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All sources NASA NTRS DOE OSTI

DOE OSTI2022

A second-order distributed memory parallel fast sweeping method for the Eikonal equation

The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. In this work, we present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Exact signed distance fields using parallel Fast Sweeping Method

Signed distance fields are often used in multiphysics simulations to track material interfaces. We present a simple methodology based on the fast sweeping method to generate the exact signed distance from triangular meshes and linear paths on Cartesian grids. The methodology propagates the closest primitive to the boundary to the rest of the domain following the characteristics. A local upwind criterion is used to decide between the new and existing closest primitive at each grid point while capturing the correct sign of the global function. The methodology has optimal computational complexity and runs efficiently in distributed-memory architectures. We include 2D and 3D test cases along with a resolution study up to 0.512 trillion zones and 1,000 computer cores. The solution strategy can also be applied to other types of meshes or collections of primitives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. In conclusion, scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1966

The potential-sweep method - A theoretical analysis.

Potential sweep method for organic and adsorption analyses, showing relation between galvanostatic and fast potential sweep transients, noting mathematical analysis of current-potential transients

ELECTROCHEMISTRY↗

NASA NTRS1985

Noise constraints effecting optimal propeller designs

A preliminary design tool for advanced propellers was developed combining a fast vortex lattice aerodynamic analysis, a fast subsonic point source noise analysis, and an optimization scheme using a conjugate directions method. Twist, chord and sweep distributions are optimized to simultaneously improve both the aerodynamic performance and the noise observed at a fixed relative position. The optimal noise/performance tradeoffs for straight and advanced concept blades are presented. The techniques used include increasing the blade number, blade sweep, reducing the rotational speed, shifting the spanwise loading and diameter changes.

Miller, C. J.↗

NASA NTRS1985

Noise constraints effecting optimal propeller designs

Miller, C. J.↗

NASA NTRS1984

Special Test Methods for Batteries

Various methods are described for measuring heat generation in primary and secondary batteries as well as the specific heat of batteries and cell thermal conductance. Problems associated with determining heat generation in large batteries are examined. Special attention is given to monitoring temperature gradients in nickel cadmium cells, the use of auxiliary electrodes for conducting tests on battery charge control, evaluating the linear sweep of current from charge to discharge, and determining zero current voltage. The fast transient behavior of batteries in the microsecond range, and the electrical conductance of nickel sinters in the thickness direction are also considered. Mechanical problems experienced in the vibration of Ni-Cd batteries and tests to simulate cyclic fatigue of the steel table connecting the plates to the comb are considered. Methods of defining the distribution of forces when cells are compressed during battery packaging are also explored.

Gross, S.↗

DOE OSTI2026

Low-Field EMR Studies of Permalloy Films and Gratings

Flat and profile-modulated permalloy films have been studied by the electron magnetic resonance (EMR) method. In addition to ferromagnetic and spin-wave resonances, the structures demonstrate low-field EMR signals of an unusual shape, which form a hysteresis loop in sweeping fields. The low-field signals are attributed to a fast reorientation of magnetic domains. The low-field EMR behavior is comparable to the behavior in magneto-dependent photovoltage previously observed in the optical experiments. The shapes of the loops and typical values of the switching fields depend on the profile modulation parameters confirming the possibility of controlling magnetic properties and the coupling of magnetic and optical effects with nanoscale geometry.

36 MATERIALS SCIENCE↗

NASA NTRS1979

Multi-level adaptive finite element methods. 1: Variation problems

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Brandt, A.↗

NASA NTRS1986

Drag-reduction characteristics of aft-swept wing tips

Results are presented of a study conducted to analyze the potential aerodynamic improvements which can be obtained with aft-swept wing tips at subsonic speeds. A review and summary of previous swept-tip applications and studies are given. Additionally, the through evolution optimized tail-fin shapes of fast-cruising aquatic animals are examined as well as the wing planform shapes of sea birds. These superior long-distance travellers both display lifting-surface planform shapes with increased leading-edge sweep towards the tip. These observations and analytical results obtained with a nonlinear surface-panel method demonstrate that substantial induced-drag improvements can be obtained through the adoption of planform shapes with highly-tapered aft-swept tips.

