Report: Symposium on Adaptive Methods for Partial Differential Equations

Description: OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Date: December 10, 1998
Creator: Pernice, M.; Johnson, C.R.; Smith, P.J. & Fogelson, A.
Partner: UNT Libraries Government Documents Department

Modeling mesoscopic phenomena in extended dynamical systems

Description: This is the final report of a three-year, Laboratory-Directed Research and Development project at the Los Alamos National Laboratory (LANL). We have obtained classes of nonlinear solutions on curved geometries that demonstrate a novel interplay between topology and geometric frustration relevant for nanoscale systems. We have analyzed the nature and stability of localized oscillatory nonlinear excitations (multi-phonon bound states) on discrete nonlinear chains, including demonstrations of successful perturbation theories, existence of quasiperiodic excitations, response to external statistical time-dependent fields and point impurities, robustness in the presence of quantum fluctuations, and effects of boundary conditions. We have demonstrated multi-timescale effects for nonlinear Schroedinger descriptions and shown the success of memory function approaches for going beyond these approximations. In addition we have developed a generalized rate-equation framework that allows analysis of the important creation/annihilation processes in driven nonlinear, nonequilibiium systems.
Date: August 1, 1997
Creator: Bishop, A.; Lomdahl, P.; Jensen, N.G.; Cai, D.S.; Mertenz, F.; Konno, Hidetoshi et al.
Partner: UNT Libraries Government Documents Department

Wavelet transforms as solutions of partial differential equations

Description: This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuous wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.
Date: October 1, 1997
Creator: Zweig, G.
Partner: UNT Libraries Government Documents Department

Sinuous oscillations and steady warps of polytropic disks

Description: In an asymptotic development of the equations governing the equilibria and linear stability of rapidly rotating polytropes we employed the slender aspect of these objects to reduce the three-dimensional partial differential equations to a somewhat simpler, ordinary integro-differential form. The earlier calculations dealt with isolated objects that were in centrifugal balance, that is the centrifugal acceleration of the configuration was balanced largely by self gravity with small contributions from the pressure gradient. Another interesting situation is that in which the polytrope rotates subject to externally imposed gravitational fields. In astrophysics, this is common in the theory of galactic dynamics because disks are unlikely to be isolated objects. The dark halos associated with disks also provide one possible explanation of the apparent warping of many galaxies. If the axis of the highly flattened disk is not aligned with that of the much less flattened halo, then the resultant torque of the halo gravity on the disk might provide a nonaxisymmetric distortion or disk warp. Motivated by these possibilities we shall here build models of polytropic disks of small but finite thickness which are subjected to prescribed, external gravitational fields. First we estimate how a symmetrical potential distorts the structure of the disk, then we examine its sinuous oscillations to confirm that they freely decay, hence suggesting that a warp must be externally forced. Finally, we consider steady warps of the disk plane when the axis of the disk does not coincide with that of the halo.
Date: May 1, 1995
Creator: Balmforth, N.J. & Spiegel, E.A.
Partner: UNT Libraries Government Documents Department

Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Partner: UNT Libraries

Overture: object-oriented tools for overset grid applications

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, data-base access and graphics. Short sample code segments are presented to show the power of this approach.
Date: April 28, 1999
Creator: Brown, D L; Henshaw, W D & Quinlan, D J
Partner: UNT Libraries Government Documents Department

Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

Description: A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Date: January 25, 2005
Creator: Lewandowski, Jerome L.V.
Partner: UNT Libraries Government Documents Department

Users' Guide to ADIC 1.1.

Description: This guide describes the use of the Automatic Differentiation in C (ADIC) system. ADIC is a suite of tools and libraries that automates the process of generating derivatives for scientific programs. In the context of solving PDEs, optimizations, sensitivity analysis, and inverse problems, researchers often require the derivatives {partial_derivative}f/{partial_derivative}x of a function f expressed as a program with respect to some input parameter(s) x. Automatic differentiation (AD) techniques augment the program with derivative computation by applying the chain rule of calculus to elementary operations in an automated fashion. ADIC uses sophisticated compiler techniques to augment the input C programs with derivative computation capability in an automatic fashion. It also provides a finer control of derivative code generation process via control scripts and pragmas. Another significant capability of ADIC is its component architecture, AIF, that allows ADIC's capability to be extended via plug-in modules.
Date: August 31, 2004
Creator: Hovland, P. D. & Norris, B.
Partner: UNT Libraries Government Documents Department

