A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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Results for “numerical mathematics”
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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Viterbi decoding of CRES signals in Project 8
Abstract Cyclotron radiation emission spectroscopy (CRES) is a modern approach for determining charged particle energies via high-precision frequency measurements of the emitted cyclotron radiation. For CRES experiments with gas within the fiducial volume, signal and noise dynamics can be modelled by a hidden Markov model. We introduce a novel application of the Viterbi algorithm in order to derive informational limits on the optimal detection of cyclotron radiation signals in this class of gas-filled CRES experiments, thereby providing concrete limits from which future reconstruction algorithms, as well as detector designs, can be constrained. The validity of the resultant decision rules is confirmed using both Monte Carlo and Project 8 data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
guppy i : a code for reducing the storage requirements of cosmological simulations
ABSTRACT As cosmological simulations have grown in size, the permanent storage requirements of their particle data have also grown. Even modest simulations present a major logistical challenge for the groups which run these boxes and researchers without access to high performance computing facilities often need to restrict their analysis to lower quality data. In this paper, we present guppy, a compression algorithm and code base tailored to reduce the sizes of dark matter-only cosmological simulations by approximately an order of magnitude. guppy is a ‘lossy’ algorithm, meaning that it injects a small amount of controlled and uncorrelated noise into particle properties. We perform extensive tests on the impact that this noise has on the internal structure of dark matter haloes, and identify conservative accuracy limits which ensure that compression has no practical impact on single-snapshot halo properties, profiles, and abundances. We also release functional prototype libraries in C, Python, and Go for reading and creating guppy data.
79 ASTRONOMY AND ASTROPHYSICS↗
Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code
A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01° was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1°, for which computation time is only increased by 2.2x.
50 EE - Wind and Water Power Program - Water (EE-4↗
Hierarchical model reduction driven by a proper orthogonal decomposition for parametrized advection-diffusion-reaction problems
This work combines the Hierarchical Model (HiMod) reduction technique with a standard Proper Orthogonal Decomposition (POD) to solve parametrized partial differential equations for the modeling of advection-diffusion-reaction phenomena in elongated domains (e.g., pipes). This combination leads to what we define as HiPOD model reduction, which merges the reliability of HiMod reduction with the computational efficiency of POD. Two HiPOD techniques are presented and assessed by an extensive numerical verification.
97 MATHEMATICS AND COMPUTING↗
Spiner: Performance Portable Routines for Generic, Tabulated, Multi-Dimensional Data
We present Spiner, a new, performance-portable library for working with tabulated data. Spiner provides efficient routines for multi-dimensional interpolation and indexing on both CPUs and GPUs—as well as more exotic hardware—including interwoven interpolation and indexing access patterns, as needed for radiation transport. Importantly, Spiner defines a data format, based on HDF5, that couples the tabulated data to the information required to interpolate it, which Spiner can read and move to GPU.
97 MATHEMATICS AND COMPUTING↗
Direct E&M Field Solver for a Plane Wave without Sources
A three dimensional direct field solver for the electric and magnetic fields using the Finite Difference Time Domain (FDTD) method is described. Example simulations using periodic and absorbing boundary conditions in a vacuum medium for a plane wave propagating in three dimensions are explored and are compared to theory.
97 MATHEMATICS AND COMPUTING↗
Classification of Orbits in Poincare Maps Using Machine Learning
Poincare plots, also called Poincare maps, are used by plasma physicists to understand the behavior of magnetically confined plasma in numerical simulations of a tokamak. These plots are created by the intersection of field lines with a two-dimensional poloidal plane that is perpendicular to the axis of the torus representing the tokamak. A plot is composed of multiple orbits, each created by a different field line as it goes around the torus. Each orbit can have one of four distinct shapes, or classes, that indicate changes in the topology of the magnetic fields confining the plasma. Given the (x, y) coordinates of the points that form an orbit, the analysis task is to assign a class to the orbit, a task that appears ideally suited for a machine learning approach. In this paper, we describe how we overcame two major challenges in solving this problem - creating a high-quality training set, with few mislabeled orbits, and converting the coordinates of the points into features that are discriminating, despite the variation within the orbits of a class and the apparent similarities between orbits of different classes. Our automated approach is not only more objective and accurate than visual classification, but is also less tedious, making it easier for plasma physicists to analyze the topology of magnetic fields from numerical simulations of the tokamak.
97 MATHEMATICS AND COMPUTING↗
Remapping between meshes with isoparametric cells: a case study
We explore an intersection-based remap method between meshes consisting of isoparametric elements. We present algorithms for the case of serendipity isoparametric elements (QUAD8 elements) and piece-wise constant (cell-centered) discrete fields. We demonstrate convergence properties of this remap method with a few numerical experiments.
97 MATHEMATICS AND COMPUTING↗
A nonsmooth nonconvex optimization algorithm for two-stage optimization problems
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.
97 MATHEMATICS AND COMPUTING↗
Review of WEC-Sim development and applications
WEC-Sim (Wave Energy Converter Simulator) is an open-source code for simulating wave energy converters, which has been actively developed and applied to simulate a wide variety of device archetypes, and has become a popular tool since its release. This paper reviewed the development efforts and the usage of WEC-Sim. The publications considered in this study have been broken down into six topic areas, namely feature development, experimental validation, device modeling, control modeling, PTO and grid modeling, and novel applications, which even includes some non-wave energy applications. This review paper has also attempted to recognize the contributions of the broader WEC-Sim development effort, meaning not only the internal WEC-Sim development team but also the external efforts from the academia researchers and technology developers around the world. The growing trend of external applications of WEC-Sim has demonstrated the broader acceptance of the open-source code, and how WEC-Sim has been used in a certain topic area also highlights the potential future development needs.
16 TIDAL AND WAVE POWER↗
Modern methods and problems of numerical weather forecasting
Numerical analysis in weather forecasting
MATHEMATICS↗
Lunar ash flows - Isothermal approximation.
Suggestion of the ash flow mechanism as one of the major processes required to account for some features of lunar soil. First the observational background and the gardening hypothesis are reviewed, and the shortcomings of the gardening hypothesis are shown. Then a general description of the lunar ash flow is given, and a simple mathematical model of the isothermal lunar ash flow is worked out with numerical examples to show the differences between the lunar and the terrestrial ash flow. The important parameters of the ash flow process are isolated and analyzed. It appears that the lunar surface layer in the maria is not a residual mantle rock (regolith) but a series of ash flows due, at least in part, to great meteorite impacts. The possibility of a volcanic contribution is not excluded. Some further analytic research on lunar ash flows is recommended.
Pai, S. I.↗
A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory
The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.
Austin, F.↗
Control optimization, stabilization and computer algorithms for aircraft applications
Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.
Source record↗
Numerical study of supersonic turbulent flow over small protuberances
Supersonic turbulent boundary layers over two-dimensional protuberances are investigated, using the numerical finite difference alternating direction implicit (ADI) method. The turbulence is modeled mathematically. The turbulence is represented here by the eddy viscosity approach. The turbulent boundary layer structure as well as an interest in thick boundary layers and much larger protuberance heights than in the laminar case lead to new difficulties. The problems encountered and the means to remove them are discussed.
Polak, A.↗
A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface
A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.
Buglia, J. J.↗