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Inf-sup estimates for the Stokes problem in a periodic channel

Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.
Date: December 10, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation

Description: We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of these solutions is a previously known, multi-periodic solution; however, the new representation unifies the subset of such solutions with a fixed spatial period and a continuously varying temporal period into a single network of smooth manifolds connected together by an infinite hierarchy of bifurcations. Our representation explicitly describes the evolution of the Fourier modes of the solution as well as the particle trajectories in a meromorphic representation of these solutions; therefore, we have also solved the problem of finding periodic solutions of the ordinary differential equation governing these particles, including a description of a bifurcation mechanism for adding or removing particles without destroying periodicity. We illustrate the types of bifurcation that occur with several examples, including degenerate bifurcations not predicted by linearization about traveling waves.
Date: July 1, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Practical error estimates for Reynolds' lubrication approximation and its higher order corrections

Description: Reynolds lubrication approximation is used extensively to study flows between moving machine parts, in narrow channels, and in thin films. The solution of Reynolds equation may be thought of as the zeroth order term in an expansion of the solution of the Stokes equations in powers of the aspect ratio {var_epsilon} of the domain. In this paper, we show how to compute the terms in this expansion to arbitrary order on a two-dimensional, x-periodic domain and derive rigorous, a-priori error bounds for the difference between the exact solution and the truncated expansion solution. Unlike previous studies of this sort, the constants in our error bounds are either independent of the function h(x) describing the geometry, or depend on h and its derivatives in an explicit, intuitive way. Specifically, if the expansion is truncated at order 2k, the error is O({var_epsilon}{sup 2k+2}) and h enters into the error bound only through its first and third inverse moments {integral}{sub 0}{sup 1} h(x){sup -m} dx, m = 1,3 and via the max norms {parallel} 1/{ell}! h{sup {ell}-1}{partial_derivative}{sub x}{sup {ell}}h{parallel}{sub {infinity}}, 1 {le} {ell} {le} 2k + 2. We validate our estimates by comparing with finite element solutions and present numerical evidence that suggests that even when h is real analytic and periodic, the expansion solution forms an asymptotic series rather than a convergent series.
Date: December 10, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

A Three-level BDDC algorithm for saddle point problems

Description: BDDC algorithms have previously been extended to the saddle point problems arising from mixed formulations of elliptic and incompressible Stokes problems. In these two-level BDDC algorithms, all iterates are required to be in a benign space, a subspace in which the preconditioned operators are positive definite. This requirement can lead to large coarse problems, which have to be generated and factored by a direct solver at the beginning of the computation and they can ultimately become a bottleneck. An additional level is introduced in this paper to solve the coarse problem approximately and to remove this difficulty. This three-level BDDC algorithm keeps all iterates in the benign space and the conjugate gradient methods can therefore be used to accelerate the convergence. This work is an extension of the three-level BDDC methods for standard finite element discretization of elliptic problems and the same rate of convergence is obtained for the mixed formulation of the same problems. Estimate of the condition number for this three-level BDDC methods is provided and numerical experiments are discussed.
Date: December 10, 2008
Creator: Tu, X.
Partner: UNT Libraries Government Documents Department

Voro++: a three-dimensional Voronoi cell library in C++

Description: Voro++ is a free software library for the computation of three dimensional Voronoi cells. It is primarily designed for applications in physics and materials science, where the Voronoi tessellation can be a useful tool in the analysis of densely-packed particle systems, such as granular materials or glasses. The software comprises of several C++ classes that can be modified and incorporated into other programs. A command-line utility is also provided that can use most features of the code. Voro++ makes use of a direct cell-by-cell construction, which is particularly suited to handling special boundary conditions and walls. It employs algorithms which are tolerant for numerical precision errors, and it has been successfully employed on very large particle systems.
Date: January 15, 2009
Creator: Rycroft, Chris
Partner: UNT Libraries Government Documents Department


