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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

High-resolution (30-m) urban land cover projections for Los Angeles California Urban Area: 2010 to 2100 under SSP3 and SSP5 [Updated simulations based on population-driven urban intensity transitions]

These data (v3) are updated from previous versions (1 and 2) in that they include consider the effects of population on transitions in urban land intensity. This leads to more reasonable differences in urban land projections under variant SSPs. For the present dataset, both SSP3 and SSP5 are provided. These data represent simulations of future land use and land cover (LULCC) for Los Angeles urban area (U.S. Census Bureau defined area) as raster tiff images at a 30-m pixel resolution and at decadal time steps from 2010 to 2100. LULCC classes in this product follow the National Land Cover Dataset (NLCD) classification. NLCD 21-24 correspond to open developed, low developed, medium developed, and high developed urban land classes, respectively. Only urban land cover classes (NLCD class 21, 22, 23, and 24) are dynamic over time; however, all NLCD classes are included in the final product. Therefore, NLCD classes that do not convert to an urban class will be similar to year 2000. The products were developed using a hybridized statistical and cellular automata approach. Linear mixed models (LMMs) were used to estimate future urban land budgets based on 1-km urban land fraction projections from Gao and Pesaresi (2021), whereas separate generalized linear mixed models (GLMMs) were used to estimate shifts in urban land intensities based on retrospective shifts in NLCD urban class intensities over a 20- year period. Based on urban land allocations from the statistical models, a cellular-automata and downscaling routine was used to simulate dynamic urban land expansion at a 30-m resolution based on suitability criteria. Scenarios of future urban landcover change projections include variant solutions for the Shared Socioeconomic Pathway 5 (SSP5) and SSP 3 based on different population assumptions, different land use intensification assumptions, variable land zoning constraints, and iterative adjustments to correct for over allocation of urban expansion across decadal time periods from 2010 to 2100. This results in 320 raster products.

Land↗
DOE OSTI2023

Graph Neural Networks and Applied Linear Algebra v.1.0

SAND2024-01365O The Graph Neural Networks and Applied Linear Algebra is companion software for the educational article with the same title. The software provides illustrative examples of graph neural networks in Matlab and Python. These stand-alone algorithms are for educational purposes. The software also includes graph neural network-based algorithms for a trainable Jacobi iteration as well as diffusion coefficient estimation. The software provides human-interpretable implementations of Graph Neural Networks in Matlab and Python. These implementations are not optimized for performance and instead emphasize readability. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2013

Accelerating Subsurface Transport Simulation on Heterogeneous Clusters

Reactive transport numerical models simulate chemical and microbiological reactions that occur along a flowpath. These models have to compute reactions for a large number of locations. They solve the set of ordinary differential equations (ODEs) that describes the reaction for each location through the Newton-Raphson technique. This technique involves computing a Jacobian matrix and a residual vector for each set of equation, and then solving iteratively the linearized system by performing Gaussian Elimination and LU decomposition until convergence. STOMP, a well known subsurface flow simulation tool, employs matrices with sizes in the order of 100x100 elements and, for numerical accuracy, LU factorization with full pivoting instead of the faster partial pivoting. Modern high performance computing systems are heterogeneous machines whose nodes integrate both CPUs and GPUs, exposing unprecedented amounts of parallelism. To exploit all their computational power, applications must use both the types of processing elements. For the case of subsurface flow simulation, this mainly requires implementing efficient batched LU-based solvers and identifying efficient solutions for enabling load balancing among the different processors of the system. In this paper we discuss two approaches that allows scaling STOMP's performance on heterogeneous clusters. We initially identify the challenges in implementing batched LU-based solvers for small matrices on GPUs, and propose an implementation that fulfills STOMP's requirements. We compare this implementation to other existing solutions. Then, we combine the batched GPU solver with an OpenMP-based CPU solver, and present an adaptive load balancer that dynamically distributes the linear systems to solve between the two components inside a node. We show how these approaches, integrated into the full application, provide speed ups from 6 to 7 times on large problems, executed on up to 16 nodes of a cluster with two AMD Opteron 6272 and a Tesla M2090 per node.

