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At least 451 records · Page 25

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DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

A geometric modeler based on a dual-geometry representation polyhedra and rational b-splines

For speed and data base reasons, solid geometric modeling of large complex practical systems is usually approximated by a polyhedra representation. Precise parametric surface and implicit algebraic modelers are available but it is not yet practical to model the same level of system complexity with these precise modelers. In response to this contrast the GEOMOD geometric modeling system was built so that a polyhedra abstraction of the geometry would be available for interactive modeling without losing the precise definition of the geometry. Part of the reason that polyhedra modelers are effective is that all bounded surfaces can be represented in a single canonical format (i.e., sets of planar polygons). This permits a very simple and compact data structure. Nonuniform rational B-splines are currently the best representation to describe a very large class of geometry precisely with one canonical format. The specific capabilities of the modeler are described.

Klosterman, A. L.↗

DOE OSTI2025

Closed-form expressions for unitaries of spin-adapted fermionic operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

fermionic algebra↗

NASA NTRS1986

Transverse acceleration of oxygen ions by electromagnetic ion cyclotron resonance with broad band left-hand polarized waves

Central plasma sheet (CPS) ion conics are oxygen-dominated, with peak energies ranging from tens to hundreds of eV centered around pitch-angles between 115 and 130 degrees. Because of the lack of correlation between the CPS conics and the observed currents and/or electron beam-like structures, it is not likely that all of these conics are generated by interactions with electrostatic ion cyclotron waves or lower hybrid waves. Instead, it is suggested that the observed intense broad band electric field fluctuations in the frequency range between 0 and 100 Hz can be responsible for the transverse energization of the ions through cyclotron resonance heating with the left-hand polarized electromagnetic waves. This process is much more efficient for heating the oxygen ions than hydrogen ions, thus providing a plausible explanation of the oxygen dominance in CPS conics. Simple algebraic expressions are given from which estimates of conic energy and pitch angle can be easily calculated. This suggested mechanism can also provide some preheating of the oxygen ions in the boundary plasma sheet (BPS) where discrete aurorae form.

Chang, T.↗

DOE OSTI2021

QLiG: Query Like a Graph For Subgraph Matching

A graph is a natural and flexible modeling approach to represent entities and relationships between them in real-world. A Knowledge Graphs (KG) is a specialized graph with formal and structured representation of facts, relationships, annotated with semantic descriptions. Subgraph matching is one of the fundamental graph problems to identify relationships, interactions and activities of interest within a large graph. A query specification is a collection of abstract components, operations, and constraints to express a pattern. The specification can be implemented in different ways based on underlying data model. Various graph query specifications have been developed over the years and have led to the development of different open-sourced and vendor-specific query languages. Such specification are modeled as an extension of relational algebra used to develop relational query languages such as SQL. Such relational concepts do not inherently support graph queries. There is a need to represent graph queries in terms on graph-based components to expedite query construction by non-database experts. We present a graph-based query approach QLiG (pronounced cleeg), to perform subgraph matching in Labeled Property Graph. We present the query specifications, salient features, and a use case to show functional examples.

Purohit, Sumit↗

NASA NTRS1988

Three dimensional flow simulation with application to aeroelastic analysis

The three-dimensional flowfield about realistic launch vehicle configurations is simulated using the Reynolds-averaged Navier-Stokes equations. Turbulent mixing is accounted for by means of the two-layer Baldwin and Lomax (1978) algebraic eddy viscosity model. The Beam and Warming (1976) implicit approximate factorization algorithm is used for the solution of the finite difference equations. Applications include the study of the flowfield about a hemisphere-cylinder configuration both in the subsonic and supersonic flight regimes, and about two hammerhead payload configurations at transonic speeds. A method is also described which permits incorporating this flow solver into a complete algorithm to perform time-domain aeroelastic stability analyses. The vehicle is modeled as a free-free beam and modal superposition techniques are used for the structural-dynamic formulation. Aeroelastic analyses were performed for the hammerhead configurations.

Azevedo, Joao Luiz F.↗

NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗

NASA NTRS1995

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Vadyak, Joseph↗

DOE OSTI2022

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗

NASA NTRS1989

Mixed formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

NASA NTRS1984

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗

NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗

NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗

DOE OSTI2023

Tomographic optical emission spectroscopy of atmospheric pressure plasma interacting with complex surfaces

