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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Viscoelastic Stresses in the Plates Containing Inclusions with Cracks

We study viscoelastic stresses in the plates containing inclusions weakened by cracks by the method of boundary integral equations and the Laplace integral transformation. The case in which the rheological relations between stresses and strains are written in the differential form is analyzed in detail. To solve the boundary problem of viscoelasticity, we use the well-known approach in which the corresponding problem of the theory of elasticity is studied by replacing the differential operators with constant quantities. The solution of the auxiliary problem is obtained by the method of boundary integral equations reduced to a system of algebraic equations. After replacing the elastic quantities in this system by the corresponding differential operators, we solve the system obtained as a result by using the Laplace integral transformation and then applying the improved numerical-analytic inversion formula adapted to this class of problems.

36 MATERIALS SCIENCE↗
DOE OSTI2026

JAXtronomy: A JAX port of lenstronomy

Gravitational lensing is a phenomenon where light bends around massive objects, resulting in distorted images seen by an observer. Studying gravitationally lensed systems provides insights into cosmology and astrophysics, including constraints of the expansion rate of the Universe and the distribution of dark matter. Thus, we introduce JAXtronomy, a re-implementation of the gravitational lensing software package lenstronomy (Birrer, 2021; Birrer & Amara, 2018) using JAX (Bradbury et al., 2018). JAX is a Python library that uses an accelerated linear algebra (XLA) compiler to improve the performance of computing software. Our core design principle of JAXtronomy is to maintain an identical API to that of lenstronomy. The main JAX features utilized in JAXtronomy are just-in-time compilation, which can lead to significant reductions in execution time, and automatic differentiation, which allows for the implementation of gradient-based algorithms that were previously impossible. Additionally, JAX allows code to be run on GPUs or parallelized across CPU cores, further boosting the performance of JAXtronomy.

astronomy↗
NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗
NASA NTRS1992

Optimal matrix approximants in structural identification

Problems of model correlation and system identification are central in the design, analysis, and control of large space structures. Of the numerous methods that have been proposed, many are based on finding minimal adjustments to a model matrix sufficient to introduce some desirable quality into that matrix. In this work, several of these methods are reviewed, placed in a modern framework, and linked to other previously known ideas in computational linear algebra and optimization. This new framework provides a point of departure for a number of new methods which are introduced here. Significant among these is a method for stiffness matrix adjustment which preserves the sparsity pattern of an original matrix, requires comparatively modest computational resources, and allows robust handling of noisy modal data. Numerical examples are included to illustrate the methods presented herein.

Beattie, C. A.↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗
NASA NTRS1981

Computational methods in nonlinear structural and solid mechanics; Proceedings of the Symposium, Washington, D.C., October 6-8, 1980. Symposium sponsored by the George Washington University and NASA

Topics discussed include computational strategies for nonlinear problems in structural mechanics, time integration techniques and the numerical solution of nonlinear algebraic equations, material characterization and nonlinear fracture mechanics, nonlinear interaction problems, and seismic response and the nonlinear analysis of concrete structures. Also considered are nonlinear problems for nuclear reactors, crash dynamics and impact problems, nonlinear problems of fibrous composites and advanced nonlinear applications, and computerized symbolic manipulation and nonlinear analysis software systems.

Noor, A. K.↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2018

A Discrete Nonlinear Schrödinger-Type Hierarchy, Its Finite-Dimensional Reduction Analysis, and the Numerical Integration Scheme

