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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 1,621 records · Page 90

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DOE OSTI2017

JDFTx: Software for joint density-functional theory

Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units). This code hosts the development of joint density-functional theory (JDFT) that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Hollands, Stefan↗

DOE OSTI2018

The basic matrix library (BML) for quantum chemistry

The basic matrix library package (BML) provides a common application programming interface (API) for linear algebra and matrix functions in C and Fortran for quantum chemistry codes. The BML API is matrix format independent. Currently the dense, compressed sparse row, and ELLPACK-R sparse matrix data types are available, each with different implementations. We show how the second-order spectral projection (SP2) algorithm used to compute the electronic structure of a molecular system represented with a tight-binding Hamiltonian can be successfully implemented with the aid of this library.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Livermore Big Artificial Neural Network Toolkit

LBANN is a toolkit that is designed to train artificial neural networks efficiently on high performance computing architectures. It is optimized to take advantages of key High Performance Computing features to accelerate neural network training. Specifically it is optimized for low-latency, high bandwidth interconnects, node-local NVRAM, node-local GPU accelerators, and high bandwidth parallel file systems. It is built on top of the open source Elemental distributed-memory dense and spars-direct linear algebra and optimization library that is released under the BSD license. The algorithms contained within LBANN are drawn from the academic literature and implemented to work within a distributed-memory framework.

Essen, BrianVan↗

DOE OSTI2017

Tempus v. 1.0

Tempus is a software framework for the time integration of ordinary differential equations (ODEs), partial differential equations (PDEs), and differential-algebraic equations (DAEs). Examples of time-integration methods available are Forward Euler, Backward Euler, Explicit Runge-Kutta and Implicit Runge-Kutta methods. Tempus can be used from small systems of equations (e.g., single ODEs for the time evolution of plasticity models) to large-scale transient simulations requiring exascale computing (e.g., flow fields around reentry vehicles and magneto-hydrodynamics). Tempus will be released as part of Trilinos under a BSD open source license.

Obert, CurtisC.↗

DOE OSTI2014

TAS: 89 0227: TAS Recovery Act - Optimization and Control of Electric Power Systems: ARRA

The name SuperOPF is used to refer several projects, problem formulations and soft-ware tools intended to extend, improve and re-define some of the standard methods of optimizing electric power systems. Our work included applying primal-dual interior point methods to standard AC optimal power flow problems of large size, as well as extensions of this problem to include co-optimization of multiple scenarios. The original SuperOPF problem formulation was based on co-optimizing a base scenario along with multiple post-contingency scenarios, where all AC power flow models and constraints are enforced for each, to find optimal energy contracts, endogenously determined locational reserves and appropriate nodal energy prices for a single period optimal power flow problem with uncertainty. This led to example non-linear programming problems on the order of 1 million constraints and half a million variables. The second generation SuperOPF formulation extends this by adding multiple periods and multiple base scenarios per period. It also incorporates additional variables and constraints to model load following reserves, ramping costs, and storage resources. A third generation of the multi-period SuperOPF, adds both integer variables and a receding horizon framework in which the problem type is more challenging (mixed integer), the size is even larger, and it must be solved more frequently, pushing the limits of currently available algorithms and solvers. The consideration of transient stability constraints in optimal power flow (OPF) problems has become increasingly important in modern power systems. Transient stability constrained OPF (TSCOPF) is a nonlinear optimization problem subject to a set of algebraic and differential equations. Solving a TSCOPF problem can be challenging due to (i) the differential-equation constraints in an optimization problem, (ii) the lack of a true analytical expression for transient stability in OPF. To handle the dynamics in TSCOPF, the set of differential equations can be approximated or converted into equivalent algebraic equations before they are included in an OPF formulation. In Chapter 4, a rigorous evaluation of using a predefined and fixed threshold for rotor angles as a mean to determine transient stability of the system is developed. TSCOPF can be modeled as a large-scale nonlinear programming problem including the constraints of differential-algebraic equations (DAE). Solving a TSCOPF problem can be challenging due to (i) the differential-equation constraints in an optimization problem, (ii) the lack of a true analytical expression for transient stability constraint in OPF. Unfortunately, even the current best TSCOPF solvers still suffer from the curse of dimensionality and unacceptable computational time, especially for large-scale power systems with multiple contingencies. In chapter 5, thse issues will be addressed and a new method to incorporate the transient stability constraints will be presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1986