Description: The steady increase in the power and complexity of modern computer systems has encouraged the implementation of automatic file migration systems which move files dynamically between mass storage devices and disk in response to user reference patterns. Using information describing thirteen months of text editor data set file references, (analyzed in detail in the first part of this paper), they develop and evaluation algorithms for the selection of files to be moved from disk to mass storage. They find that algorithms based on both the file size and the time since the file was last used work well. The best realizable algorithms tested condition on the empirical distribution of the times between file references. Acceptable results are also obtained by selecting for replacement that file whose size times time to last reference is maximal. Comparisons are made with a number of standard algorithms developed for paging, such as Working Set. Sufficient information (parameter values, fitted equations) is provided that our algorithms may be easily implemented on other systems.
Date: October 1, 1978
Creator: Jay Smith, Alan
Partner: UNT Libraries Government Documents Department

Phase patterns of coupled oscillators with application to wireless communication

Description: Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
Date: January 2, 2008
Creator: Arenas, A.
Partner: UNT Libraries Government Documents Department

Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

Description: We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two- and three-dimensional flow problems.
Date: December 31, 2008
Creator: Persson, P.-O.
Partner: UNT Libraries Government Documents Department

Visualization and Analysis-Oriented Reconstruction of Material Interfaces

Description: Reconstructing boundaries along material interfaces from volume fractions is a difficult problem, especially because the under-resolved nature of the input data allows for many correct interpretations. Worse, algorithms widely accepted as appropriate for simulation are inappropriate for visualization. In this paper, we describe a new algorithm that is specifically intended for reconstructing material interfaces for visualization and analysis requirements. The algorithm performs well with respect to memory footprint and execution time, has desirable properties in various accuracy metrics, and also produces smooth surfaces with few artifacts, even when faced with more than two materials per cell.
Date: March 5, 2010
Creator: Childs, Henry R.
Partner: UNT Libraries Government Documents Department

Monte Carlo without chains

Description: A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the Edwards-Anderson spin glass in three dimensions.
Date: December 12, 2007
Creator: Chorin, Alexandre J.
Partner: UNT Libraries Government Documents Department

Conditioning analysis of incomplete Cholesky factorizations with orthogonal dropping

Description: The analysis of preconditioners based on incomplete Cholesky factorization in which the neglected (dropped) components are orthogonal to the approximations being kept is presented. General estimate for the condition number of the preconditioned system is given which only depends on the accuracy of individual approximations. The estimate is further improved if, for instance, only the newly computed rows of the factor are modified during each approximation step. In this latter case it is further shown to be sharp. The analysis is illustrated with some existing factorizations in the context of discretized elliptic partial differential equations.
Date: March 16, 2012
Creator: Napov, Artem
Partner: UNT Libraries Government Documents Department

When Workflow Management Systems and Logging Systems Meet: Analyzing Large-Scale Execution Traces

Description: This poster shows the benefits of integrating a workflow management system with logging and log mining capabilities. By combing two existing, mature technologies: Pegasus-WMS and Netlogger, we are able to efficiently process execution logs of earthquake science workflows consisting of hundreds of thousands to one million tasks. In particular we show results of processing logs of CyberShake, a workflow application running on the TeraGrid. Client-side tools allow scientists to quickly gather statistics about a workflow run and find out which tasks executed, where they were executed, what was their runtime, etc. These statistics can be used to understand the performance characteristics of a workflow and help tune the execution parameters of the workflow management system. This poster shows the scalability of the system presenting results of uploading task execution records into the system and by showing results of querying the system for overall workflow performance information.
Date: July 31, 2008
Creator: Gunter, Daniel
Partner: UNT Libraries Government Documents Department

Large Data Visualization on Distributed Memory Mulit-GPU Clusters

Description: Data sets of immense size are regularly generated on large scale computing resources. Even among more traditional methods for acquisition of volume data, such as MRI and CT scanners, data which is too large to be effectively visualization on standard workstations is now commonplace. One solution to this problem is to employ a 'visualization cluster,' a small to medium scale cluster dedicated to performing visualization and analysis of massive data sets generated on larger scale supercomputers. These clusters are designed to fit a different need than traditional supercomputers, and therefore their design mandates different hardware choices, such as increased memory, and more recently, graphics processing units (GPUs). While there has been much previous work on distributed memory visualization as well as GPU visualization, there is a relative dearth of algorithms which effectively use GPUs at a large scale in a distributed memory environment. In this work, we study a common visualization technique in a GPU-accelerated, distributed memory setting, and present performance characteristics when scaling to extremely large data sets.
Date: March 1, 2010
Creator: Childs, Henry R.
Partner: UNT Libraries Government Documents Department

