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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

FORTRAN subroutines for out-of-core solutions of large complex linear systems

The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.

Yip, E. L.↗
NASA NTRS1991

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

Park, K. C.↗
NASA NTRS1995

Nonlinear structural analysis on distributed-memory computers

A computational strategy is presented for the nonlinear static and postbuckling analyses of large complex structures on massively parallel computers. The strategy is designed for distributed-memory, message-passing parallel computer systems. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a nested dissection (or multilevel substructuring) ordering scheme; (3) parallel assembly of global matrices; and (4) a parallel sparse equation solver. The effectiveness of the strategy is assessed by applying it to thermo-mechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of HSCT models on Intel Paragon XP/S computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed memory machines.

Watson, Brian C.↗
NASA NTRS1995

Postbuckling and large-deflection nonlinear analyses on distributed-memory computers

A computational strategy is presented for postbuckling and nonlinear static analyses of large complex structures on distributed-memory parallel computers. The strategy is designed for message-passing parallel computer systems. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a nested dissection (or multilevel substructuring) ordering scheme; (3) parallel assembly of global matrices; and (4) a parallel sparse equation solver. The effectiveness of the strategy is assessed by performing thermomechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of High Speed Civil Transport models on three distributed-memory computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed-memory machines.

Watson, Brian C.↗
NASA NTRS2010

The OMPS Limb Profiler Instrument: Two-Dimensional Retrieval Algorithm

The upcoming Ozone Mapper and Profiler Suite (OMPS), which will be launched on the NPOESS Preparatory Project (NPP) platform in early 2011, will continue monitoring the global distribution of the Earth's middle atmosphere ozone and aerosol. OMPS is composed of three instruments, namely the Total Column Mapper (heritage: TOMS, OMI), the Nadir Profiler (heritage: SBUV) and the Limb Profiler (heritage: SOLSE/LORE, OSIRIS, SCIAMACHY, SAGE III). The ultimate goal of the mission is to better understand and quantify the rate of stratospheric ozone recovery. The focus of the paper will be on the Limb Profiler (LP) instrument. The LP instrument will measure the Earth's limb radiance (which is due to the scattering of solar photons by air molecules, aerosol and Earth surface) in the ultra-violet (UV), visible and near infrared, from 285 to 1000 nm. The LP simultaneously images the whole vertical extent of the Earth's limb through three vertical slits, each covering a vertical tangent height range of 100 km and each horizontally spaced by 250 km in the cross-track direction. Measurements are made every 19 seconds along the orbit track, which corresponds to a distance of about 150km. Several data analysis tools are presently being constructed and tested to retrieve ozone and aerosol vertical distribution from limb radiance measurements. The primary NASA algorithm is based on earlier algorithms developed for the SOLSE/LORE and SAGE III limb scatter missions. All the existing retrieval algorithms rely on a spherical symmetry assumption for the atmosphere structure. While this assumption is reasonable in most of the stratosphere, it is no longer valid in regions of prime scientific interest, such as polar vortex and UTLS regions. The paper will describe a two-dimensional retrieval algorithm whereby the ozone distribution is simultaneously retrieved vertically and horizontally for a whole orbit. The retrieval code relies on (1) a forward 2D Radiative Transfer code (to model limb radiances within a non-uniform atmosphere and evaluate 2D analytical partial derivatives) and (2) an optimal estimator inversion routine. The algorithm uses the typically sparse nature of the kernel matrices as well as fast matrix inversion techniques to allow for fast inversion of limb data with efficient memory management (as was done for MIPAS data processing). While the method has so far only been developed in the context of Single Scatter, the paper will show how the CPU intensive Multiple Scatter modeling can be implemented using parallel CPU processing. Initial results will be presented in terms of retrieved ozone profiles and code performance.

Rault, Didier F.↗
NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. IV: Coherent Backscattering

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered.The analysis is performed in a linear-polarization basis and includes a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, the design of an approximate method for computing the ladder and cross reflection matrices in the case of a semi-infinite medium with a sparse distribution of particles, the derivation of the relations between the elements of the ladder and cross reflection matrices in the exact backscattering direction for dense and sparse media, and the development of practical algorithms for solving the underlying integral equations by the method of Picard iterations and the discrete ordinate method. Simulation results for particles with large size parameters are also presented.