GPU↗
DOE OSTI2012

The Quantum Hydrodynamic Description of Tunneling

The quantum hydrodynamic approach is based on the de Broglie-Bohm formulation of quantum mechanics. The resulting fluid-like equations of motion describe the flow of probability and an accurate solution to these equations is equivalent to solving the time-dependent Schroedinger equation. Furthermore, the hydrodynamic approach provides new insight into the mechanisms as well as an alternative computational approach for treating tunneling phenomena. New concepts include well-defined 'quantum trajectories', 'quantum potential', and 'quantum force' all of which have classical analogues. The quantum potential and its associated force give rise to all quantum mechanical effects such as zero point energy, tunneling, and interference. A new numerical approach called the Iterative Finite Difference Method (IFDM) will be discussed. The IFDM is used to solve the set of non-linear coupled hydrodynamic equations. It is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a 'smart' Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is also capable of treating anharmonic potentials. Example calculations using the IFDM will be presented which include: a one-dimensional Gaussian wave packet tunneling through an Eckart barrier, a one-dimensional bound-state Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. Approximate treatments of the quantum hydrodynamic equations will also be discussed which could allow scaling of the calculations to hundreds of degrees of freedom which is important for treating tunneling phenomena in condensed phase systems.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Exact and inexact subsampled Newton methods for optimization

Abstract The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of the paper analyzes an inexact Newton method that solves linear systems approximately using the conjugate gradient (CG) method, and that samples the Hessian and not the gradient (the gradient is assumed to be exact). We provide a complexity analysis for this method based on the properties of the CG iteration and the quality of the Hessian approximation, and compare it with a method that employs a stochastic gradient iteration instead of the CG method. We report preliminary numerical results that illustrate the performance of inexact subsampled Newton methods on machine learning applications based on logistic regression.

Mathematics↗
DOE OSTI2025

FLORA Equilibrium and Stability Code Archive

FLORA solves, in a 2-D domain (radial and axial dimensions) with a specified azimuthal Fourier mode, for the linearized stability of a long, thin, axisymmetric plasma equilibrium in an applied magnetic field. Before the stability equation is solved, FLORA solves a set of simple equations for pressure balance that specify the equilibrium magnetic field and plasma pressure in the long-thin limit given a simplified description of the magnetic coils. It uses an initial-value method for the linear stability problem in which an equilibrium is given an initial perturbation to its magnetic field, and the temporal behavior of the perturbation is followed. The perturbation has been Fourier expanded in the azimuthal coordinate; each azimuthal mode must be examined separately. The complex partial differential equation of motion for the perturbed radial displacement of the field lines is solved as a coupled system of two real p.d.e.'s and the solution consists of two parts, the real part and the imaginary part. The system is solved by bringing the coupling terms in each equation to the right side and using an iterative technique.

Cohen, Bruce [Lawrence Livermore National Laborato↗
DOE OSTI2013

A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, one derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. Here, we show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.

42 ENGINEERING↗
DOE OSTI2016

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

2D/1D approximations to the 3D neutron transport equation. I: Theory

A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Multigrid solution of a distributed optimal control problem constrained by the Stokes equations

We construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a linear system (the KKT system) connecting the state, adjoint, and control variables. Our approach is to eliminate the state and adjoint variables by essentially solving two Stokes systems, and to construct efficient multigrid preconditioners for the Schur-complement of the block associated with the state and adjoint variables. These multigrid preconditioners are shown to be of optimal order with respect to the convergence properties of the discrete methods used to solve the Stokes system. In particular, the number of conjugate gradient iterations is shown to decrease as the resolution increases, a feature shared by similar multigrid preconditioners for elliptic constrained optimal control problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Deblurring galaxy images with Tikhonov regularization on magnitude domain