Multi-core and Many-core Shared-memory Parallel Raycasting Volume Rendering Optimization and Tuning

Description: Given the computing industry trend of increasing processing capacity by adding more cores to a chip, the focus of this work is tuning the performance of a staple visualization algorithm, raycasting volume rendering, for shared-memory parallelism on multi-core CPUs and many-core GPUs. Our approach is to vary tunable algorithmic settings, along with known algorithmic optimizations and two different memory layouts, and measure performance in terms of absolute runtime and L2 memory cache misses. Our results indicate there is a wide variation in runtime performance on all platforms, as much as 254% for the tunable parameters we test on multi-core CPUs and 265% on many-core GPUs, and the optimal configurations vary across platforms, often in a non-obvious way. For example, our results indicate the optimal configurations on the GPU occur at a crossover point between those that maintain good cache utilization and those that saturate computational throughput. This result is likely to be extremely difficult to predict with an empirical performance model for this particular algorithm because it has an unstructured memory access pattern that varies locally for individual rays and globally for the selected viewpoint. Our results also show that optimal parameters on modern architectures are markedly different from those in previous studies run on older architectures. And, given the dramatic performance variation across platforms for both optimal algorithm settings and performance results, there is a clear benefit for production visualization and analysis codes to adopt a strategy for performance optimization through auto-tuning. These benefits will likely become more pronounced in the future as the number of cores per chip and the cost of moving data through the memory hierarchy both increase.
Date: January 31, 2012
Creator: Howison, Mark
Partner: UNT Libraries Government Documents Department


Description: The purpose of this Note is to consider the agreement of self-consistent field and configuration interaction (SCF-CI) surface with pressure broadening data. Since pressure broadening traditionally has been used to obtain information about intermolecular forces, it is of particular interest to inquire whether these two surfaces predict any differences in pressure broadening which might provide a means of differentiating among them on the basis of experimental data. The cross sections from the SCF-CI potential would appear to be in marginally better agreement with experiment than those from the electron gas potential.
Date: June 1, 1980
Creator: Green, Sheldon & Thomas, Lowell D.
Partner: UNT Libraries Government Documents Department

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

Variational particle scheme for the porous medium equation and for the system of isentropic Euler equations

Description: We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.
Date: December 10, 2008
Creator: Westdickenberg, Michael & Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains

Description: We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
Date: January 13, 2009
Creator: Persson, P.-O.; Bonet, J. & Peraire, J.
Partner: UNT Libraries Government Documents Department

Domain evolution and polarization of continuously graded ferroelectric films

Description: A thermodynamic analysis of graded ferroelectric films demonstrates that in the equilibrium state the films are subdivided into a single-domain band and a polydomain band which consists of wedge-shape domains. Polarization under an external electrostatic field proceeds through an inter-band boundary movement due to growth or shrinkage of the wedge domains. It is shown how the domain structure and evolution are determined by the principal characteristics of the film: the distribution of the spontaneous polarization and dielectric constant. Graded films exhibit a sharp increase of polarization with the field for weak fields, with a drop of the dielectric constant when the field is increasing. A general approach to finding the dependence of the displacement and the wedge-domain shape on the field as well as analytical solutions for the p{sup 4} Landau-Devonshire and parabolic potentials are presented.
Date: January 1, 2008
Creator: Roytburd, A. & Roytburd, V.
Partner: UNT Libraries Government Documents Department

Mesoscopic structure conditions the emergence of cooperation on social networks

Description: We study the evolutionary Prisoner's Dilemma on two social networks substrates obtained from actual relational data. We find very different cooperation levels on each of them that cannot be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding a good agreement with the observations in both real substrates. Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. Further, the study allows us to define new quantitative parameters that summarize the mesoscopic structure of any network. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.
Date: December 1, 2008
Creator: Lozano, S.; Arenas, A. & Sanchez, A.
Partner: UNT Libraries Government Documents Department

