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At least 1,513 records · Page 84

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NASA NTRS2020

Object-Based Comparison of Data-Driven and Physics-Driven Satellite Estimates of Extreme Rainfall

The Global Precipitation Measurement (GPM) constellation of spaceborne sensors provides a variety of direct and indirect measurements of precipitation processes. Such observations can be employed to derive spatially and temporally consistent gridded precipitation estimates either via data-driven retrieval algorithms or by assimilation into physically based numerical weather models. We compare the data-driven Integrated Multisatellite Retrievals for GPM (IMERG) and the assimilation-enabled NASA-Unified Weather Research and Forecasting (NU-WRF) model against Stage IV reference precipitation for four major extreme rainfall events in the southeastern United States using an object-based analysis framework that decomposes gridded precipitation fields into storm objects. As an alternative to conventional ‘‘grid-by-grid analysis,’’ the object-based approach provides a promising way to diagnose spatial properties of storms, trace them through space and time, and connect their accuracy to storm types and input data sources. The evolution of two tropical cyclones are generally captured by IMERG and NU-WRF, while the less organized spatial patterns of two mesoscale convective systems pose challenges for both. NU-WRF rain rates are generally more accurate, while IMERG better captures storm location and shape. Both show higher skill in detecting large, intense storms compared to smaller, weaker storms. IMERG’s accuracy depends on the input microwave and infrared data sources; NU-WRF does not appear to exhibit this dependence. Findings highlight that an object-oriented view can provide deeper insights into satellite precipitation performance and that the satellite precipitation community should further explore the potential for ‘‘hybrid’’ data-driven and physics-driven estimates in order to make optimal usage of satellite observations.

extreme events↗

DOE OSTI2020

TriC: Distributed-memory Triangle Counting by Exploiting the Graph Structure

Graph analytics has emerged as an important tool in the analysis of large scale data from diverse application domains such as social networks, cyber security and bioinformatics. Counting the number of triangles in a graph is a fundamental kernel with several applications such as detecting the community structure of a graph or in identifying important vertices in a graph. The ubiquity of massive datasets is driving the need to scale graph analytics on parallel systems. However, numerous challenges exist in efficiently parallelizing graph algorithms, especially on distributed-memory systems. Irregular memory accesses and communication patterns, low computation to communication ratios, and the need for frequent synchronization are some of the leading challenges. In this paper, we present TriC, our distributed-memory implementation of triangle counting in graphs using the Message Passing Interface (MPI), as a submission to the 2020 GraphChallenge competition. Using a set of synthetic and real-world inputs from the challenge, we demonstrate a speedup of up to 90x relative to previous work on 32 processor-cores of a NERSC Cori node. We also provide details from distributed runs with up to8192 processes along with strong scaling results. The observations presented in this work provide an understanding of the system-level bottlenecks at scale that specifically impact sparse-irregular workloads and will therefore benefit other efforts to parallelize graph algorithms.

Halappanavar, Mahantesh↗

DOE OSTI2026

QuadSync: Quadrifocal tensor synchronization via Tucker decomposition

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Miao, Daniel [University of Minnesota]↗

NASA NTRS1971

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.↗

NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗

DOE OSTI2020

A parallel hierarchical blocked adaptive cross approximation algorithm

This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Algorithm for in-flight gyroscope calibration

An optimal algorithm for the in-flight calibration of spacecraft gyroscope systems is presented. Special consideration is given to the selection of the loss function weight matrix in situations in which the spacecraft attitude sensors provide significantly more accurate information in pitch and yaw than in roll, such as will be the case in the Hubble Space Telescope mission. The results of numerical tests that verify the accuracy of the algorithm are discussed.

Davenport, P. B.↗

NASA NTRS1994

Computationally efficient multibody simulations

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

Ramakrishnan, Jayant↗

NASA NTRS1993

Feedback control for unsteady flow and its application to the stochastic Burgers equation

The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.

Choi, Haecheon↗

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 OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2019

Thermal Property Estimation of Fibrous Insulation: Heat Transfer Modeling and the Continuous Genetic Algorithm

Thermal properties of high-temperature fibrous insulation materials were estimated from transient thermal tests using an inverse heat transfer technique. Transient temperature data from an experimental set up was collected and a simple, one-dimensional numerical model was constructed to replicate the temperatures within the test assembly. The Continuous Genetic Algorithm optimization technique in conjunction with a numerical thermal model and transient test data was used to estimate coefficients of a functional representation of the thermal property. The thermal properties, i.e., thermal conductivity and specific heat, of an alumina insulation felt were estimated over the temperature range of 300 K to 1700 K at various constant static pressures in nitrogen gas and compared with published data. The resulting thermal property estimates were within 10% of published values over the entire temperature range at various pressures. The methodology, application, and results are presented.

Frye, Elora↗

NASA NTRS1996

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗

NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. The paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third-order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation is quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows, Kristine R.↗

NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. This paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation in quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows,, Kristine r.↗

DOE OSTI2022

Testing and Expertise for Marine Energy (TEAMER) Program Support - Numerical Modeling Assistance for iProTech's "PIP" WEC Device: Cooperative Research and Development Final Report, CRADA Number CRD-20-17303

Develop a time-domain, 3 degree of freedom numerical model of IProTech's PIP device, including power take-off (PTO), that can be used to develop control algorithms and establish a baseline technology performance level (TPL). This is important to IProTech because having a good numerical model allows IProTech to optimize design and control algorithms on an ongoing basis. A baseline TPL enables the PIP technology to be benchmarked against other wave energy converter (WEC) concepts, providing (i) justification (or not) for investment in wave tank model testing, (ii) identifying optimum design parameters and control algorithms for the test model, (iii) specifying test conditions and (iv) interpreting wave tank test results. An accredited WEC-Sim model of the PIP device is an essential tool for further development of the technology. 1) The development of numerical models of the PIP concept will enable iProTech to evaluate the potential performance of this concept, and to investigate how sensitive the device is to different variables within the system (e.g. hydraulic components, geometry dimensions, etc.) 2) The numerical models were developed with WEC-Sim and PTO-Sim -- the de-facto industry standard WEC numerical modeling tools. A detailed model of the system's hydraulic circuit was developed with PTO-Sim. However, WEC-Sim is based on linear hydrodynamics and has several limitations; validation against high fidelity models/physical scale models would help to build confidence in the results.

16 TIDAL AND WAVE POWER↗

NASA NTRS1996

Homotopy Algorithm for Fixed Order Mixed H2/H(infinity) Design

Recent developments in the field of robust multivariable control have merged the theories of H-infinity and H-2 control. This mixed H-2/H-infinity compensator formulation allows design for nominal performance by H-2 norm minimization while guaranteeing robust stability to unstructured uncertainties by constraining the H-infinity norm. A key difficulty associated with mixed H-2/H-infinity compensation is compensator synthesis. A homotopy algorithm is presented for synthesis of fixed order mixed H-2/H-infinity compensators. Numerical results are presented for a four disk flexible structure to evaluate the efficiency of the algorithm.

Whorton, Mark↗

DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