Abstract We propose a regularization-based deblurring method that works efficiently for galaxy images. The spatial resolution of a ground-based telescope is generally limited by seeing conditions and is much worse than space-based telescopes. This circumstance has generated considerable research interest in the restoration of spatial resolution. Since image deblurring is a typical inverse problem and often ill-posed, solutions tend to be unstable. To obtain a stable solution, much research has adopted regularization-based methods for image deblurring, but the regularization term is not necessarily appropriate for galaxy images. Although galaxies have an exponential or Sérsic profile, the conventional regularization assumes the image profiles to behave linearly in space. The significant deviation between the assumption and real situations leads to blurring of the images and smoothing out the detailed structures. Clearly, regularization on logarithmic domain, i.e., magnitude domain, should provide a more appropriate assumption, which we explore in this study. We formulate a problem of deblurring galaxy images by an objective function with a Tikhonov regularization term on a magnitude domain. We introduce an iterative algorithm minimizing the objective function with a primal–dual splitting method. We investigate the feasibility of the proposed method using simulation and observation images. In the simulation, we blur galaxy images with a realistic point spread function and add both Gaussian and Poisson noise. For the evaluation with the observed images, we use galaxy images taken by the Subaru HSC-SSP. Both of these evaluations show that our method successfully recovers the spatial resolution of the deblurred images and significantly outperforms the conventional methods. The code is publicly available from the GitHub 〈https://github.com/kzmurata-astro/PSFdeconv_amag〉.

Murata, Kazumi↗
DOE OSTI2019

Sparse, iterative simulation methods for one-dimensional laminar flames

Sparse, iterative simulation methods for one-dimensional laminar flames are proposed. The resulting steady and unsteady flame solvers exploit approximate Jacobians to greatly reduce the computational cost associated with matrix operations. The constant, non-unity Lewis number assumption is introduced to further reduce the computational cost. The solvers are also parallelized to reduce time-to-solution on distributed memory computer systems. Computed laminar flame speeds and species profiles for a range of chemical mechanisms (from 10 to 2878 species) are compared against a well-validated commercial code and are found to be consistent within solver tolerances. The computation times of both the unsteady and steady solutions increase only linearly with the number of species, which is a significant improvement over the quadratic or cubic scaling of existing steady-state flame solvers. For the largest mechanism tested, the steady-state flame solver is two orders of magnitude faster than commonly-used codes. The use of an approximate Jacobian is shown to reduce the rate of convergence for the steady-state solver, but does not significantly affect the domain of convergence. The steady-state solver with approximate Jacobian is thus well suited for computationally efficient laminar flame speed sweeps with large kinetic mechanisms.

42 ENGINEERING↗
DOE OSTI2017

Next generation extended Lagrangian first principles molecular dynamics

Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett., 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density functional theory and compared to the extended Lagrangian framework of rst principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Materials systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born- Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on-the- y updates of the kernel, this formulation provides an efficient and general framework for quantum based Born-Oppenheimer molecular dynamics simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Repair and Resource Scheduling in Unbalanced Distribution Systems Using Neighborhood Search

—This paper proposes an optimization strategy to assist utility operators to recover power distribution systems after large outages. Specifically, a mixed-integer linear programming (MILP) model is developed for co-optimizing crews, resources, and network operations. The MILP model coordinates damage isolation, network reconfiguration, distributed generator re-dispatch, and crew/resource logistics. In addition, a framework for integrating different types of photovoltaic (PV) systems in the restoration process is developed. We consider two different types of crews, namely, line crews for damage repair and tree crews for obstacle removal. We also model the repair resource logistic constraints. Furthermore, a new algorithm is developed for solving the distribution system repair and restoration problem (DSRRP). The algorithm starts by solving DSRRP using an assignmentbased method, then a neighborhood search method is designed to iteratively improve the solution. The proposed method is validated on modified IEEE 123- and 8500-bus distribution test systems.

Outage management↗