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Results for “Operator approximation”

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 235 records · Page 13

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NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗

NASA NTRS1986

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator-theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are used to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗

DOE OSTI2024

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. Here, we use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Watertight Tensor-Product Spline Reconstruction (KCNSC PDRD Technical Report)

The standard for representing geometric models in Computer Aided Design (CAD) systems is boundary representation with trimmed surfaces. However, the approximate nature of surface-surface intersections in CAD systems leaves many small gaps between mating surfaces. These gaps lead to problems for downstream analysis and manufacturing applications, requiring time consuming repair operations and further approximation of the geometry as polygonal meshes, which do not support design iteration. In this study, nVariate, Inc. evaluated its watertight reconstruction technology on a test part. The resulting watertight model has the same absolute model accuracy of the original model zero gaps, providing a representation that requires no repair and supports further design iterations in the CAD system.

42 ENGINEERING↗

NASA NTRS2019

Seeker 1.0: Prototype Robotic Free Flying Inspector Mission Overview

Seeker 1.0 is a prototype free flying robot that will one day be capable of inspecting human-rated spacecraft. Building off previous free flyer experience, this technology will eventually improve safety of human spacecraft by offering a variety of inspection capabilities for both routine and emergency scenarios providing increased capability and safety over current inspection methods. Seeker 1.0 is capable of 6 degree of freedom flight via a cold gas propulsion system and can operate up to 1 hour via a semi-autonomous guidance, navigation, and control system. The prototype spacecraft is capable of capturing still images at a variety of resolutions up to 13 MP. The initial test flight utilizes a command and data relay box called Kenobi. Kenobi is a derivative of the Seeker design and will communicate between Cygnus and Seeker and store data for post-mission downlink. Seeker and Kenobi have launched inside a NanoRacks External CubeSat Deployer (NRCSD-E) attached to the NG-11 Cygnus ISS resupply vehicle and will operate after Cygnus departs ISS and moves to a safe altitude. Operations will last approximately 30 minutes and will consist of basic vehicle maneuvers while capturing high-resolution still images. With any remaining time and propellant, Seeker will demonstrate additional safety capabilities and maneuvers required for operations around a crewed spacecraft. The Seeker project utilized the Class IE process that allows for streamlined flight hardware development and increased mission risk tolerance.

Spacecraft Inspection↗

NASA NTRS1993

Analysis and demonstration of a Scramaccelerator system

The Scramaccelerator, a novel type of supersonic-combustion, tube-based launcher has been developed that can accelerate almost any mass to velocities of 3 to over 7 km/sec. This paper describes the technology demonstration of the concept by firing 120-g projectiles into a 38 mm barrel at 2.8 to 3.2 km/sec. The results from the technology demonstration are presented along with calculated performance of the demonstration tests. Critical test issues discussed include sabot separation, venting requirements, and test performance. The results, obtained during testing indicate projectile accelerations were achieved of approximately 5000 g. Hence, these tests demonstrate successful Scramaccelerator operation and acceleration at approximately 1.95 times the Chapman Jouguet detonation velocity, far greater than the 1.15 to 1.3 times previously demonstrated. In addition, the tests demonstrate hypersonic propulsion at Mach numbers above 8, acceleration at greater than 3 km/s, and system integration technology sufficient to accomplish this success.

Humphrey, Joseph W.↗

NASA NTRS1996

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Deng, Qingping↗

NASA NTRS2019

Impact of Facility Pressure on the Wear of the NASA HERMeS Hall Thruster

This work presents an overview and summary of the results acquired during the final segment of the TDU-3 Long Duration Wear Test, which was completed in October 2018. The overall goal of this segment was to quantify the impact of facility pressure on the wear of the Hall Effect Rocket with Magnetic Shielding Technology Demonstration Unit Three (TDU-3) Hall thruster. This was accomplished by operating TDU-3 for approximately 270 hours at the nominal 600 V/12.5 kW operating condition while a bleed or auxiliary flow of xenon propellant was injected into the vacuum facility in order to raise the operating pressure to match that of another test facility in which previous wear segments had been performed. The performance, plume, stability, and wear results acquired at this elevated pressure (11.7 µTorr) are compared with the equivalent data previously taken at the nominal operating pressure (4.2 µTorr).

