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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

36 MATERIALS SCIENCE↗
DOE OSTI2017

On the use of reverse Brownian motion to accelerate hybrid simulations

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantum Search Compiler (Qsearch) v2.0

Quantum Gate Synthesis is the process of taking a desired quantum gate operation, in this case specified as a unitary matrix, and decomposing it into a list of operations that can actually be performed on a quantum computer. Qsearch is an implementation of a quantum synthesis algorithm based on combining A* search with numerical optimization. It is designed to minimize CNOT count at the expense of having a long runtime. It produces particularly efficient quantum circuits in terms of CNOT count, up until about 4 qubits. It is generally impractical to run Qsearch on circuits with more than 4 qubits, but it can be used as a subroutine in algorithms designed to work with these larger circuits. Qsearch takes the form of a Python package, taking advantage of Numpy and Scipy, with part of the package written in Rust and taking advantage of OpenBLAS, NLOPT, and Google Ceres for faster runtime.

Lancu, Costin↗
DOE OSTI2020

Securing machine learning models

We discuss the challenges and approaches to securing numeric computation against adversaries who may want to discover hidden parameters or values used by the algorithm. We discuss techniques that are both cryptographic and non-cryptographic in nature. Cryptographic solutions are either not yet algorithmically feasible or currently require more computational resources than are reasonable to have in a deployed setting. Non-cryptographic solutions may be computationally faster, but these cannot stop a determined adversary. For one such non-cryptographic solution, mixed Boolean arithmetic, we suggest a number of improvements that may protect the obfuscated calculation against current automated deobfuscation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Multiscale Simulation of Blood Flow in Brain Arteries with an Aneurysm

Multi-scale modeling of arterial blood flow can shed light on the interaction between events happening at micro- and meso-scales (i.e., adhesion of red blood cells to the arterial wall, clot formation) and at macro-scales (i.e., change in flow patterns due to the clot). Coupled numerical simulations of such multi-scale flow require state-of-the-art computers and algorithms, along with techniques for multi-scale visualizations.This animation presents results of studies used in the development of a multi-scale visualization methodology. First we use streamlines to show the path the flow is taking as it moves through the system, including the aneurysm. Next we investigate the process of thrombus (blood clot) formation, which may be responsible for the rupture of aneurysms, by concentrating on the platelet blood cells, observing as they aggregate on the wall of the aneurysm.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Self-learning Monte Carlo method and cumulative update in fermion systems

In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Effect of Yagi–Uda nano-antenna element shape on the directivity and radiation efficiency

In this paper, different optimal designs of Yagi–Uda nano-antennas (NAs) are introduced and analyzed based on different element shapes to maximize the directivity and radiation efficiency. The studied element shapes include triangular, hexagonal, cube, square, rotated square, rectangular, ellipsoid, and elliptical cylinder shapes. The NAs parameters for each design are optimized using particle swarm optimization algorithm to achieve high directivity at a wavelength of 500 nm for wireless point-to-point applications. The designs are numerically analysed using 3-D finite difference time domain method (3-D FDTD) via Lumerical software package. To illustrate the performance of the proposed antennas, different radiation parameters such as radiation pattern, directivity, and radiation efficiency have been studied. Moreover, a tolerance of ± 5% is calculated to consider the imperfections that may appear in the fabrication process at a nanoscale. The optimized rectangular prism NA achieves the highest directivity of 24.21 with an efficiency of 50.74%. However, the optimized triangular prism NA has the highest efficiency of 73% with a directivity of 20.89. This enhancement is mainly attributed to the efficient coupling between array elements along with low side lobe level. However, a trade-off between directivity and radiation efficiency is obtained by the hexagonal prism NA with directivity of 21.9 and radiation efficiency of 69.1%.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A computationally efficient method for tempered fractional differential equations with application

This paper investigates the numerical approximation of the tempered fractional integral by using the Sinc-collocation scheme. The algorithm is extended to solve a class of tempered fractional differential equations that converges to the solution with exponential rate. Several numerical examples compare the numerical approximations with the exact solutions. The behavioral responses of the lumped capacitance model with tempered fractional order for transient conduction are investigated. The efficiency and accuracy of the proposed scheme are analyzed in the perspective of the L{sub 2}-norm error and convergence order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods

Here, this study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky’s procedure; however, the proposed approach allows for overlapped internal computations and, therefore, represents a generalization of the classical numerical schemes for solving differential equations with global error estimation. The resulting algorithms can be effectively represented as general linear methods. Finally, several explicit self-starting schemes akin to Runge–Kutta methods with global error estimation are introduced, and the theoretical considerations are illustrated in several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Computational capacity in hydrodynamic real-time hybrid simulation applied to simulate the dynamic response of floating offshore wind turbines

