Search NASA⌕ Search

SEARCH · Search NASA

Results for “sparsity”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Consistency of ARESE II Cloud Absorption Estimates and Sampling Issues

Data from three cloudy days (March 3, 21, 29, 2000) of the ARM Enhanced Shortwave Experiment II (ARESE II) were analyzed. Grand averages of broadband absorptance among three sets of instruments were compared. Fractional solar absorptances were approx. 0.21-0.22 with the exception of March 3 when two sets of instruments gave values smaller by approx. 0.03-0.04. The robustness of these values was investigated by looking into possible sampling problems with the aid of 500 nm spectral fluxes. Grand averages of 500 nm apparent absorptance cover a wide range of values for these three days, namely from a large positive (approx. 0.011) average for March 3, to a small negative (approximately -0.03) for March 21, to near zero (approx. 0.01) for March 29. We present evidence suggesting that a large part of the discrepancies among the three days is due to the different nature of clouds and their non-uniform sampling. Hence, corrections to the grand average broadband absorptance values may be necessary. However, application of the known correction techniques may be precarious due to the sparsity of collocated flux measurements above and below the clouds. Our analysis leads to the conclusion that only March 29 fulfills all requirements for reliable estimates of cloud absorption, that is, the presence of thick, overcast, homogeneous clouds.

Oreopoulos, L.↗
NASA NTRS2002

An Efficient Scheme for Updating Sparse Cholesky Factors

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Raghavan, Padma↗
NASA NTRS1999

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Lockard, David P.↗
NASA NTRS1997

Efficient Computation of Closed-loop Frequency Response for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, full-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open and closed loop loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, a speed-up of almost two orders of magnitude was observed while accuracy improved by up to 5 decimal places.

Maghami, Peiman G.↗
NASA NTRS2005

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Nguyen, Duc T.↗
NASA NTRS2006

Compilation of a Global Emission Inventory from 1980 to 2000 for Global Model Simulations of the Long-term Trend of Tropospheric Aerosols

The approach to create a comprehensive emission inventory for the time period 1980 to 2000 is described in this paper. We have recently compiled an emission database, which we will use for a 21 year simulation of tropospheric aerosols with the GOCART model. Particular attention was paid to the time-dependent SO2, black carbon and organic carbon aerosol emissions. For the emission of SO2 from sporadically erupting volcanoes, we assembled emission data from the Global Volcanism Program of the Smithsonian Institution, using the VEI to derive the volcanic cloud height and the SO2 amount, and amended this dataset by the SO2 emission data from the TOMS instrument when available. 3-dimensional aircraft emission data was obtained for a number of years from the AEAP project, converted from burned fuel to SO2 and interpolated to each year, taking the sparsity of the flight patterns into account. Other anthropogenic SO2 emissions are based on gridded emissions from the EDGAR 2000 database (excluding sources from aircraft, biomass burning and international ship traffic), which were scaled to individual years with country/regional based emission inventories. Gridded SO2 emissions from international ship traffic for 2000 and the scaling factors for other years are from [Eyring et al., 2005]. We used gridded anthropogenic black and organic carbon emissions for 1996 [Bond et al., 2005], again excluding aircraft, biomass burning and ship sources. These emissions were scaled with regional based emission inventories from 1980 to 2000 to derive gridded emissions for each year. The biomass burning emissions are based on a climatology, which is scaled with regional scaling factors derived from the TOMS aerosol index and the AVHRR/ASTR fire counts to each year [Duncan et al., 2003]. Details on the integration of the information from the various sources will be provided and the distribution patterns and total emissions in the final product will be discussed.