We investigate the procedures of discretization of the integrable nonlinear Schrödinger dynamical system, well known as the Ablowitz–Ladik equation, the corresponding symplectic structures, and the finite-dimensional invariant reductions. We develop an efficient scheme of invariant reduction of the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter. We construct a finite set of recurrence algebraic regular relations that allows one to generate solutions of the discrete nonlinear Schrödinger dynamical system and discuss the related functional spaces of solutions. Finally, we analyze the Fourier-transform approach to the study of the set of solutions of the discrete nonlinear Schrödinger dynamical system and its functional-analytic aspects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born–Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions. Our scheme is based on quadratic response theory and includes orbital relaxation terms neglected in previous approaches. Simultaneous computation of multiple derivative couplings and energy gradients enables efficient multistate nonadiabatic molecular dynamics simulations in conjunction with Tully's fewest switches surface hopping (SH) method. We benchmark the thus obtained multistate TDDFT-SH scheme by simulating ultrafast decay of UV-photoexcited thymine, for which accurate gas-phase data from ultrafast spectroscopy experiments are available. The calculations predict a fast 153 fs decay from the bright S 2 to the dark S 1 excited state, followed by a much slower 14 ps S 1 deactivation to the ground state; statistical uncertainties were estimated using bootstrap sampling. These results agree well with the experimentally observed time constants of 100–200 fs and 5–7 ps, respectively, unlike previous multiconfigurational self-consistent field and second-order algebraic diagrammatic construction calculations. Furthermore, our results support the S 1 -trapping hypothesis. For thymine, the computational cost of a single TDDFT-SH time-step including the lowest 3 states, all couplings and gradients, is ~5 times larger than the cost of a single Born–Oppenheimer dynamics time step for the ground state in our implementation. Thus, ps nonadiabatic dynamics simulations using multistate hybrid TDDFT-SH for systems with up to ~100 atoms are possible without drastic approximations on single workstation nodes. Our implementation will be made available through Turbomole.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

JDFTx: Software for joint density-functional theory

Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units). This code hosts the development of joint density-functional theory (JDFT) that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Application of Hybrid Optimization-Expert System for Optimal Power Management on Board Space Power Station

The space power system has two sources of energy: photo-voltaic blankets and batteries. The optimal power management problem on-board has two broad operations: off-line power scheduling to determine the load allocation schedule of the next several hours based on the forecast of load and solar power availability. The nature of this study puts less emphasis on speed requirement for computation and more importance on the optimality of the solution. The second category problem, on-line power rescheduling, is needed in the event of occurrence of a contingency to optimally reschedule the loads to minimize the 'unused' or 'wasted' energy while keeping the priority on certain type of load and minimum disturbance of the original optimal schedule determined in the first-stage off-line study. The computational performance of the on-line 'rescheduler' is an important criterion and plays a critical role in the selection of the appropriate tool. The Howard University Center for Energy Systems and Control has developed a hybrid optimization-expert systems based power management program. The pre-scheduler has been developed using a non-linear multi-objective optimization technique called the Outer Approximation method and implemented using the General Algebraic Modeling System (GAMS). The optimization model has the capability of dealing with multiple conflicting objectives viz. maximizing energy utilization, minimizing the variation of load over a day, etc. and incorporates several complex interaction between the loads in a space system. The rescheduling is performed using an expert system developed in PROLOG which utilizes a rule-base for reallocation of the loads in an emergency condition viz. shortage of power due to solar array failure, increase of base load, addition of new activity, repetition of old activity etc. Both the modules handle decision making on battery charging and discharging and allocation of loads over a time-horizon of a day divided into intervals of 10 minutes. The models have been extensively tested using a case study for the Space Station Freedom and the results for the case study will be presented. Several future enhancements of the pre-scheduler and the 'rescheduler' have been outlined which include graphic analyzer for the on-line module, incorporating probabilistic considerations, including spatial location of the loads and the connectivity using a direct current (DC) load flow model.

Momoh, James↗
DOE OSTI2018

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

Intelligent machines in the twenty-first century: foundations of inference and inquiry

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Review↗
NASA NTRS1974

HAL/S - The programming language for Shuttle

HAL/S is a higher order language and system, now operational, adopted by NASA for programming Space Shuttle on-board software. Program reliability is enhanced through language clarity and readability, modularity through program structure, and protection of code and data. Salient features of HAL/S include output orientation, automatic checking (with strictly enforced compiler rules), the availability of linear algebra, real-time control, a statement-level simulator, and compiler transferability (for applying HAL/S to additional object and host computers). The compiler is described briefly.

Martin, F. H.↗
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.↗
DOE OSTI2016

Infrared computations of defect Schur indices

We conjecture a formula for the Schur index of four-dimensional N = 2 theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebra and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