Van Dam, C. P.↗

NASA NTRS1990

Novel laser gain and time-resolved FTIR studies of photochemistry

Several techniques are discussed which can be used to explore laboratory photochemical processes and kinetics relevant to planetary atmospheres; these include time-resolved laser gain-versus-absorption spectroscopy and time-resolved Fourier transform infrared (FTIR) emission studies. The laser gain-versus-absorption method employed tunable diode and F-center lasers to determine the yields of excited photofragments and their kinetics. The time-resolved FTIR technique synchronizes the sweep of a commercial FTIR with a pulsed source of light to obtain emission spectra of novel transient species in the infrared. These methods are presently being employed to investigate molecular photodissociation, the yields of excited states of fragments, their subsequent reaction kinetics, Doppler velocity distributions, and velocity-changing collisions of translationally fast atoms. Such techniques may be employed in future investigations of planetary atmospheres, for example to study polycyclic aromatic hydrocarbons related to cometary emissions, to analyze acetylene decomposition products and reactions, and to determine spectral features in the near infrared and infrared wavelength regions for planetary molecules and clusters.

Leone, Stephen R.↗

NASA NTRS1990

Implicit methods for the Navier-Stokes equations

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Yoon, S.↗

DOE OSTI2022

Fast yaw optimization for wind plant wake steering using Boolean yaw angles

Abstract. In wind plants, turbines can be yawed into the wind to steer their wakes away from downstream turbines and achieve an overall increase in plant power. Mathematical optimization is typically used to determine the best yaw angles at which to operate the turbines in a plant. In this paper, we present a new heuristic to rapidly determine the yaw angles in a wind plant. In this method, we define the turbine yaw angles as Boolean – either yawed at a predefined angle or nonyawed – as opposed to the typical methods of defining yaw angles as continuous or with fine discretizations. We then optimize which turbines should be yawed with an algorithm that sweeps through the turbines from the most upstream to the most downstream. We demonstrate that our new Boolean optimization method can find turbine yaw angles that perform well compared to a traditionally used gradient-based optimizer for which the yaw angles are defined as continuous. There is less than 0.6 % difference in the optimized power between the two optimization methods for randomly placed turbine layouts and less than a 0.6 % difference in the optimal annual energy production between the two optimization methods for a real wind farm. Additionally, we show that our new method is much more computationally efficient than the traditional method. For plants with nonzero optimal yaw angles, our new method is generally able to solve for the turbine yaw angles 50–150 times faster, and in some extreme cases up to 500 times faster, than the traditional method.

17 WIND ENERGY↗

NASA NTRS1980

Data acquisition techniques for exploiting the uniqueness of the time-of-flight mass spectrometer: Application to sampling pulsed gas systems

Mass spectra are produced in most mass spectrometers by sweeping some parameter within the instrument as the sampled gases flow into the ion source. It is evident that any fluctuation in the gas during the sweep (mass scan) of the instrument causes the output spectrum to be skewed in its mass peak intensities. The time of flight mass spectrometer (TOFMS) with its fast, repetitive mode of operation produces spectra without skewing or varying instrument parameters and because all ion species are ejected from the ion source simultaneously, the spectra are inherently not skewed despite rapidly changing gas pressure or composition in the source. Methods of exploiting this feature by utilizing fast digital data acquisition systems, such as transient recorders and signal averagers which are commercially available are described. Applications of this technique are presented including TOFMS sampling of vapors produced by both pulsed and continuous laser heating of materials.

Lincoln, K. A.↗

DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Plane waves and structures in turbulent channel flow

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

Sirovich, L.↗