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Results for “Mathematical Computing”
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Gaining Insight from Data by Learning Graphical Model Structure
Abstract Not Provided
Legion, Domain-Specific Languages and In Situ Data Analysis & Visualization
Abstract Not Provided
Analyzing Task-Based User Study Data to Determine Colormap Efficiency
Domain scientists use colormaps to visualize their data. These are useful for identifying areas of interest including Eddy Identification and Characterizing Currents. New colormaps have been designed by visual artist Francesca Samsel. User studies have been implemented to determine whether or not these colormaps are an improvement.
Analyzing task-based user study data to determine colormap efficiency
Domain scientists need colormaps to visualize their data and are especially useful for identifying areas of interest, like in ocean data to identify eddies or characterize currents. However, traditional Rainbow colormap performs poorly for understanding details, because of the small perceptual range. In order to assist domain scientists in recognizing and identifying important details in their data, different colormaps need to be applied to allow higher perceptual definition. Visual artist Francesca Samsel used her understanding of color theory to create new colormaps to improve perception. While domain scientists find the new colormaps to be useful, we implemented a rigorous and quantitative study to determine whether or not the new colormaps have perceptually more colors. Color count data from one of these studies will be analyzed in depth in order to determine whether or not the new colormaps have more perceivable colors and what affects the number of perceivable colors.
HPC - Platforms Penta Chart
Strategy, Planning, Acquiring- very large scale computing platforms come and go and planning for immensely scalable machines often precedes actual procurement by 3 years. Procurement can be another year or more. Integration- After Acquisition, machines must be integrated into the computing environments at LANL. Connection to scalable storage via large scale storage networking, assuring correct and secure operations. Management and Utilization – Ongoing operations, maintenance, and trouble shooting of the hardware and systems software at massive scale is required.
HPC - Facilities Penta
Strategy, Planning, Acquiring- very large scale computing require very large physical infrastructures, pipes, pumps, power, etc. Planning and acquiring $25M+ infrastructure projects and bringing in more power to the county takes a lot of long lead time / planning. Integration- New physical infrastructure must be integrated into our buildings, with the LANL site power and water systems, with existing infrastructure, and with the machines. Very large physical infrastructure projects are necessary. Management and Utilization – Ongoing operations, monitoring, maintenance, and trouble shooting of the physical infrastructure is required.
Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom
In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.
C1-continuous Virtual Element Method for Poisson-Kirchhoff plate problem
We present a family of C1-continuous high-order Virtual Element Methods for Poisson-Kirchho plate bending problem. The convergence of the methods is tested on a variety of meshes including rectangular, quadrilateral, and meshes obtained by edge removal (i.e. highly irregular meshes). The convergence rates are presented for all of these tests.
Annotations on the virtual element method for second-order elliptic problems
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).
Strengthening LLNL Missions through Laboratory Directed Research and Development in High Performance Computing
High performance computing (HPC) has been a defining strength of Lawrence Livermore National Laboratory (LLNL) since its founding. Livermore scientists have designed and used some of the world’s most powerful computers to drive breakthroughs in nearly every mission area. Today, the Laboratory is recognized as a world leader in the application of HPC to complex science, technology, and engineering challenges. Most importantly, HPC has been integral to the National Nuclear Security Administration’s (NNSA’s) Stockpile Stewardship Program—designed to ensure the safety, security, and reliability of our nuclear deterrent without nuclear testing. A critical factor behind Lawrence Livermore’s preeminence in HPC is the ongoing investments made by the Laboratory Directed Research and Development (LDRD) Program in cutting-edge concepts to enable efficient utilization of these powerful machines. Congress established the LDRD Program in 1991 to maintain the technical vitality of the Department of Energy (DOE) national laboratories. Since then, LDRD has been, and continues to be, an essential tool for exploring anticipated needs that lie beyond the planning horizon of our programs and for attracting the next generation of talented visionaries. Through LDRD, Livermore researchers can examine future challenges, propose and explore innovative solutions, and deliver creative approaches to support our missions. The present scientific and technical strengths of the Laboratory are, in large part, a product of past LDRD investments in HPC. Here, we provide seven examples of LDRD projects from the past decade that have played a critical role in building LLNL’s HPC, computer science, mathematics, and data science research capabilities, and describe how they have impacted LLNL’s mission.
Parameter Estimation for Thurstone Choice Models
We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one or more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.
iVPIC: A low-dispersion, energy-conserving relativistic PIC solver for LPI simulations
We have developed a novel low-dispersion, exactly energy-conserving PIC algorithm for the relativistic Vlasov-Maxwell system. The approach features an exact energy conservation theorem while preserving the favorable performance and numerical dispersion properties of explicit PIC. The new algorithm has the potential to enable much longer laser-plasma-interaction (LPI) simulations than are currently possible.
Sensitivity Analysis and Uncertainty Quantification for the LAMMPS Molecular Dynamics Simulation Code
We examine sensitivity analysis and uncertainty quantification for molecular dynamics simulation. Extreme (large or small) output values for the LAMMPS code often occur at the boundaries of input regions, and uncertainties in those boundary values are overlooked by common SA methods. Similarly, input values for which code outputs are consistent with calibration data can also occur near boundaries. Upon applying approaches in the literature for imprecise probabilities (IPs), much more realistic results are obtained than for the complacent application of standard SA and code calibration.
Final Technical Report of the project "Controlling Quantum Information by Quantum Correlations"
The report describes hypotheses, aims, methods and results of the project 20170675PRD2, “Controlling Quantum Information by Quantum Correlations”, which has been run from July 31, 2017 to January 7, 2018. The technical work has been performed by Director’s Fellow Davide Girolami of the T-4 Division, Physics of Condensed Matter and Complex Systems, under the supervision of Wojciech Zurek (T-4), Lukasz Cincio (T-4), and Marcus Daniels (CCS-7). The project ended as Davide Girolami has been converted to J. R. Oppenheimer Fellow to work on the project 20180702PRD1, “Optimal Control of Quantum Machines”, started on January 8, 2018.
Corrections to the General (2,4) and (4,4) FDTD Schemes
The sampling weights associated with two general higher order FDTD schemes were derived by Smith, et al. and published in a IEEE Transactions on Antennas and Propagation article in 2012. Inconsistencies between governing equations and their resulting solutions were discovered within the article. In an effort to track down the root cause of these inconsistencies, the full three-dimensional, higher order FDTD dispersion relation was re-derived using Mathematica TM . During this process, two errors were identi ed in the article. Both errors are highlighted in this document. The corrected sampling weights are also provided. Finally, the original stability limits provided for both schemes are corrected, and presented in a more precise form. It is recommended any future implementations of the two general higher order schemes provided in the Smith, et al. 2012 article should instead use the sampling weights and stability conditions listed in this document.