Diehl, Thomas L.↗
NASA NTRS2006

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Watson, Willie R.↗
NASA NTRS2007

Compilation of a Global Emission Inventory from 1980 to 2000 for Global Model Simulations of the Long-term Trend of Tropospheric Aerosols

The approach to create a comprehensive emission inventory for the time period 1980 to 2000 is described in this paper. We have recently compiled an emission database, which we will use for a 21 year simulation of tropospheric aerosols with the GOCART model. Particular attention was paid to the time-dependent SO2, black carbon and organic carbon aerosol emissions. For the emission of SO2 from sporadically erupting volcanoes, we assembled emission data from the Global Volcanism Program of the Smithsonian Institution, using the VEI to derive the volcanic cloud height and the SO2 amount, and amended this dataset by the SO2 emission data from the TOMS instrument when available. 3-dimensional aircraft emission data was obtained for a number of years from the AEAP project, converted from burned fuel to SO2 and interpolated to each year, taking the sparsity of the flight patterns into account. Other anthopogenic SO2 emissions are based on gridded emissions from the EDGAR 2000 database (excluding sources from aircraft, biomass burning and international ship traffic), which were scaled to individual years with country/regional based emission inventories. Gridded SO2 emissions from international ship traffic for 2000 and the scaling factors for other years are from [Eyring et al., 2005]. We used gridded anthropogenic black and organic carbon emissions for 1996 [Bond et al., 2005], again excluding aircraft, biomass burning and ship sources. These emissions were scaled with regional based emission inventories from 1980 to 2000 to derive gridded emissions for each year. The biomass burning emissions are based on a climatology, which is scaled with regional scaling factors derived from the TOMS aerosol index and the AVHRR/ATSR fire counts to each year [Duncan et al., 2003]. Details on the integration of the information from the various sources will be provided and the distribution patterns and total emissions in the final product will be discussed.

Diehl, T. L.↗
NASA NTRS1989

Vector excitation speech or audio coder for transmission or storage

A vector excitation coder compresses vectors by using an optimum codebook designed off line, using an initial arbitrary codebook and a set of speech training vectors exploiting codevector sparsity (i.e., by making zero all but a selected number of samples of lowest amplitude in each of N codebook vectors). A fast-search method selects a number N.sub.c of good excitation vectors from the codebook, where N.sub.c is much smaller tha ORIGIN OF INVENTION The invention described herein was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 USC 202) under which the inventors were granted a request to retain title.

Davidson, Grant↗
NASA NTRS2009

Satellite Contributions to Global Change Studies

By providing a global view with a level playing field (no region missed because of unfavorable surface conditions or political boundaries), satellites have made major contributions to improved monitoring and understanding of our constantly changing planet. The global view has allowed surprising realizations like the relative sparsity of lightning strikes over oceans and the large-scale undulations on the massive Antarctic ice sheet. It has allowed the tracking of all sorts of phenomena, including aerosols, both natural and anthropogenic, as they move with the atmospheric circulation and impact weather and human health. But probably nothing that the global view allows is more important in the long term than its provision. of unbiased data sets to address the issue of global change, considered by many to be among the most important issues facing humankind today. With satellites we can monitor atmospheric temperatures at all latitudes and longitudes, and obtain a global average that lessens the likelihood of becoming endlessly mired in the confusions brought about by the certainty of regional differences. With satellites we can monitor greenhouse gases such as CO2 not just above individual research stations but around the globe. With satellites we can monitor the polar sea ice covers, as we have done since the late 1970s, determining and quantifying the significant reduction in Arctic sea ice and the slight growth in Antarctic sea ice over that period, With satellites we can map the full extent and changes in the Antarctic stratospheric ozone depletions that were first identified from using a single ground station; and through satellite data we have witnessed from afar land surface changes brought about by humans both intentionally, as with wide-scale deforestation, and unintentionally, as with the decay of the Aral Sea. The satellite data are far from sufficient for all that we need in order to understand the global system and forecast its changes, as we also need sophisticated climate models, in situ process studies, and data sets that extend back well before the introduction of satellite technology. Nonetheless, the repetitive, global view provided by satellites is contributing in a major way to our improved recognition of how the Earth im changing, a recognition that is none too soon in view of the magnitude of the impacts that humans can now have.

