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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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Mathematical and Computational Tools for Predictive Simulation of Complex Coupled Systems under Uncertainty

Methods and algorithms are developed to enable the accurate analysis of problems that exhibit interacting physical processes with uncertainties. These uncertainties can pertain either to each of the physical processes or to the manner in which they depend on each others. These problems are cast within a polynomial chaos framework and their solution then involves either solving a large system of algebraic equations or a high dimensional numerical quadrature. In both cases, the curse of dimensionality is manifested. Procedures are developed for the efficient evaluation of the resulting linear equations that advantage of the block sparse structure of these equations, resulting in a block recursive Schur complement construction. In addition, embedded quadratures are constructed that permit the evaluation of very high-dimensional integrals using low-dimensional quadratures adapted to particular quantities of interest. The low-dimensional integration is carried out in a transformed measure space in which the quantity of interest is low-dimensional. Finally, a procedure is also developed to discover a low-dimensional manifold, embedded in the initial high-dimensional one, in which scalar quantities of interest exist. This approach permits the functional expression of the reduced space in terms of the original space, thus permitting cross-scale sensitivity analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A Mathematical Analysis of Atomistic-to-Continuum (AtC) Multiscale Coupling Methods

We have worked on several projects aimed at improving the efficiency and understanding of multiscale methods, especially those applicable to problems involving atomistic-to-continuum coupling. Activities include blending methods for AtC coupling and efficient quasi-continuum methods for problems with long-range interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Algorithms for Mathematical Programming with Emphasis on Bi-level Models (Final Scientific/Technical Report)

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Multiscale Mathematics for Plasma Kinetics Spanning Multiple Collisionality Regimes (Final Technical Report)

This is the Final Technical Report on this grant. The subject of this grant is accelerated simulation for plasma kinetics, in particular for Coulomb collisions in a plasma. The goal of this project is the development of accelerated simulation methods for plasma kinetics and the application of these methods to prob lems of interest for plasma fusion. Specifically, this project is developing methods for simulation of Coulomb collisions between charged particles. Collisional effects can be significant in the edge plasma of a fusion device, but correct simulation of the collisional effects is a computational bottleneck for current simulation methods. We developed two approaches to acceleration of simulation for Coulomb collisions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

We have treated the modeling, analysis, numerical analysis, and algorithmic development for nonlocal models of diffusion and mechanics. Variational formulations were developed and finite element methods were developed based on those formulations for both steady state and time dependent problems. Obstacle problems and optimization problems for the nonlocal models were also treated and connections made with fractional derivative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Modeling Mathematical Programs with Equilibrium Constraints in Pyomo

We describe new capabilities for modeling MPEC problems within the Pyomo modeling software. These capabilities include new modeling components that represent complementarity conditions, modeling transformations for re-expressing models with complementarity conditions in other forms, and meta-solvers that apply transformations and numeric optimization solvers to optimize MPEC problems. We illustrate the breadth of Pyomo's modeling capabilities for MPEC problems, and we describe how Pyomo's meta-solvers can perform local and global optimization of MPEC problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Mathematical Foundations for Uncertainty Quantification in Materials Design. Final Report

Final report DE-SC0010723. Our key accomplishment in the first year of the grant is that we started developing pathwise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of nonequilibrium extended systems. The combination of these novel methodologies provide the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale models with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, etc. The first two such publications sponsored by the grant, have just been published.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Development of mathematical model and simulation tool for the high capacity production of carbon fiber

Weight reduction in the transportation is the most effective way for reducing fuel consumption. Carbon fiber composites have been increasingly used by automotive manufacturers in vehicle nonstructural and structural parts. Larger penetration of carbon fiber-based materials requires very large quantities of fiber at a low price, and of consistently high quality. The advancements in carbon fiber technology that are required to achieve this production scale-up and cost reduction, are very challenging. The most expensive production step is the conversion of textile-grade polyacrylonitrile (PAN) precursor to carbon fiber. The conversion takes place in three main stages: stabilization, low and high temperature carbonization. Most of the research to date has focused on the stabilization of the PAN precursors and oxidized PAN fibers. Comparingly little effort has been dedicated to the investigation of processing conditions during low temperature (LT) carbonization. During this stage of fiber conversion, the largest fiber mass loss occurs, and the fundamental carbon fiber structure and material properties are established. The understanding of the conversion processes in the LT furnace, and the effects of spatial and temporal variations of the LT process parameters on the carbon fiber properties are necessary to identify possible process improvements and cost savings. The objective of this research was to develop computational models for gas flow and energy transport in the gas and fiber phases of the LT furnace, and to couple them with the fiber conversion process models. The model is implemented in the three-dimensional framework that enables analysis of process condition variations in all directions. The formulation is based on modified transport equation to simulate steady state conditions and thus significantly reduce computational effort associated with transient methods. The model is implemented in open source computational fluid dynamics (CFD) code OpenFOAM. The model has been demonstrated on a prototype carbon fiber LT furnace and can be extended to other geometries and process conditions. Extensions to other physical effects, such as accounting evolution of multiple gas species, and fiber tensioning are straightforward. The model uses High Performance Computing (HPC) capabilities of OpenFOAM and can be implemented on multi-processor workstations or mid-size computer clusters common in the industrial setting.

