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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue Computation

The central importance of large scale eigenvalue problems in scientific computation necessitates the development massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing excessive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions which will be explored in future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Quantum transport modelling of silicon nanobeams using heterogeneous computing scheme

We report the development of a powerful method for quantum transport calculations of nanowire/nanobeam structures with large cross sectional area. Our approach to quantum transport is based on Green's functions and tight-binding potentials. A linear algebraic formulation allows us to harness the massively parallel nature of Graphics Processing Units (GPUs) and our implementation is based on a heterogeneous parallel computing scheme with traditional processors and GPUs working together. Using our software tool, the electronic and quantum transport properties of silicon nanobeams with a realistic cross sectional area of ∼22.7 nm{sup 2} and a length of ∼81.5 nm—comprising 105 000 Si atoms and 24 000 passivating H atoms in the scattering region—are investigated. The method also allows us to perform significant averaging over impurity configurations—all possible configurations were considered in the case of single impurities. Finally, the effect of the position and number of vacancy defects on the transport properties was considered. It is found that the configurations with the vacancies lying closer to the local density of states (LDOS) maxima have lower transmission functions than the configurations with the vacancies located at LDOS minima or far away from LDOS maxima, suggesting both a qualitative method to tune or estimate optimal impurity configurations as well as a physical picture that accounts for device variability. Finally, we provide performance benchmarks for structures as large as ∼42.5 nm{sup 2} cross section and ∼81.5 nm length.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Evaporative thermal resistance and its influence on microlayer evaporation

The ability to predict various aspects of boiling is important for both safety and design of water-cooled reactors. Component-scale modelling is necessarily done by semi-mechanistic, semi-empirical approaches, generally based on heat flux partitioning. This needs to be informed by multiple detailed experimental observations of boiling behavior. Such measurements are difficult to make, and much effort is being applied to microscopic computational modelling of the detailed boiling process. Aims of such activities include the mechanistic prediction of growth and detachment of one bubble during nucleate boiling, and the quantification of the associated heat transfer partitioning (evaporation, micro-convection, quenching). We here study a subset of the full problem, and focus on the thermal response of the boiling substrate to the early growth of a single vapour bubble during pool boiling of water at atmospheric pressure. In such conditions, a thin liquid film ('microlayer') is left behind beneath the bubble as this expands. The microlayer evaporates due to the temperature difference between the solid-liquid and vapour-liquid interface. Its thickness being small, of order of microns, the local evaporation rate per unit area of bubble base can be high, up to one kilogram per second. Microlayer evaporation can therefore be important in early stages of bubble growth. In this contribution, thermal response of the boiling substrate to microlayer evaporation is studied with a two-dimensional, axisymmetric transient conduction model, coupled with an algebraic sub-model of the liquid film. The flow of heat through the microlayer is modelled as conduction in the liquid and with a pseudo-convective 'evaporative' heat transfer coefficient at the liquid-vapor interface, accounting for the interface superheat driving the evaporation process. Thermal coupling (conjugate heat transfer) between microlayer and solid substrate is obtained with a time dependent non-homogeneous Neumann boundary condition, derived from the algebraic microlayer sub-model and applied at the top surface of the solid computational domain. The thermal resistance associated to the evaporative heat transfer mechanism is shown to depend on a highly uncertain parameter, termed an 'evaporation coefficient'. After some exploratory calculations of the likely importance of the evaporative resistance in the present context, the model is employed to interpret some recent microlayer measurements. Satisfactory agreement between computed and measured evolution of the microlayer profile is obtained if small values (between 0.01 and 0.10) of the evaporation coefficient are used. The order of magnitude of the predicted evaporation rate from the microlayer is consistent with experimental observations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Cyclotomic Shuffles

Analogues of 1-shuffle elements for complex reflection groups of type G(m,1,n) are introduced. A geometric interpretation for G(m,1,n) in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group G(m,1,n). Considering shuffling as a random walk on the group G(m,1,n), we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra H(m,1,n) for m=2 and small n.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Para-particle oscillator simulations on a trapped-ion quantum computer

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles remain hypothetical and unobserved in nature; yet, they can model physical phenomena, such as topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allows us to identify the para-particle oscillator Hamiltonian as an XY model and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Topology for Statistical Modeling of Petascale Data

Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A multiscale two-point flux-approximation method