Parkinson, Claire L.↗
NASA NTRS2010

Applied Meteorology Unit (AMU) Quarterly Report

By providing a global view with a level playing field (no region missed because of unfavorable surface conditions or political boundaries), satellites have made major contributions to improved monitoring and understanding of our constantly changing planet. The global view has allowed surprising realizations like the relative sparsity of lightning strikes over oceans and the large-scale undulations on the massive Antarctic ice sheet. It has allowed the tracking of all sorts of phenomena, including aerosols, both natural and anthropogenic,as they move with the atmospheric circulation and impact weather and human health. But probably nothing that the global view allows is more important in the long term than its provision of unbiased data sets to address the issue of global change, considered by many to be among the most important issues facing humankind today. With satellites we can monitor atmospheric temperatures at all latitudes and longitudes, and obtain a global average that lessens the likelihood of becoming endlessly mired in the confusions brought about by the certainty of regional differences. With satellites we can monitor greenhouse gases such as CO2 not just above individual research stations but around the globe. With satellites we can monitor the polar sea ice covers, as we have done since the late 1970s, determining and quantifying the significant reduction in Arctic sea ice and the slight growth in Antarctic sea ice over that period. With satellites we can map the full extent and changes in the Antarctic stratospheric ozone depletions that were first identified from a single ground station; and through satellite data we have witnessed from afar land surface changes brought about by humans both intentionally, as with wide-scale deforestation, and unintentionally, as with the decay of the Aral Sea. The satellite data are far from sufficient for all that we need in order to understand the global system and forecast its changes, as we also need sophisticated climate models, in situ process studies, and data sets that extend back well before the introduction of satellite technology. Nuomthc)cmm, the repetitive, global view provided by satellites is contributing in a major way to our improved recognition of how the Earth is changing, a recognition that is none too soon in view of the magnitude of the impacts that humans can now have.

Bauman, William↗
NASA NTRS2012

RXTE Observations of Anomalous X-ray Pulsar 1E 1547.0-5408 During and After its 2008 and 2009 Outbursts

We present the results of Rossi X-ray Timing Explorer (RXTE) and Swift monitoring observations of the magnetar 1E 1547.0-5408 following the pulsar's radiative outbursts in 2008 October and 2009 January. We report on a study of the evolution of the timing properties and the pulsed flux from 2008 October 4 through 2009 December 26. In our timing study, a phase-coherent analysis shows that for the first 29 days following the 2008 outburst, there was a very fast increase in the magnitude of the rotational frequency derivative upsilon-dot, such that upsilon-dot-dot was a factor of 60 larger than that reported in data from 2007. This upsilon-dot magnitude increase occurred in concert with the decay of the pulsed flux following the start of the 2008 event. Following the 2009 outburst, for the first 23 days, upsilon-dot-dot was consistent with zero, and upsilon-dot had returned to close to its 2007 value. In contrast to the 2008 event, the 2009 outburst showed a major increase in persistent flux, relatively little change in the pulsed flux, and sudden significant spectral hardening approx 15 days after the outburst. We show that, excluding the month following each of the outbursts, and because of the noise and the sparsity in the data, multiple plausible timing solutions fit the pulsar's frequency behavior. We note similarities in the behavior of 1E 1547.0-5408 following the 2008 outburst to that seen in the AXP 1E 1048.1-5937 following its 2001-2002 outburst and discuss this in terms of the magnetar model.

