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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Angular-Rate Estimation Using Star Tracker Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quatemion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quatemion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quatemion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Azor, R.↗
NASA NTRS1999

Angular-Rate Estimation using Star Tracker Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quaternion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Azor, R.↗
NASA NTRS2013

Uncertainties in Atomic Data and Their Propagation Through Spectral Models. I.

We present a method for computing uncertainties in spectral models, i.e., level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data.We provide analytic expressions, in the form of linear sets of algebraic equations, for the coupled uncertainties among all levels. These equations can be solved efficiently for any set of physical conditions and uncertainties in the atomic data. We illustrate our method applied to spectral models of Oiii and Fe ii and discuss the impact of the uncertainties on atomic systems under different physical conditions. As to intrinsic uncertainties in theoretical atomic data, we propose that these uncertainties can be estimated from the dispersion in the results from various independent calculations. This technique provides excellent results for the uncertainties in A-values of forbidden transitions in [Fe ii]. Key words: atomic data - atomic processes - line: formation - methods: data analysis - molecular data - molecular processes - techniques: spectroscopic

linear sets↗
DOE OSTI2022

Composing preconditioners for multiphysics PDE systems with applications to Generalized MHD

New patch smoothers or relaxation techniques are developed for solving linear matrix equations coming from systems of discretized partial differential equations (PDEs). One key linear solver challenge for many PDE systems arises when the resulting discretization matrix has a near null space that has a large dimension, which can occur in generalized magnetohydrodynamic (GMHD) systems. Patch-based relaxation is highly effective for problems when the null space can be spanned by a basis of locally supported vectors. The patch-based relaxation methods that we develop can be used either within an algebraic multigrid (AMG) hierarchy or as stand-alone preconditioners. These patch-based relaxation techniques are a form of well-known overlapping Schwarz methods where the computational domain is covered with a series of overlapping sub-domains (or patches). Patch relaxation then corresponds to solving a set of independent linear systems associated with each patch. In the context of GMHD, we also reformulate the underlying discrete representation used to generate a suitable set of matrix equations. In general, deriving a discretization that accurately approximates the curl operator and the Hall term while also producing linear systems with physically meaningful near null space properties can be challenging. Unfortunately, many natural discretization choices lead to a near null space that includes non-physical oscillatory modes and where it is not possible to span the near null space with a minimal set of locally supported basis vectors. Further discretization research is needed to understand the resulting trade-offs between accuracy, stability, and ease in solving the associated linear systems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Patel, R. V.↗
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↗
NASA NTRS1993

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗
NASA NTRS1979

Exact solution of some linear matrix equations using algebraic methods

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

Djaferis, T. E.↗
NASA NTRS1993

Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.

Jain, A.↗
NASA NTRSDate not supplied

Memory Optimizations for Sparse Linear Algebra on GPU Hardware

An effort to maximize memory bandwidth utilization for a sparse linear algebra kernel executing on NVIDIA® Tesla V100 and A100 Graphics Processing Units (GPUs) is described. The kernel consists of a block-sparse matrix-vector product and a series of forward/backward triangular solves. The computation is memory-bound and exhibits low arithmetic intensity. Along with a relatively small block size, the data layout poses a challenge to effectively utilize the available memory bandwidth on common GPU architectures. An earlier implementation using a warp to process a single row of the matrix was found to yield good memory performance on the V100 architecture. However, anew approach, which assigns a warp to six rows of the matrix, is proposed for the A100. In addition, two new features offered by the A100 architecture are explored.L2residency control enables a portion of theL2cache to be used for persistent data access, and the asynchronous copy instruction allows data to be loaded directly from main memory into shared memory. Demonstrations show that the new implementation improves memory bandwidth utilization from 71.5% to 81.2% of the peak available on theA100 architecture.

GPU↗
NASA NTRS1992

Computation of the flow field in a centrifugal impeller with splitter blades

To support the design effort of the Space Transportation Main Engine (STME) Fuel Pump Stage, viscous flow calculations were performed in a centrifugal impeller with splitter blades. These calculations were carried out with a Navier-Stokes solver (MINT), which employs a linearized block-implicit Alternating Direction Implicit (ADI) procedure to iteratively solve a finite difference form of the system of conservation equations of mass, momentum, and energy in body-fitted coordinates. A computational grid was generated algebraically for the 'channel' between two main blades of the impeller and extended both upstream of the impeller inlet and downstream of the impeller exit so that the appropriate boundary conditions could be applied. The results of the calculations show that although the overall level of flow distortion near the impeller exit is not very large, there is a noticeable difference between the flow patterns in the two 'passages' (one passage between the pressure side of the splitter blade and the suction side of the next full blade).