Plasma distribution in 3D space is heavily influenced by complex surfaces and the coupling interactions between plasma properties and interfacing material properties. For example, guided streamers that transition to surface ionization waves (SIWs) and propagate over structured dielectrics experience field enhancements that can lead to localized increases in ionization rates and complex 3D configurations that are difficult to analyze. Investigating these configurations requires techniques than can provide a more complete 3D picture. To help address this capability gap, a tomographic optical emission spectroscopy (tomo-OES) diagnostic system has been developed at Sandia National Laboratories that can resolve SIWs. The system includes four intensified cameras that measure the angular projections of the plasma light emission through bandpass filters. A dot calibration target co-registers each angular projection to the same voxel grid and an algebraic reconstruction technique (ART) recovers the light intensity at each voxel. An atmospheric pressure plasma jet (APPJ), provided by Peter Bruggeman, has been investigated and representative results are shown in Figure 1. Here, a bandpass filter was used to isolate emission from the N 2 second positive system (SPS) at 337.1 nm to capture the transition of the streamer to SIW on a planar dielectric surface (relative permittivity 3.3) located 3 mm below the APPJ [3]. The surface wave velocity was 3.5x10 4 (m/s), consistent with measurements made by Steven Shannon. Characterization of this APPJ will support the group effort of standing up a reproducible APPJ across institutions for applications such as liquid treatment, catalysis, and plasma aided combustion. Future work will investigate non-planar surfaces and eventually develop tomographic laser-induced fluorescence (tomo-LIF) approaches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1992

Viscous three-dimensional calculations of transonic fan performance

A 3-D flow analysis code was used to compute the design speed operating line of a transonic fan rotor, and the results were compared with experimental data. The code is an explicit finite difference code with an algebraic turbulence model. The transonic fan, called Rotor 67, was tested experimentally at NASA Lewis conventional aerodynamic probes and with user anemometry and was included as one of the AGARD test cases for the computation of internal flows. The experimental data are described. Maps of total pressure ratio and adiabatic efficiency vs mass flow were computed and are compared with the experimental maps, with good agreement. Detailed comparisons between calculations and experiment are made at two operating points, one near peak efficiency and the other near stall. Blade-to-blade contour plots are used to show the shock structure. Comparisons of circumferentially integrated flow quantities downstream of the rotor show spanwise distributions of several aerodynamic parameters. Calculated Mach number distributions are compared with laser anemometer data within the blade row and the wake to quantify the accuracy of the calculations. Particle traces are used to show the nature of secondary flow.

Chima, Rodrick V.↗

NASA NTRS2000

The Use of Vegetation For Estimating Broken-Cloud Optical Properties From Surface Measurements

It is known that because of complex three-dimensional (3D) radiative effects of broken clouds, the retrieval of cloud optical properties from upward measurements based on a one-dimensional (1D) inversion technique almost surely fails. To remove radiative effects of 3D cloud structure, we have developed a new technique that retrieves cloud optical thickness for broken clouds above green vegetation from simultaneous surface measurements in the VIS and Near Infrared (NIR) spectral regions. The theoretical basis of the method is the very different spectral behavior of cloud liquid water drops and green vegetation. For example, cloud optical properties, and hence cloud reflectivities, change little between 650 and 860 nm, while the vegetated surface albedo changes from 0.05 to 0.5 between the same two wavelengths. This spectral contrast in surface albedo suggests using ground measurements at both wavelengths not independently, but as an algebraic combination (a spectral index). For a spectral band in the NIR region, the green vegetation acts as a powerful reflector that "illuminates" horizontally inhomogeneous clouds from below. This provides the extra information needed to largely remove the 3D radiative effects, especially in the case of broken clouds; this in turn allows the retrieval of cloud optical depth using traditional 1D radiative transfer theory. This approach is similar to the so-called Green's function problem for radiative transfer where a laser beam illuminates clouds and the resulting "spot-size" of the reflected light around the beam characterizes cloud properties. We generalize Green's function theory to surf ace-cloud interaction and develop new spectral indices from which broken-cloud optical depth can be retrieved.

Marshak, A.↗

DOE OSTI2021

Single-Molecule Kinetics of Styrene Hydrogenation on Silica-Supported Vanadium: The Role of Disorder for Single-Atom Catalysts

We report a theoretical approach for the study of supported atom catalysis is developed based on recent advances in the study of single-molecule kinetics. This view is particularly useful in exhibiting the role of disorder in single-atom and single-site catalysts on amorphous supports. The distribution of passage times (or waiting times) through a complex catalytic network originating from a set of coupled active sites is described by a probability distribution function (PDF), f(t), that reflects the local environment of the reaction center. An efficient algorithm is developed based on the linear algebra of the Markov transition matrix that produces f(t) or its moments. The kinetics of the hydrogenation reaction of styrene on an organovanadium(III) catalyst supported on amorphous silica is studied. A kinetic model consisting of three intertwined catalytic cycles emanating from three chemically distinct active sites is proposed to describe the chemistry. Density functional theory (DFT) calculations are employed to determine the free energy barriers of the reactions, which are used to construct the rate coefficient matrix. The disorder induced by the amorphous support material is divided into a low-dimensional short-range component reflecting the covalent structures near the reaction center and a weaker long-range component modeling the bulk randomness. The results are computed and analyzed for a wide range of concentration values and disorder scenarios. The unusual structure in the f(t) PDF is found to occur for certain cases that reveal the contribution of multiple catalytic pathways acting in concert.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