Adrian Doicu↗
NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗
DOE OSTI2022

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel -statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion () with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Implicit Kalman filtering

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Non-NASA Center↗
NASA NTRS1986

Preconditioning matrices for Chebyshev derivative operators

The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

Rothman, Ernest E.↗
DOE OSTI2022

High performance sparse multifrontal solvers on modern GPUs

Here, we have ported the numerical factorization and triangular solve phases of the sparse direct solver STRUMPACK to GPU. STRUMPACK implements sparse LU factorization using the multifrontal algorithm, which performs most of its operations in dense linear algebra operations on so-called frontal matrices of various sizes. Our GPU implementation off-loads these dense linear algebra operations, as well as the sparse scatter–gather operations between frontal matrices. For the larger frontal matrices, our GPU implementation relies on vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs and rocBLAS and rocSOLVER for AMD GPUs. For the smaller frontal matrices we developed custom CUDA and HIP kernels to reduce kernel launch overhead. Overall, high performance is achieved by identifying submatrix factorizations corresponding to sub-trees of the multifrontal assembly tree which fit entirely in GPU memory. The multi-GPU setting uses SLATE (Software for Linear Algebra Targeting Exascale) as a modern GPU-aware replacement for ScaLAPACK. On 4 nodes of SUMMIT the code runs ~10X faster when using all 24 V100 GPUs compared to when it only uses the 168 POWER9 cores. On 8 SUMMIT nodes, using 48 V100 GPUs, the sparse solver reaches over 50TFlop/s. Compared to SuperLU, on a single V100, for a set of 17 matrices our implementation is faster for all but one matrix, and is on average 5X (median 4X) faster

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗
DOE OSTI2023

Optimal Power Flow Derived Sparse Linear Solver Benchmarks

Due to the changing nature of the power grid, it is increasingly important to be able to solve a high-fidelity optimal power-flow models on large power networks. This high-fidelity problem, called AC Optimal Power Flow (ACOPF), is a nonlinear, nonconvex optimization problem. One of the few reliable ways of solving such a problem is interior point methods. These methods result in sparse linear systems where the coefficient matrix is symmetric, indefinite and nearly always ill-conditioned. As such, they are particularly challenging for sparse linear solvers and represent a considerable computational bottleneck in solving the ACOPF problem. In this paper, we introduce a repository of linear systems captured from ACOPF problems when solved by the open-source optimizer IPOPT. These matrices are meant to be used as a test suite for sparse linear solver development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Begušić, Tomislav (ORCID:0000000279424134)↗
DOE OSTI2024

NeuroFEM

SAND2025-00525O NeuroFEM is a software tool that demonstrates a neuromorphic algorithm for solving finite element problems. It sets up a 2D finite element problem for the Poisson equation on a disk, constructs synaptic matrices, and simulates neural dynamics to solve the resulting sparse linear system. The software illustrates how the algorithm converges to the solution and plots the results, showcasing a neuromorphic counterpart to traditional methods like Conjugate Gradient or GMRES. This tool is designed to highlight the potential of neuromorphic algorithms for solving sparse linear systems, which are prevalent in various computational applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2025

powersqueeze

powersqueeze (psqz) is a truncated power iteration library intended for high-performance computing platforms. psqz efficiently produces low-dimensional, linear measurements of graph matrix spectra by combining classical power iteration with sparse Johnson-Lindenstrauss transforms. psqz is intended to produce high-quality, fast, data-oblivious low-dimensional representations of high-dimensional sparse data such as graphs and term-document matrices. psqz is intended to replace similar workflows that depend on directly approximating a truncated eigendecomposition (e.g., the first step of spectral clustering), which is a much more expensive operation.

Priest, BenjaminW [Lawrence Livermore National Lab↗
NASA NTRS1976

An algorithm for reducing the bandwidth and profile of a sparse matrix

A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill-McKee algorithm, yet requires significantly less computation time.

Gibbs, N. E.↗
DOE OSTI2021

Online Voltage Event Detection Using Synchrophasor Data with Structured Sparsity-Inducing Norms

This paper develops an accurate and computationally efficient data-driven framework to detect voltage events from PMU data streams. It develops an innovative Proximal Bilateral Random Projection (PBRP) algorithm to quickly decompose the PMU data matrix into a low-rank matrix, a row-sparse event-pattern matrix and a noise matrix. Here, the row-sparse pattern matrix significantly distinguishes events from normal behavior. These matrices are then fed into a clustering algorithm to separate voltage events from normal operating conditions. Large-scale numerical study results on real-world PMU data show that the proposed algorithm is computationally more efficient and achieves higher F scores than state-of-the-art benchmarks.

24 POWER TRANSMISSION AND DISTRIBUTION↗