36 MATERIALS SCIENCE↗
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

The major goal of the project was to invent, analyze, implement, and apply new algorithms to speed up the computational simulation of complex systems in settings in which multiple simulations are needed. The main efforts we undertook are as follows: 1. Develop novel reduced order methods to reduce the costs of simulations, especially in settings (e.g., UQ, inference, optimization and control) for which numerous simulation are needed and also for nonlocal problems (e.g., fractional derivative, anomalous diffusion, nonlocal mechanics) for which lack of sparsity results in more expensive full-order simulation than encountered in partial differential equations settings; rigorous analyses as well as computational tests were carried out, 2. Develop multifidelity methods based on the usage of a variety of models having different fidelities and different costs to accelerate simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, 3. Develop ensemble methods to reduced the costs of simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, and 4. Analyze a model for Richardson pair dispersion in turbulent flows and develop discretization methods for the efficient and accurate approximations of the solution of the model; rigorous analyses as well as computational tests were carried out.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Two new SciDAC institutes promote mathematical tools and software technology for high-performance computing

Bigger is often said to be better, and the newest extreme-scale computers certainly are bigger, with millions of processing units. Moreover, the breadth of science performed on the U.S. Department of Energy (DOE) computing facilities is expanding, with new technology such as artificial intelligence emerging. These advances are exciting, creating new opportunities for scientific discovery; however, they also raise new questions for scientists who want to exploit these advances for tackling more complex problems. Will my simulation code be able to utilize the accelerators in extreme-scale computing systems? Can I take advantage of the deepening memory hierarchy in heterogeneous processors? Is there a way around bottlenecks caused by the widening ratio of peak floating-point operations per second to I/0 bandwidth? How can I manage my huge amounts of data effectively? Can I analyze data in situ, or must I transfer it to offline storage for later analysis? To address such questions, DOE announced that it is providing $57.5 million over the next five years for two multidisciplinary teams — FASTMath and RAPIDS2 — to develop new tools and techniques to harness supercomputers for scientific discovery. The teams, called SciDAC Institutes, are part of the Scientific Discovery through Advanced Computing program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute

As computational models scale to larger computers, the rate at which they produce data has far outstripped the same computers ability to write that data and further the file systems ability to store that data. Almost all of the SciDAC applications, but especially those related to fusion solve very large scale PDEs whose scientific output his impacted by this problem. To gain access to dynamics in an exascale simulation that are not identifiable a priori and to make that dynamical data available to machine learning requires fundamental research in the area of in situ data data analytics. Here data analytics includes compression, visualization, uncertainty quantification, and machine learning. This in situ data analytics will enable on-the-fly spatial and temporal compression of solution dynamics, expose that space-time compressed field to machine learning algorithms that have been specialized to work with dynamically evolving data (existing machine learning algorithms treat data sets as static), greatly improving the opportunity for machine learning to provide feedback to the compression, all within an ongoing simulation, without the need to write data to files. The same concepts are also being applied to uncertainty quantification and multi-fidelity modeling which have similar needs for spatial and temporal compression of the ongoing exascale simulation to perform either without the typical, unacceptable writing of data to files.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

CHROTRAN: a mathematical and computational model for in situ heavy metal remediation in heterogeneous aquifers

Groundwater contamination by heavy metals is a critical environmental problem for which in situ remediation is frequently the only viable treatment option. For such interventions, a three-dimensional reactive transport model of relevant biogeochemical processes is invaluable. To this end, we developed a model, CHROTRAN, for in situ treatment, which includes full dynamics for five species: a heavy metal to be remediated, an electron donor, biomass, a nontoxic conservative bio-inhibitor, and a biocide. Direct abiotic reduction by donor-metal interaction as well as donor-driven biomass growth and bio-reduction are modeled, along with crucial processes such as donor sorption, bio-fouling and biomass death. Our software implementation handles heterogeneous flow fields, arbitrarily many chemical species and amendment injection points, and features full coupling between flow and reactive transport. We describe installation and usage and present two example simulations demonstrating its unique capabilities. One simulation suggests an unorthodox approach to remediation of Cr(VI) contamination.

54 ENVIRONMENTAL SCIENCES↗