Real-time hybrid simulation (RTHS) mitigates similitude distortions in model-scale tests of floating offshore wind turbines (FOWTs) by coupling physical experiments with numerical models in real time. The coupling requires faster-than-real-time numerical computations to satisfy temporal similitude with the physical experiment, presenting a bottleneck for using more complex numerical models in RTHS. This paper presents a hydrodynamic-RTHS (hydro-RTHS) framework for FOWTs that simulates the hydrodynamics physically and the aerodynamics numerically with sensor feedback from the physical testing. The framework adapts the three-loop hardware architecture to leverage greater computational resources and mitigate strict temporal requirements, enabling more computationally demanding numerical analyses in hydro-RTHS. The three-loop hardware architecture integrates multiple machines, each dedicated to either numerical analysis or RTHS controls, with a rate-transition algorithm to synchronize the tasks executed across the different machine processors. Virtual and physical tests verified and validated the hydro-RTHS framework, respectively. The ”virtual” tests, which approximates the physical domain numerically, verified the RTHS framework with respect to a numerical full-scale complete FOWT model simulated in the open-source software, OpenFAST. The virtual tests were able to maintain comparable control signals while enabling greater computational resources for the numerical calculations. Real-world physical tests demonstrated that the hydro-RTHS framework computes aerodynamic forces similar to the complete OpenFAST model, validating the hydro-RTHS framework using the three-loop hardware architecture. Findings show that the hydro-RTHS framework with the three-loop hardware architecture is computationally efficient, with reserve capacity to simulate more complex problems due to the customized software, hardware, and rate-transition algorithm.

17 WIND ENERGY↗
DOE OSTI2013

Transport-constrained extensions of collision and track length estimators for solutions of radiative transport problems

In this paper we develop novel extensions of collision and track length estimators for the complete space-angle solutions of radiative transport problems. We derive the relevant equations, prove that our new estimators are unbiased, and compare their performance with that of more conventional estimators. Such comparisons based on numerical solutions of simple one dimensional slab problems indicate the the potential superiority of the new estimators for a wide variety of more general transport problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

BEYOND MIXING-LENGTH THEORY: A STEP TOWARD 321D

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier–Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier–Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear beyond the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier–Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Numerical methods for high-dimensional probability density function equations

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Pseudo-differential representation of the metaplectic transform and its application to fast algorithms

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping that is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function $ψ$ on an $N$-dimensional continuous space q , the MT of $ψ$ is parameterized by a rotation (or more generally, a linear symplectic transformation) of the 2$N$-dimensional phase space ( q,p ), where p is the wavevector space dual to q . In this study, we derive a pseudo-differential form of the MT. For small-angle rotations, or near-identity transformations of the phase space, it readily yields asymptotic differential representations of the MT, which are easy to compute numerically. Rotations by larger angles are implemented as successive applications of $K \gg 1$ small-angle MTs. The algorithm complexity scales as $O(KN^3N_p)$ where $N_p$ is the number of grid points. Here, we present a numerical implementation of this algorithm and discuss how to mitigate the associated numerical instabilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Xyce TM Parallel Electronic Simulator: Users’ Guide, Version 5.3

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: ■ Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). Note that this includes support for most popular parallel and serial computers. ■ Improved performance for all numerical kernels (e.g., time integrator, nonlinear and linear solvers) through state-of-the-art algorithms and novel techniques. ■ Device models which are specifically tailored to meet Sandia’s needs, including some radiation-aware devices (for Sandia users only). ■ Object-oriented code design and implementation using modern coding practices that ensure that the Xyce Parallel Electronic Simulator will be maintainable and extensible far into the future. Xyce is a parallel code in the most general sense of the phrase - a message passing parallel implementation - which allows it to run efficiently on the widest possible number of computing platforms. These include serial, shared-memory and distributed-memory parallel as well as heterogeneous platforms. Careful attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The development of Xyce provides a platform for computational research and development aimed specifically at the needs of the Laboratory. With Xyce, Sandia has an “in-house” capability with which both new electrical (e.g., device model development) and algorithmic (e.g., faster time-integration methods, parallel solver algorithms) research and development can be performed. As a result, Xyce is a unique electrical simulation capability, designed to meet the unique needs of the laboratory

42 ENGINEERING↗