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Results for “Mathematics of computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Control of multi-agent systems: Results, open problems, and applications

The purpose of this review article is to present some recent results on the modeling and control of large systems of agents. We focus on particular applications where the agents are capable of independent actions instead of simply reacting to external forces. In the literature, such agents were referred to as autonomous, intelligent, self-propelled, greedy, and others. The main applications we have in mind are social systems (as opinion dynamics), pedestrians’ movements (also called crowd dynamics), animal groups, and vehicular traffic. We note that the last three examples include physical constraints; however, the agents are able to inject energy into the system, thus preventing the typical conservation of momentum and energy. In addition, the control problems posed by such systems are new and require innovative methods. We illustrate some ideas developed recently, including the use of sparse controls, limiting the total variation of controls, and defining new control problems for measures. After reviewing various approaches, we discuss some future research directions of potential interest. The latter encompasses both new types of equations and new types of limiting procedures to connect several scales at which a system can be represented. We conclude by illustrating a recent real-life experiment using autonomous vehicles on an open highway to smooth traffic waves. This opens the door to a new era of interventions to control real-time multi-agent systems and to increase the societal impact of such interventions guided by control research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

"Spectrally gapped" random walks on networks: a Mean First Passage Time formula

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices H=\langle H\rangle +\delta H H = ⟨ H ⟩ + δ H , with \langle H\rangle ⟨ H ⟩ rank- 1 1 and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Emergent long-range couplings in arrays of fluid cells

We present a system exhibiting extraordinarily long-range cooperative effects, on a length scale far exceeding the bulk correlation length. We give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coexistence in finite systems, which is confirmedly Monte Carlo (MC) simulation studies. Our work demonstrates that such action-at-a-distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures, or ferromagnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

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.

Computer Hardware↗
DOE OSTI2015

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.

Computer Hardware↗
DOE OSTI2016

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

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).

97 MATHEMATICS AND COMPUTING↗