Dib, Rim↗
NASA NTRS2016

Evaluation of the Effect of Surface Finish on High-Cycle Fatigue for SLM-IN718

A high-cycle fatigue (HCF) knockdown factor was estimated for Inconel 718, manufactured with the selective laser melt (SLM) process. This factor is the reduction at a common fatigue life from the maximum stress in fatigue for low-stress ground (LSG) specimens to the maximum stress of those left with the original surface condition. Various vendors provided specimens. To reduce the number of degrees-of-freedom, only one heat treat condition was evaluated. Testing temperatures included room temperature, 800F, 1000F, and 1200F. The two surface conditions were compared at constant lives, where data was available. The recommended knockdown factor of the as-built surface condition (average roughness of approximately 245 micro-inches/inch) versus low-stress ground condition (roughness <= 4 micro-inches/inch) is approximately 1/3 or 33%. This is to say that for the as-built surface condition, a maximum stress of 2/3 of the stress for LSG can be expected to produce the same life in the as built surface condition. As an alternative method, the surface finish was incorporated into a new parameter with the maximum stress. The new parameter was formulated to be similar to the fracture mechanics stress intensity factor, and it was named the pseudo stress intensity factor, Kp. Using Kp, the variance seemed acceptable across all sources, and the knockdown factor was estimated over the range of data identified by Kp where data occurred. A plot of the results suggests that the knockdown factor is a function of temperature, and that for low lives the knockdown is greater than the knockdown observed above about one million cycles, where it stabilizes. One data point at room temperature was clearly different, and the sparsity of data in the higher life region reduces the value of these results. The method does appear to provide useful results, and further characterization of the method is suggested.

Lambert, Dennis M.↗
NASA NTRS2016

Role of Updraft Velocity in Temporal Variability of Global Cloud Hydrometeor Number

Understanding how dynamical and aerosol inputs affect the temporal variability of hydrometeor formation in climate models will help to explain sources of model diversity in cloud forcing, to provide robust comparisons with data, and, ultimately, to reduce the uncertainty in estimates of the aerosol indirect effect. This variability attribution can be done at various spatial and temporal resolutions with metrics derived from online adjoint sensitivities of droplet and crystal number to relevant inputs. Such metrics are defined and calculated from simulations using the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) and the National Center for Atmospheric Research Community Atmosphere Model Version 5.1 (CAM5.1). Input updraft velocity fluctuations can explain as much as 48% of temporal variability in output ice crystal number and 61% in droplet number in GEOS-5 and up to 89% of temporal variability in output ice crystal number in CAM5.1. In both models, this vertical velocity attribution depends strongly on altitude. Despite its importance for hydrometeor formation, simulated vertical velocity distributions are rarely evaluated against observations due to the sparsity of relevant data. Coordinated effort by the atmospheric community to develop more consistent, observationally based updraft treatments will help to close this knowledge gap.

cloud condensation nuclei↗
NASA NTRS2018

Impact of Assimilating AIRS Cloud-Cleared Radiances on Atmospheric Dynamics and Polar Low Representation at High Latitudes

This study explores the sensitivity of planetary boundary layer height and related atmospheric dynamics to the assimilation of cloud-cleared AIRS (Atmospheric Infrared Sounder) radiances in the Goddard Earth Observing System (GEOS, version 5) data assimilation and forecast system during the boreal fall 2014 season using observing system experiments (OSEs). Examined here are comparisons between the current, operational approach of assimilating AIRS clear-sky radiances against the assimilation of cloud-cleared radiances (CCR). In polar regions, assimilation of AIRS CCRs is particularly beneficial because of the sparsity of conventional observations and the prevalence of extended low-level stratus cloud cover, which limit the ingestion of clear-sky data. Assimilation of hyperspectral infrared information from AIRS over the Arctic region slightly modifies the lower midtropospheric temperature structure, which in turn contributes to adjustments in geopotential height, affecting the baroclinic instability properties over the entire hemisphere and explaining the overall improvement in global forecast skill. In addition, it is shown that the assimilation of CCRs benefits the representation of convectively-driven small-scale cyclones at high latitudes in the same way as previously noted for tropical cyclones. Specifically, assimilation of CCRs create a temperature dipole over the top of meteorologically active and strongly convective systems such as polar, arctic, and antarctic lows, which helps constrain the analyzed representation of their scale and vertical structure.