Exact sub-grid interface correction schemes for elliptic interface problems

Description: We introduce a non-conforming finite element method for second order elliptic interface problems. Our approach applies to problems in which discontinuous coefficients and singular sources on the interface may give rise to jump discontinuities in either the solution or its normal derivative. Given a standard background mesh and an interface that passes between elements, the key idea is to construct a singular correction function which satisfies the prescribed jump conditions, providing accurate sub-grid resolution of the discontinuities. Utilizing the closest point extension and an implicit interface representation by the signed distance function, an algorithm is established to construct the correction function. The result is a function which is supported only on the interface elements, represented by the regular basis functions, and bounded independently of the interface location with respect to the background mesh. In the particular case of a constant second order coefficient, our regularization by singular function is straightforward, and the resulting left-hand-side is identical to that of a regular problem without introducing any instability. The influence of the regularization appears solely on the right-hand-side, which simplifies the implementation. In the more general case of discontinuous second order coefficients, a normalization is invoked which introduces a constraint equation on the interface. This results in a problem statement similar to that of a saddle-point problem. We employ two-level-iteration as the solution strategy, which exhibits aspects similar to those of iterative preconditioning strategies.
Date: December 9, 2008
Creator: Huh, J.S. & Sethian, J.A.
Partner: UNT Libraries Government Documents Department

Electronic structure of disordered conjugated polymers: Polythiophenes

Description: Electronic structure of disordered semiconducting conjugated polymers was studied. Atomic structure was found from a classical molecular dynamics simulation and the charge patching method was used to calculate the electronic structure with the accuracy similar to the one of density functional theory in local density approximation. The total density of states, the local density of states at different points in the system and the wavefunctions of several states around the gap were calculated in the case of poly(3-hexylthiophene) (P3HT) and polythiophene (PT) systems to gain insight into the origin of disorder in the system, the degree of carrier localization and the role of chain interactions. The results indicated that disorder in the electronic structure of alkyl substituted polythiophenes comes from disorder in the conformation of individualchains, while in the case of polythiophene there is an additional contribution due to disorder in the electronic coupling between the chains. Each of the first several wavefunctions in the conduction and valence band of P3HT is localized over several rings of a single chain. It was shown that the localization can be caused in principle both by ring torsions and chain bending, however the effect of ring torsions is much stronger. PT wavefunctions are more complicated due to larger interchain electronic coupling and are not necessarily localized on a single chain.
Date: November 26, 2008
Creator: Vukmirovic, Nenad & Wang, Lin-Wang
Partner: UNT Libraries Government Documents Department

Effects of d-electrons in pseudopotential screened-exchange density functional calculations

Description: We report a theoretical study on the role of shallow d states in the screened-exchange local density approximation (sX-LDA) band structure of binary semiconductor systems.We found that inaccurate pseudo-wavefunctions can lead to 1) an overestimation of the screened-exchange interaction betweenthe localized d states and the delocalized higher energy s and p states and 2) an underestimation of the screened-exchange interaction between the d states. The resulting sX-LDA band structures have substantially smaller band gaps compared with experiments. We correct the pseudo-wavefunctions of d states by including the semicore s and p states of the same shell in the valence states. The correction of pseudo-wavefunctions yields band gaps and d state binding energies in good agreement with experiments and the full potential linearized augmented plane wave sX-LDA calculations. Compared with the quasi-particle GW method, our sX-LDA results shows not only similar quality on the band gaps but also much better d state binding energies. Combined with its capability of ground state structure calculation, the sX-LDA is expected to be a valuable theoretical tool for the II-VI and III-V (especially the III-N) bulk semiconductors and nanostructure studies.
Date: September 12, 2007
Creator: Lee, Byounghak; Canning, Andrew & Wang, Lin-Wang
Partner: UNT Libraries Government Documents Department

Curved mesh generation and mesh refinement using Lagrangian solid mechanics

Description: We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements even for highly distorted or anisotropic initial meshes. We describe the method and the solution procedures, and we show a number of examples of two and three dimensional simplex meshes with curved boundaries. We also demonstrate how to use the technique for local refinement of non-curved meshes in the presence of curved boundaries.
Date: December 31, 2008
Creator: Persson, P.-O. & Peraire, J.
Partner: UNT Libraries Government Documents Department