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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 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning

We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. We present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Time history solution program, L225 (TEV126). Volume 2: Supplemental system design and maintenance document

The time history solution program L225 (TEV126) is described. The program calculates the time responses of a linear system by convoluting the impulsive response functions with the time dependent excitation. The convolution is performed as a multiplication in the frequency domain. Fast Fourier transform techniques are used to transform the product back into the time domain to obtain response time histories. The design and structure of the program is presented.

Tornallyay, A.↗
DOE OSTI2022

QUIC-URB and QUIC-fire extension to complex terrain: Development of a terrain-following coordinate system

Ensemble-based approaches to prescribed fire planning cannot be supported by CFD-based models like FIRETEC and WFDS because they are too computationally expensive and cannot leverage LES approaches like CAWFE and WRF-SFIRE because too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, typical for instance of the Western United States. In this paper, we describe the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. In particular, the paper presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captured the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. We report the model agreed well with measurements on the upwind side of the peak, but overestimated speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field was obtained in 6 s, making the solver appealing for coupled fire–atmosphere simulations. The Socorro Mountain was highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect was addressed in this work). Results highlight that future work should focus on the implementation of parameterizations of wake-eddies, similar to QUIC-URB’s building parameterizations, and on thermodynamic-driven flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Xyce(™) Parallel Electronic Simulator

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗
DOE OSTI2022

Xyce(™) Parallel Electronic Simulator v.7.5

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗
DOE OSTI2013

Xyce(™) Parallel Electronic Simulator v.7.6

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Keiter, Eric↗
NASA NTRS1971

Satellite tracking by combined optimal estimation and control techniques.

Combined optimal estimation and control techniques are applied for the first time to satellite tracking systems. Both radio antenna and optical tracking systems of NASA are considered. The optimal estimation is accomplished using an extended Kalman filter resulting in an estimated state of the satellite and of the tracking system. This estimated state constitutes an input to the optimal controller. The optimal controller treats a linearized system with a quadratic performance index. The maximum principle is applied and a steady-state approximation to the resulting Riccati equation is obtained. A computer program, RATS, implementing this algorithm is described. A feasibility study of real-time implementation, tracking simulations, and parameter sensitivity studies are also reported.

Dressler, R. M.↗
NASA NTRS1973

Aeroelastic instabilities of hingeless helicopter blades.

In this study the stability boundaries of a hingeless helicopter blade are studied using a system of coupled flap-lag-pitch equations of motion. Divergence and flutter boundaries for the linearized system of equations are presented. Flap-lag, flap-pitch and coupled flap-lag-pitch instabilities in hovering flight are studied. The effect of the torsional degree of freedom on the flap-lag type of instability is investigated. Similarly the effect of lag on the flap pitch type of instability is also considered. Results illustrating these effects, together with the effect of various important blade parameters on blade stability are presented.

Friedmann, P.↗
NASA NTRS1977

Effect of virtual memory on efficient solution of two model problems

Computers with virtual memory architecture allow programs to be written as if they were small enough to be contained in memory. Two types of problems are investigated to show that this luxury can lead to quite an inefficient performance if the programmer does not interact strongly with the characteristics of the operating system when developing the program. The two problems considered are the simultaneous solutions of a large linear system of equations by Gaussian elimination and a model three-dimensional finite-difference problem. The Control Data STAR-100 computer runs are made to demonstrate the inefficiencies of programming the problems in the manner one would naturally do if the problems were indeed, small enough to be contained in memory. Program redesigns are presented which achieve large improvements in performance through changes in the computational procedure and the data base arrangement.

Lambiotte, J. J., Jr.↗
NASA NTRS1982

Rotor vibration caused by external excitation and rub

For turbomachinery with low natural frequencies, considerations have been recently required for rotor vibrations caused by external forces except unbalance one, such as foundation motion, seismic wave, rub and so forth. Such a forced vibration is investigated analytically and experimentally in the present paper. Vibrations in a rotor-bearing system under a harmonic excitation are analyzed by the modal technique in the case of a linear system including gyroscopic effect. For a nonlinear system a new and powerful quasi-modal technique is developed and applied to the vibration caused by rub.

Matsushita, O.↗
NASA NTRS1993

H(sub infinity)-type filter for spacecraft attitude estimation

A nonlinear filtering theory from a deterministic point of view is presented and an application to attitude determination is considered. The approach that is taken in this paper is motivated largely by the H(sun infinity) control and estimation theory for linear systems which has been evolved within the last decade. Rather than formulating the estimation problem as a game played by two adversaries, as has been done in the linear case, we employ in this work some notions from the theory of dissipative systems as a vehicle for arriving at certain Hamilton-Jacobi inequality, which in turn, provides a solution to the filtering problem, whenever it is satisfied. Application of this method to a linear estimation problem and to the problem of estimating a spacecraft attitude quaternion and gyro drift bias vector are presented. In limiting cases, these give the Kalman filter and the extended Kalman filter, respectively. The main advantages of this approach over its probabilistic counterpart are that this approach does not require a prior knowledge of any statistics, and that in general it is more amenable to a quantitative assessment regarding approximations such as linearization, and that in certain cases this approach yields an exact solution to the nonlinear filtering.

Markley, F. Landis↗
NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗
NASA NTRS1996

Output Tracking for Systems with Non-Hyperbolic and Near Non-Hyperbolic Internal Dynamics: Helicopter Hover Control

A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.

Devasia, Santosh↗
DOE OSTI2023

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1984

Output feedback and generic stabilizability

Attention is given to questions of pole placement and stabilization for generic linear systems with prescribed state, input and output dimension for the case where the controller must be implemented by linear memoryless output feedback. A criterion is presented in terms of a special pole placement property for generic stabilizability, and this criterion is used to describe constraints on the dimension which are consistent with generic stabilizability. Also treated are the rationality and solvability by radicals of stabilizing or pole positioning gains, and the way in which decision algebra can theoretically handle existence questions for generic systems is described.

Byrnes, C. I.↗
DOE OSTI2019

Asymptotics of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations

By using the theory of polynomial matrix pencils, we construct the asymptotics of linearly independent solutions of homogeneous singularly perturbed system of linear differential equations of any order m with matrices at higher derivatives degenerating as a small parameter approaches zero. The general case is analyzed. In this case, the limit matrix pencil has several finite and infinite elementary divisors of both the same and different multiplicities. The corresponding asymptotic estimates are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