Dejong, Frederik J.↗
NASA NTRS2007

Newton-Euler Dynamic Equations of Motion for a Multi-body Spacecraft

The Magnetospheric MultiScale (MMS) mission employs a formation of spinning spacecraft with several flexible appendages and thruster-based control. To understand the complex dynamic interaction of thruster actuation, appendage motion, and spin dynamics, each spacecraft is modeled as a tree of rigid bodies connected by spherical or gimballed joints. The method presented facilitates assembling by inspection the exact, nonlinear dynamic equations of motion for a multibody spacecraft suitable for solution by numerical integration. The building block equations are derived by applying Newton's and Euler's equations of motion to an "element" consisting of two bodies and one joint (spherical and gimballed joints are considered separately). Patterns in the "mass" and L'force" matrices guide assembly by inspection of a general N-body tree-topology system. Straightforward linear algebra operations are employed to eliminate extraneous constraint equations, resulting in a minimum-dimension system of equations to solve. This method thus combines a straightforward, easily-extendable, easily-mechanized formulation with an efficient computer implementation.

Stoneking, Eric↗
DOE OSTI2022

Improving the Performance of DGEMM with MoA and Cache-Blocking: Preprint

The goal of this paper is to demonstrate performance enhancements of the high performance dense linear algebra matrix-matrix multiply DGEMM kernel, widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses in combination with Church-Rosser complete language constructs optimized for target processor architectures [3]. Our performance studies demonstrate that the MoA implementation of DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on both Intel Xeon Skylake and IBM Power-9 processors over the vendor supplied Intel MKL and IBM ESSL basic linear algebra libraries. Results are presented for the NREL Eagle and ORNL Summit supercomputers.

cache-blocking↗
DOE OSTI2023

QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation

The rapid development of quantum computing (QC) in the NISQ era urgently demands a low-level benchmark suite and insightful evaluation metrics for characterizing the properties of prototype NISQ devices, the efficiency of QC programming compilers, schedulers and assemblers, and the capability of quantum system simulators in a classical computer. In this work, we fill this gap by proposing a low-level, easy-to-use benchmark suite called QASMBench based on the OpenQASM assembly representation. It consolidates commonly used quantum routines and kernels from a variety of domains including chemistry, simulation, linear algebra, searching, optimization, arithmetic, machine learning, fault tolerance, cryptography, and so on, trading-off between generality and usability. To analyze these kernels in terms of NISQ device execution, in addition to circuit width and depth, we propose four circuit metrics including gate density, retention lifespan, measurement density, and entanglement variance, to extract more insights about the execution efficiency, the susceptibility to NISQ error, and the potential gain from machine-specific optimizations. Applications in QASMBench can be launched and verified on several NISQ platforms, including IBM-Q, Rigetti, IonQ and Quantinuum. For evaluation, we measure the execution fidelity of a subset of QASMBench applications on 12 IBM-Q machines through density matrix state tomography, comprising 25K circuit evaluations. In addition we also compare the fidelity of executions among the IBM-Q machines, the IonQ QPU and the Rigetti Aspen M-1 system.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

REDUCE 2: A computer program for the symbolic reduction of large block diagrams

REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.

Lorenzo, C. F.↗
NASA NTRS1987

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Badavi, F. F.↗
NASA NTRS1973

Numerical marching techniques for fluid flows with heat transfer

The finite difference formulation and method of solution is presented for a wide variety of fluid flow problems with associated heat transfer. Only a few direct results from these formulations are given as examples, since the book is intended primarily to serve a discussion of the techniques and as a starting point for further investigations; however, the formulations are sufficiently complete that a workable computer program may be written from them. In the appendixes a number of topics are discussed which are of interest with respect to the finite difference equations presented. These include a very rapid method for solving certain sets of linear algebraic equations, a discussion of numerical stability, the inherent error in flow rate for confined flow problems, and a method for obtaining high accuracy with a relatively small number of mesh points.

Hornbeck, R. W.↗