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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1977

On the representation matrices of the spin permutation group

A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.

Wilson, S.↗
NASA NTRS1989

Monotonically improving approximate answers to relational algebra queries

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Smith, Kenneth P.↗
DOE OSTI2023

Integrating Learning and Physics based Computation for Fast Online Transient Analysis

In this work, a novel method that integrates learning and physics based computation is developed for greatly accelerating the simulation of full power system transient trajectories. To solve the dynamic algebraic equations, the method replaces the time-consuming dynamic computation for generator dynamics with trained predictors, while retaining the time-efficient algebraic computation of solving AC-power flow (PF) for power systems. In particular, a predictor is trained for each generator, and the system trajectories are computed by alternating steps of calling the predictors and solving AC-PF. The proposed method also allows fully parallelizable training strategies and a flexible trade-off between training time and testing accuracy. Comprehensive evaluations of the proposed method for transient/dynamic contingency analysis of the New York/New England 16-machine 68-bus power systems demonstrate excellent performance and significant acceleration of computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

Comparison of methods for developing the dynamics of rigid-body systems

Several approaches for developing the equations of motion for a three-degree-of-freedom PUMA robot were compared on the basis of computational efficiency (i.e., the number of additions, subtractions, multiplications, and divisions). Of particular interest was the investigation of the use of computer algebra as a tool for developing the equations of motion. Three approaches were implemented algebraically: Lagrange's method, Kane's method, and Wittenburg's method. Each formulation was developed in absolute and relative coordinates. These six cases were compared to each other and to a recursive numerical formulation. The results showed that all of the formulations implemented algebraically required fewer calculations than the recursive numerical algorithm. The algebraic formulations required fewer calculations in absolute coordinates than in relative coordinates. Each of the algebraic formulations could be simplified, using patterns from Kane's method, to yield the same number of calculations in a given coordinate system.

Ju, M. S.↗
DOE OSTI2021

EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Universal corner symmetry and the orbit method for gravity

A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners – codimension-2 surfaces supporting Noether charges. It applies to both finite distance and asymptotic corners. In this paper, we study this algebra and its representations, via the coadjoint orbit method. We show that generic orbits of the universal algebra split into sub-orbits spanned by finite distance and asymptotic corner symmetries, such that the full universal symmetry algebra gives rise to a unified treatment of corners in a manifold. We then identify the geometric structure that captures these algebraic properties on corners, which is the Atiyah Lie algebroid associated to a principal GL(2,R) $\ltimes$ R 2 -bundle. This structure is suggestive of the existence of a novel quantum gravitational theory which would unitarily glue such geometric structures, with spacetime geometries appearing as semi-classical configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1979

On the Routh approximation technique and least squares errors

A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated. The necessary conditions have been obtained in terms of algebraic equations. The method is useful for low frequency as well as high frequency reduced-order models.

Aburdene, M. F.↗
NASA NTRS1990

Surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for Space Station Freedom

The surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for the Space Station Freedom are described. The purpose of the surface definition and grid generation is to provide the necessary geometry information for CFD calculations about the vehicle. There are two salient features in this description. The first is that the numerical model representing the ACRV configuration is obtained from the measurement of an existing wind tunnel model. The method for smoothing the measured data and obtaining the numerical model is described. The second feature is the description of the algebraic grid generation method and software to compute volume grids about the ACRV. The methods and software allow rapid computation of volume grids for a wide range of flow conditions.

Smith, R. E.↗
DOE OSTI2021

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Generalized Bootstrap AMG and AIR-AMG for coupled PDE systems with a focus on spacetime discretizatoins

The Pennsylvania State University (“Subcontractor”) has worked on the design of new algebraic, parallel, multilevel methods that obtain the full space and time solution of systems of PDEs. In particular, the PI and his collaborators explored semi-intrusive approaches based on algebraic multigrid (AMG). The focus of the research has been on the development of these techniques for the Euler equations in 1d and 2d. The overall research focused on the development of adaptive AIR (approximate ideal restriction) AMG solvers for these problems. The PI also explored the use of smoothed aggregation and root-node energy-based AMG solvers for these problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Multi-window spectrum estimation - A linear algebraic approach

The purpose of this paper is to elucidate the multi-window method for spectral estimation and sinusoid detection. The multi-window method, devised by D.J. Thomson, has many features that distinguish it from other spectrum estimation techniques. It has an elegant derivation, starting from first principles and using optimality arguments. It lends itself to performance analysis and provides a built-in measure of its reliability. In contrast to Thomson's integral equation derivation, we use linear algebraic methods both to treat the problem and to develop the solution. In addition to the tutorial, we present an overview of published generalizations and analyses of the method.

Onn, Ruth↗
NASA NTRS1984

Minimizing Weight of Structural Designs

Approximation Concepts Code for Efficient Structural Synthesis (ACCESS3) combines methods to offer structural system designer powerful, efficient tool for synthesis of minimum-weight designs. Approximation concepts convert general structural synthesis problem into sequence of explicit problems of separable algebraic form; dual method exploits separable form to construct sequence of explicit dual functions.

Schmit, L. A., Jr.↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
DOE OSTI2024

Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems

Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

A finite element method for diffusion dominated unsteady viscous flows

A general conforming finite element scheme for computing viscous flows is presented which is of second-order accuracy in space and time. Viscous terms are treated implicitly and advection terms are treated explicitly in the time marching segment of the algorithm. A method for solving the algebraic equations at each time step is given. The method is demonstrated on two test problems, one of them being a plane vortex flow for which asymptotic methods are used to obtain suitable numerical boundary conditions at each time step.

Gunzburger, M. D.↗
DOE OSTI2024

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