Numerical simulation of scramjet inlet flow fields

A computer program was developed to analyze supersonic combustion ramjet (scramjet) inlet flow fields. The program solves the three-dimensional Euler or Reynolds averaged Navier-Stokes equations in full conservation form by either the fully explicit or explicit-implicit, predictor-corrector method of MacCormack. Turbulence is modeled by an algebraic eddy-viscosity model. The analysis allows inclusion of end effects which can significantly affect the inlet flow field. Detailed laminar and turbulent flow results are presented for a symmetric-wedge corner, and comparisons are made with the available experimental results to allow assessment of the program. Results are then presented for two inlet configurations for which experimental results exist at the NASA Langley Research Center.

Kumar, Ajay↗

NASA NTRS1989

A numerical and experimental study of confined swirling jets

A numerical and experimental study of a confined strong swirling flow is presented. Detailed velocity measurements are made using a two-component laser Doppler velocimeter (LDV) technique. Computations are performed using a differential second-moment (DSM) closure. The effect of inlet dissipation rate on calculated mean and turbulence fields is investigated. Various model constants are employed in the pressure-strain model to demonstrate their influences on the predicted results. Finally, comparison of the DSM calculations with the algebraic second-monent (ASM) closure results shows that the DSM is better suited for complex swirling flow analysis.

Nikjooy, M.↗

NASA NTRS1992

Robot Control Based On Spatial-Operator Algebra

Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.

Rodriguez, Guillermo↗

NASA NTRS1999

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Kiris, Cetin↗

DOE OSTI2016

Livermore Big Artificial Neural Network Toolkit

Essen, Brian Van↗

DOE OSTI2013

The Coulomb problem on a 3-sphere and Heun polynomials

The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Properties of the Graph Modularity Matrix and its Applications

We study the popular modularity matrix and respective functional used in connection with graph clustering and derive some properties useful when performing vertex aggregation of the associated graph. These properties are employed in the derivation of a multilevel parallel pairwise aggregation algorithm. Some illustrative examples which include algebraic multigrid (AMG) coarsening that follows strong direction of anisotropy in finite element problems as well as comparative performance results of the studied algorithm are presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

SUSPECT: MINLP special structure detector for Pyomo

We present SUSPECT, an open source toolkit that symbolically analyzes mixed-integer nonlinear optimization problems formulated using the Python algebraic modeling library Pyomo. We present the data structures and algorithms used to implement SUSPECT. SUSPECT works on a directed acyclic graph representation of the optimization problem to perform: bounds tightening, bound propagation, monotonicity detection, and convexity detection. We show how the tree-walking rules in SUSPECT balance the need for lightweight computation with effective special structure detection. SUSPECT can be used as a standalone tool or as a Python library to be integrated in other tools or solvers. Here, we highlight the easy extensibility of SUSPECT with several recent convexity detection tricks from the literature. We also report experimental results on the MINLPLib 2 dataset.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Derivation of K-matrix reaction theory in a discrete basis formalism

The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann–Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present a simpler alternative derivation that is carried out completely in the Hamiltonian representation, using a discrete basis of configurations for the scattering channels as well as the quasi-bound configurations of the combined fragments. We use matrix algebra to derive an explicit expression for the K matrix in terms of the Hamiltonian of the internal states of the compound system and the coupling between the channels and the internal states. The formula for the K matrix includes explicitly a real dispersive shift matrix to the internal Hamiltonian that is easily computed in the formalism. That expression is applied to derive the usual form of the S matrix as a sum over poles in the complex energy plane. Some extensions and limitations of the discrete-basis Hamiltonian formalism are discussed in the concluding remarks and in the Appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

P3A

Portably Performant Physical Algebra (P3A) is a C++ library that provides classes representing variables in a physical algebra equation. These equations are the fundamental way that physics models are written ("f = ma" for example). P3A provides a way to write in the C++ programming language similar to how one would do math on paper. P3A provides support tools for rapidly solving equations in a way that is common in scientific computing. 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. SAND2021-3183 O

Ibanez-Granados, Daniel↗

DOE OSTI2021

Numerical solution of large scale Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size N b . We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\mathcal{O}$(N b 2 ) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with N b up to 2.88 × 10 6 , and the wall clock time is less than 100 s using 17 280 CPU cores. Finally, this enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

97 MATHEMATICS AND COMPUTING↗