Frieman, Jason D.↗

NASA NTRS2019

Impact of Facility Pressure on the Wear of the NASA HERMeS Hall Thruster

This work presents an overview and summary of the results acquired during the final segment of the TDU-3 Long Duration Wear Test, which was completed in October 2018. The overall goal of this segment was to quantify the impact of facility pressure on the wear of the Hall Effect Rocket with Magnetic Shielding Technology Demonstration Unit Three (TDU-3) Hall thruster. This was accomplished by operating TDU-3 for approximately 270 hours at the nominal 600 V/12.5 kW operating condition while a bleed or auxiliary flow of xenon propellant was injected into the vacuum facility in order to raise the operating pressure to match that of another test facility in which previous wear segments had been performed. The performance, plume, stability, and wear results acquired at this elevated pressure (11.7 ÂµTorr) are compared with equivalent data taken at the nominal operating pressure (4.2 ÂµTorr) in the same facility as well at the elevated operating pressure in the other facility. Implications of these results for acquiring facility-independent service life estimates are discussed.

Frieman, Jason D.↗

NASA NTRS1986

Preconditioning matrices for Chebyshev derivative operators

The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

Rothman, Ernest E.↗

NASA NTRS2009

Effects of Thermal Exposure on the Optical Properties of LORD Aeroglaze A276

A lunar outpost will require electrical energy. One potential source is fission surface power where heat from a reactor is converted into electricity utilizing an energy conversion system, and waste heat will need to be rejected from the system. The Second Generation Radiator Demonstration Unit is a technology demonstration unit leading towards operational radiators. To approximate the infrared emittance of the lunar outpost radiators, a low-cost coating compatible with the test conditions was sought. LORD Aeroglaze A276 has a similar emittance, but its performance in air and vacuum at the desired operating temperatures was unknown. This study determined that the emittance remained above 0.86 for all conditions tested and that LORD Aeroglaze A276 is a suitable surrogate coating for the Second Generation Radiator Demonstration Unit.

Ellis, David L.↗

DOE OSTI2022

Operator inference for non-intrusive model reduction with quadratic manifolds

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.

42 ENGINEERING↗

NASA NTRS1990

Semigroup theory and numerical approximation for equations in linear viscoelasticity

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.↗

DOE OSTI2025

Minimally Intrusive Data-Driven Approximation of Schur Complement-based Coupling Operators for Heterogeneous Numerical Methods

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de Castro, Amy Grace [Sandia National Laboratories↗

NASA NTRS1987

On Lipschitz continuity of nonlinear differential operators

In connection with approximations for nonlinear evolution equations, it is standard to assume that nonlinear terms are at least locally Lipschitz continuous. However, it is shown here that f = f(X,del sub u(X)) is Lipschitz continuous from the subspace W sup 1, infinity is a subset of L sub 2 into W sup 1,2, and maps W sup 2, infinity into W sup 1, infinity, if and only if f is affine with W sup 1, infinity coefficients. In fact, a local version of this claim is proved.

Keeling, Stephen L.↗

DOE OSTI2024

Progress towards the completion of the proton power upgrade project

The Proton Power Upgrade project at the Spallation Neutron Source at Oak Ridge National Laboratory will increase the proton beam power capability from 1.4 to 2.8 MW. Upon completion in early 2025, 2 MW of beam power will be available for neutron production at the existing first target station (FTS) with the remaining beam power available for the future second target station (STS). The project has installed seven superconducting radio-frequency (RF) cryomodules and supporting RF power systems to increase the beam energy by 30% to 1.3 GeV, and the beam current will be increased by 50%. The injection and extraction region of the accumulator ring are being upgraded, and a new 2 MW mercury target has been developed along with supporting equipment for high-flow gas injection to mitigate cavitation and fatigue stress. The first four cryomodules and supporting systems were commissioned in 2022-2023 and supported neutron production at 1.05 GeV, 1.7 MW with high reliability. The first-article 2 MW target was operated successfully for approximately 4400 MW-Hours over two run periods. The long outage began in August 2023 for installation of the remaining technical equipment and construction of the Ring-to-Target Beam Transport tunnel stub that will enable connection to the STS without interrupting operation of the FTS. The upgrade is proceeding on-schedule and on-budget, and resumption of neutron production for the user program is planned for July 2024.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Progress towards the completion of the proton power upgrade project

Champion, Mark↗

NASA NTRS1987

Piecewise linear approximation for hereditary control problems

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Propst, Georg↗