Mcgrath-Spangler, E. L.↗
NASA NTRS2019

Impact of Assimilating AIRS Cloud-Cleared Radiances on Atmospheric Dynamics and Boundary Layer Height at High Latitudes

High latitude weather forecasts, on scales ranging from mesoscale to synoptic, present difficulties due, in part, to the sparsity of conventional observations. In addition, the prevalence of extended low-level stratus cloud cover limits the use of infrared data, which are operationally assimilated only in areas unaffected by clouds. Use of cloud-cleared AIRS (Atmospheric Infrared Sounder) radiances (AIRS CCR), allows the assimilation of infrared information in cloudy regions, permitting data ingestion in regions usually undersampled. This study explores the sensitivity of planetary boundary layer height and related atmospheric dynamics to the assimilation of these data in the Goddard Earth Observing System (GEOS, version 5) data assimilation and forecast system during the boreal fall 2014 season using observing system experiments (OSEs). Examined here are comparisons between the current, operational approach of assimilating AIRS clear-sky radiances against the assimilation of CCR. Assimilation of hyperspectral infrared information from AIRS over the Arctic region slightly modifies the lower midtropospheric temperature structure, which in turn contributes to adjustments in geopotential height, affecting the baroclinic instability properties over the entire hemisphere and explaining the overall improvement in global forecast skill.

McGrath-Spangler, E. L.↗
NASA NTRS2019

Using Graph Coloring to Compute Total Derivatives More Efficiently in OpenMDAO

When they are applicable, gradient based optimization algorithms are the most efficient way to solve design optimization problems. Although gradient based methods are generally efficient, they can be made significantly more so through the usage of analytic techniques to compute the necessary total derivatives. The traditional forward (direct) and reverse (adjoint) analytic techniques have computational costs that scale linearly with the number of design variables and the number of constraints, respectively. In this work, we present an application of a graph coloring algorithm to the analytic techniques for computing total derivative Jacobians in order to achieve much better computational scaling than the pure analytic methods can provide alone. A detailed theoretical explanation of how coloring algorithms interact with analytic derivative methods is presented that illustrates specific types of sparsity patterns that must be present in total derivative Jacobians in order for this coloring technique to be effective. The new technique has been implemented as a feature in the OpenMDAO framework and the implementation is demonstrated on two example problems. The performance on the example problems up to 50% reduction in compute cost for optimizations with bi-directional coloring compared to traditional constraint aggregation. Additionally, the results show how coloring technique alleviates some of the numerical difficulties that constraint aggregation can cause, leading to the ability to solve larger problems. It is expected that the new method will have wide applicability to multidisciplinary optimization problems, and that its availability in OpenMDAO will offer significant computational savings for users without the need for them to implement the coloring algorithm themselves.

Trajectory↗
NASA NTRS2020

Implicit Formulations of Bounded-Impulse Trajectory Models for Preliminary Interplanetary Low-Thrust Analysis

The bounded-impulse approach to low-thrust interplanetary trajectory optimization is widely used. In an effort to efficiently implement this approach using NASA’s OpenMDAO optimization software, the authors have implemented implicit formulations of the forward shooting/backwards-shooting methods commonly used in bounded-impulse models. These implicit approaches allow for vectorization of the underlying calculations which can significantly reduce runtime in interpreted languages. An implicit approach may be either converged by using an underlying nonlinear solver to converge the state propagation, or as a constraint in an optimizer-driven multiple-shooting approach. Significant computational efficiency gains are realized through the utilization of the modular approach to unified derivatives. Further computational efficiency is achieved by capitalizing on the sparsity of the constraint Jacobian matrix. This work demonstrates that a vectorized multiple-shooting approach for propagating a state-time history is superior in terms of computational efficiency as the number of segments in the state-propagation is increased.

Falck, Robert D↗