Spectral Representations of Uncertainty: Algorithms and Applications

Description: The objectives of this project were: (1) Develop a general algorithmic framework for stochastic ordinary and partial differential equations. (2) Set polynomial chaos method and its generalization on firm theoretical ground. (3) Quantify uncertainty in large-scale simulations involving CFD, MHD and microflows. The overall goal of this project was to provide DOE with an algorithmic capability that is more accurate and three to five orders of magnitude more efficient than the Monte Carlo simulation.
Date: April 24, 2005
Creator: Karniadakis, George Em
Partner: UNT Libraries Government Documents Department

An object-oriented approach to development and testing of parallel solution algorithms for nonlinear PDES

Description: An object-oriented design that provides flexibility in simulation codes is presented. This flexibility allows programmers freedom to easily change solution algorithms and discretization schemes as well as add new solver packages as they become available. Careful attention is paid to separating algorithm, data, and specific problem classes to provide for ease in changing any of these components. Furthermore, data structures are chosen so that each component works with data in a form best suited to its needs. Lastly, we present some experiences and comments on the tradeoffs involved with this design.
Date: September 17, 1998
Creator: Hornung, R & Woodward, C
Partner: UNT Libraries Government Documents Department

Reducing the memory requirement in reverse mode automatic differentiation by solving TBR flow equations.

Description: The fast computation of gradients in reverse mode Automatic Differentiation (AD) requires the generation of adjoint versions of every statement in the original code. Due to the resulting reversal of the control flow certain intermediate values have to be made available in reverse order to compute the local partial derivatives. This can be achieved by storing these values or by recomputing them when they become required. In any case one is interested in minimizing the size of this set. Following an extensive introduction of the ''To-Be-Recorded'' (TBR) problem the authors present flow equations for propagating the TBR status of variables in the context of reverse mode AD of structured programs.
Date: January 11, 2002
Creator: Naumann, U.
Partner: UNT Libraries Government Documents Department

ROSE: Compiler Support for Object-Oriented Frameworks

Description: ROSE is a preprocessor generation tool for the support of compile time performance optimizations in Overture. The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, database access and graphics. In this paper we briefly present Overture, and discuss our approach toward performance within Overture and the A++P++ array class abstractions upon which Overture depends, this work represents some of the newest work in Overture. The results we present show that the abstractions represented within Overture and the A++P++ array class library can be used to obtain application codes with performance equivalent to that of optimized C and Fortran 77. ROSE, the preprocessor generation tool, is general in its application to any object-oriented framework or application and is not specific to Overture.
Date: November 17, 1999
Creator: Qainlant, D.
Partner: UNT Libraries Government Documents Department

Pressure Waves Induced by Megasonic Agitation in a LIGA Development Tank

Description: Megasonic agitation is used to improve the uniformity of the LIGA{sup 1} development process. To investigate the acoustic wave fields induced by megasonic agitation, we compute wave fields for a development tank containing a submerged wafer and for a typical trench-like feature on the wafer face. This separate treatment of these two problems is advantageous, because the length scales of the tank and the feature differ by three to four orders of magnitude. A spectral method based on Green's functions is used to construct the acoustic wave field, avoiding the alternative of solving partial differential equations over the entire domain. The total acoustic wave field is obtained by superposing of the primary wave field and the first reflected wave field, which are computed in sequence without any need for iterations. The wafer interference to the wave field is treated directly by a priori recognition of shadow regions in the primary field and a concept of boundary of dependence in the reflected field. Unlike a divergent wave field produced by ultrasonic agitation, results show that the wave field in the tank becomes narrowly focused at megasonic frequencies such that the most effective agitation is confined in a region directly above the acoustic source; this numerical expectation has been verified analytically and further confirmed experimentally by Sandia's LIGA Group.{sup [13]} The amplitude of the focused wave pressure is proportional to square root of the wave frequency. The wave pattern in a feature cavity also depends strongly on the orientation of the wafer and the aspect ratio of the cavity. It is concluded that the LIGA development process will be greatly accelerated, if the orientation and the location of the immersed wafer is arranged so that the wafer spends more time in the focused wave field of high frequency agitation.
Date: August 1, 2002
Creator: Ting, Aili
Partner: UNT Libraries Government Documents Department

Overture: Object-Oriented Tools for Application with Complex Geometry

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, data-base access and graphics. Short sample code segments are presented to show the power of this approach.
Date: May 31, 1999
Creator: Brown, D.; Henshaw, B. & Quinlan, D.
Partner: UNT Libraries Government Documents Department