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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 703 records · Page 39

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NASA NTRS1977

Probe corrected far-field reconstruction from measurements on a cylinder: A novel formulation and efficient algorithm

A novel and numerically efficient method of far field evaluation from measurements taken on a cylinder is based on the representation of both the antenna and the probe fields as superpositions of plane waves. A system of two integral equations are established whose unknown functions are the azimuthal and elevation components of the antenna pattern and whose known terms are the set of measurement data taken with two different probes - the second probe in most practical instances being simply the same probe with a different geometrical orientation. The equations express the known data - for each angular position of the antenna under measurement - as the integrals of the products of the corresponding components of the unknown antenna and known probe patterns multiplied by a phase term. The convolutional nature of the integral equations makes their solutions straight-forward. If, as is virtually always the case, the probe is small or of moderate size so that the axis of rotation of the antenna mount is in the far field of the probe, the intervention of asymptotic techniques makes the solution numerically very efficient. The agreement of calculated and experimental patterns is excellent.

Borgiotti, G. V.↗

NASA NTRS1988

Numerical simulation of underexpanded plumes using upwind algorithms

The solution of the flow characteristics of highly underexpanded plumes is presently sought by means of a high-resolution total variation-diminishing upwind scheme featuring finite-volume metrics, Roe averaging with entropy correction, and monotonic upstream schemes for conservation laws. The existing approximate factorization schemes are used both as preconditioners and in order to apply the conjugate residual algorithm. The plumes treated are axisymmetric and laminar, and for an ideal gas that is allowed to be thermally incomplete. Simulations of the SSME and SRB plumes have been successfully conducted.

Obayashi, Shigeru↗

DOE OSTI2026

Towards a Verifiable Domain-Specific Language for Hardware-Accelerated Stencils

Defining a domain-specific language (DSL) that supports vector-calculus abstractions eases the porting of partial differential equation (PDE) solvers to specialized architectures. Sufficiently high-level abstractions empower users to express universal laws with sufficient generality that the laws must always hold true within their domain of validity. A broad class of PDE solvers employs stencil-based algorithms, the target domain of Berkeley Lab's stencil accelerator chip co-design project. First released as open-source in January 2026, the Formal software framework lays a foundation for defining an embedded DSL based on composable operators that implement mimetic numerical methods -- stencil algorithms that guarantee satisfaction of discrete versions of important vector calculus theorems. The Formal DSL will be the frontend to a new class of stencil-PDE accelerators developed jointly by LBNL, UHCL, and UC Berkeley through the DOE Competitive Portfolios for Computer Science Project. This offers the potential of an order of magnitude acceleration for this important category of computational methods to serve the DOE mission. Future work on the Formal DSL will facilitate software verification via type-safe templates that enable problem-specific correctness proofs relying upon generic function theory and carefully crafted unit tests.

Rouson, Damian↗

NASA NTRS1990

Efficient numerical simulation of electron states in quantum wires

A new algorithm is presented for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schroedinger's equation coupled with Poisson's equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. The effectiveness of this approach is demonstrated in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.

Kerkhoven, Thomas↗

DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗

NASA NTRS2006

Standardized Radiation Shield Design Methods: 2005 HZETRN

Research committed by the Langley Research Center through 1995 resulting in the HZETRN code provides the current basis for shield design methods according to NASA STD-3000 (2005). With this new prominence, the database, basic numerical procedures, and algorithms are being re-examined with new methods of verification and validation being implemented to capture a well defined algorithm for engineering design processes to be used in this early development phase of the Bush initiative. This process provides the methodology to transform the 1995 HZETRN research code into the 2005 HZETRN engineering code to be available for these early design processes. In this paper, we will review the basic derivations including new corrections to the codes to insure improved numerical stability and provide benchmarks for code verification.

Wilson, John W.↗

NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗

DOE OSTI2026

Rapid Quantum Ground State Preparation via Dissipative Dynamics

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of noncommuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Together, these results show that dissipation can be a powerful tool for ground state preparation, with potential applications across condensed matter physics, quantum materials science, and beyond.

decoherence↗

NASA NTRS1978

Filtering and error analysis via the UDU super T covariance factorization

Kalman filter algorithms based on the UDU super T covariance factorization are discussed, with special attention given to algorithm implementation efficiency. A U-D-factored covariance error-analysis algorithm is formulated, and its efficiency and numerical stability are demonstrated in a representative orbit determination problem. The numerical results are compared with those obtained using covariance error-analysis formulas, and the comparison highlights the numerical superiority of the present algorithm. A byproduct of the U-D analysis is a highly efficient algorithm mechanization of the arbitrary gain covariance update formula.

Thornton, C. L.↗

NASA NTRS1972

The computation of optimal control programmes using a modified successive sweep method.

A second-order method for numerically solving control optimization problems has been developed. The method, referred to as the modified sweep method (MSM), differs from the successive sweep method (SSM) proposed by McReynolds and Bryson (1965) in that the conditions for local control optimality are used to determine the control as an explicit function of the state variables and time. The control is eliminated from the problem and the solution to the resulting two-point boundary value problem can be obtained by linear perturbation methods. The modified sweep method proposed here uncouples the perturbation equations for the state variables and the Lagrange multipliers by using a generalized matrix-Riccati transformation of variables. The resulting algorithm for the numerical iteration process is concerned with determining the initial values of a set of Lagrange multipliers rather than correcting a numerical control programme over the entire time interval of interest.

Colunga, D.↗

NASA NTRS1994

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗

NASA NTRS1991

An efficient DSMC algorithm applied to a delta wing

A new algorithm for 3D direct simulation Monte Carlo (DSMC) is tested and numerical results are compared with wind tunnel data and results obtained earlier with a more traditional DSMC code. The test case is the flowfield around a delta wing at incidence at Knudsen number of 0.016 and Mach number of 20.2. The results are shown to compare favorably with both experimental and earlier numerical results. The new algorithm is described with special emphasis placed on its distinctive features: Cartesian/unstructured combination grid, special body surface definition, discretization in physical space.

Rault, D. F. G.↗

NASA NTRS1989

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Baker, A. J.↗

NASA NTRS2017

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].

Algorithm↗

NASA NTRS2017

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

Computational Aeroacoustics↗

NASA NTRS1991

Reliable numerical computation in an optimal output-feedback design

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Vansteenwyk, Brett↗

NASA NTRS1983

Close-mode identification performance of the ITD algorithm

Results of Monte Carlo numerical simulations conducted to study the close-mode performance of the Ibrahim Time-Domain (ITD) modal identification algorithm are presented. The ITD technique is a matrix eigensolution method for obtaining structural modal parameters directly from free-response test data without using the FFT. Thus, the well-known resolution and leakage limitations of the FFT procedure, that are particularly significant with short records, are avoided. As an example, one of several experimental data analyses where close modes have been accurately identified using very short records is shown. Although the identification scatter is found to increase as the square of reductions in frequency separation at small separations, the ability to differentiate modes spaced at fractions of the FFT resolution is substantiated.

Pappa, R. S.↗

NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for hypersonic flowfield simulations on supercomputers

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The relaxation strategy is well suited for computers employing either vector or parallel architectures, and the relation between computer architecture and algorithm is emphasized. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large. block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over a blunt body. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km.) over the Aeroassist Flight Experiment (AFE) configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