A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely on a compatible primal–dual coarse partition, which makes it challenging to extend them to stratigraphic and unstructured grids. Herein, we propose a general idea for how one can formulate multiscale finite-volume methods using only a primal coarse partition. To this end, we use two key ingredients that are computed numerically: (i) elementary functions that correspond to flow solutions used in transmissibility upscaling, and (ii) partition-of-unity functions used to combine elementary functions into basis functions. We exemplify the idea by deriving a multiscale two-point flux-approximation (MsTPFA) method, which is robust with regards to strong heterogeneities in the permeability field and can easily handle general grids with unstructured fine- and coarse-scale connections. The method can easily be adapted to arbitrary levels of coarsening, and can be used both as a standalone solver and as a preconditioner. Several numerical experiments are presented to demonstrate that the MsTPFA method can be used to solve elliptic pressure problems on a wide variety of geological models in a robust and efficient manner.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Complex-plane generalization of scalar Levin transforms: A robust, rapidly convergent method to compute potentials and fields in multi-layered media

We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the method of weighted averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier–Hankel (F–H) integral transforms. This “complex-plane” MWA, effected via a linear-path detour in the complex plane, results in rapid, absolute convergence of field and potential solutions in multi-layered environments regardless of the source-observer geometry and anisotropy/loss of the media present. In this work, we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra. Subsequently, we (1) exhibit the foundational relations behind the complex-plane extension to a general Levin-type sequence convergence accelerator, (2) specialize this analysis to one member of the Levin transform family (the MWA), (3) address and circumvent restrictions, arising for two-dimensional integrals associated with wave dynamics problems, through minimal complex-plane detour restrictions and a novel partition of the integration domain, (4) develop and compare two formulations based on standard/real-axis MWA variants, and (5) present validation results and convergence characteristics for one of these two formulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Solvability of a Matrix Boundary-Value Problem

We found solvability conditions and a construction of the generalized Green operator for a linear matrix boundary-value problem; we present an operator that reduces a linear matrix equation to the conventional linear Noether boundary-value problem. To solve a linear matrix system, we use the operator that reduces a linear matrix equation to a linear algebraic equation with a rectangular matrix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On volumes of classical supermanifolds

We consider the volumes of classical supermanifolds (such as the supersphere, complex projective superspace, Stiefel and Grassmann supermanifolds) with respect to natural metrics or symplectic structures. We show that the formulae for the volumes of these supermanifolds can be obtained from the formulae for the volumes of the corresponding ordinary manifolds (under some universal normalization of the volume) by analytic continuation with respect to parameters. The volumes of nontrivial supermanifolds may be identically equal to zero. In the 1970s Berezin showed that the total Haar measure of the unitary supergroup U(n|m) vanishes except in the cases m=0 and n=0, when the supergroup is the ordinary unitary group U(n) or U(m). Some time ago Witten conjectured that the Liouville volume of a compact even symplectic supermanifold is always equal to zero (except for ordinary manifolds). We give counterexamples to this conjecture, present a simple explanation of Berezin's theorem, and generalize this theorem to the Stiefel supermanifold V{sub r|s}(C{sup n|m}). We mention a connection with recent work of Mkrtchyan and Veselov on universal formulae in Lie algebra theory. Bibliography: 32 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Accurate Numerical Simulations Of Chemical Phenomena Involved in Energy Production and Storage with MADNESS and MPQC: ALCF-2 Early Science Program Technical Report

In order to solve the electronic structure of large molecular systems on petascale computers using MADNESS, a numerical tool kit, are required fast and accurate implementations for linear algebra. MADNESS uses multiresolution analysis and low separation rank which translates high dimensional functions in tensor products using Legendre polynomial. The multiple tensor products make to the singular value decomposition and matrix multiplication the most intense operations in MADNESS. This work discusses the interfacing of Eigen3 as a C++ substitute of LAPACK and introduces Elemental for the diagonalization of large matrices. Furthermore, the present paper shows the performance these libraries on Blue Gene/ Q.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world’s largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including a real utility network, show good scalability on different computing architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

The Coulomb, exchange, and correlation components of the electron-electron repulsion in harmonium atoms

Highly accurate Coulomb, exchange, and correlation components of the electron-electron repulsion energies of the three-electron harmonium atoms in the {sup 2}P{sub −} and {sup 4}P{sub +} states are obtained for 19 values of the confinement strength ω ranging from 10{sup −3} to 10{sup 3}. The computed data are consistent with their ω → 0 and ω → ∞ asymptotics that are given by closed-form algebraic expressions. Robust approximants that accurately reproduce the actual values of the energy components while strictly conforming to these limits are constructed, opening an avenue to stringent tests capable of predicting the performance of electronic structure methods for systems with varying extents of the dynamical and nondynamical electron correlation. The values of the correlation components, paired with the computed 1-matrices are expected to be particularly useful in the context of benchmarking of approximate density matrix functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Chiral algebras, localization and surface defects

Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