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Results for “adaptive cross approximation”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Reduction of Raman Spectroscopy Data for H2-CO2-Air Tubular Flame Measurements

An approach of reducing spontaneous Raman spectroscopy data, based on the matrix inversion method which logically removes undesired sources of the Raman scattering signals including cross-talk due to the signals from other species, is discussed. The approach contains extensive calibration of temperature-dependent system response. The Raman spectra of several cold and hot calibration flames and their resulting calibration matrix are elaborated. The structure of H2-CO2-air tubular flames, in terms of major species (CO2, O2, N2, H2O, and H2) concentrations and temperature, was successfully measured with the optical technique. The Raman spectra data used in this study are taken from a uniquely designed experimental apparatus – a tubular burner and Raman spectroscopy system at Vanderbilt University. The characteristic uncertainties for chemical species are approximately ±2% by mole fraction for hot products and ±0.5% for room temperature reactants. The approach described here for hydrogen/air tubular flames may be adapted to hydrocarbon/air tubular flames when other necessary major species, for example, CH4 and CO for methane/air tubular flame, are considered in the whole process.

Raman Spectroscopy↗
NASA NTRS1994

Changes in intervertebral disc cross-sectional area with bed rest and space flight

STUDY DESIGN. We measured the cross-sectional area of the intervertebral discs of normal volunteers after an overnight rest; before, during, and after 5 or 17 weeks of bed rest; and before and after 8 days of weightlessness. OBJECTIVES. This study sought to determine the degree of expansion of the lumbar discs resulting from bed rest and space flight. SUMMARY OF BACKGROUND DATA. Weightlessness and bed rest, an analog for weightlessness, reduce the mechanical loading on the musculoskeletal system. When unloaded, intervertebral discs will expand, increasing the nutritional diffusion distance and altering the mechanical properties of the spine. METHODS. Magnetic resonance imaging was used to measure the cross-sectional area and transverse relaxation time (T2) of the intervertebral discs. RESULTS. Overnight or longer bed rest causes expansion of the disc area, which reaches an equilibrium value of about 22% (range 10-40%) above baseline within 4 days. Increases in disc area were associated with modest increases in disc T2. During bed rest, disc height increased approximately 1 mm, about one-half of previous estimates based on body height measurements. After 5 weeks of bed rest, disc area returned to baseline within a few days of ambulation, whereas after 17 weeks, disc area remained above baseline 6 weeks after reambulation. After 8 days of weightlessness, T2, disc area, and lumbar length were not significantly different from baseline values 24 hours after landing. CONCLUSIONS. Significant adaptive changes in the intervertebral discs can be expected during weightlessness. These changes, which are rapidly reversible after short-duration flights, may be an important factor during and after long-duration missions.

Non-NASA Center↗
NASA NTRS1986

Analysis of nystagmus response to a pseudorandom velocity input

Space motion sickness was not reported during the first Apollo missions; however, since Apollo 8 through the current Shuttle and Skylab missions, approximately 50% of the crewmembers have experienced instances of space motion sickness. Space motion sickness, renamed space adaptation syndrome, occurs primarily during the initial period of a mission until habilation takes place. One of NASA's efforts to resolve the space adaptation syndrome is to model the individual's vestibular response for basis knowledge and as a possible predictor of an individual's susceptibility to the disorder. This report describes a method to analyse the vestibular system when subjected to a pseudorandom angular velocity input. A sum of sinusoids (pseudorandom) input lends itself to analysis by linear frequency methods. Resultant horizontal ocular movements were digitized, filtered and transformed into the frequency domain. Programs were developed and evaluated to obtain the (1) auto spectra of input stimulus and resultant ocular resonse, (2) cross spectra, (3) the estimated vestibular-ocular system transfer function gain and phase, and (4) coherence function between stimulus and response functions.

Lessard, C. S.↗
NASA NTRS1977

The human as a detector of changes in variance and bandwidth

The detection of changes in random process variance and bandwidth was studied. Psychophysical thresholds for these two parameters were determined using an adaptive staircase technique for second order random processes at two nominal periods (1 and 3 seconds) and damping ratios (0.2 and 0.707). Thresholds for bandwidth changes were approximately 9% of nominal except for the (3sec,0.2) process which yielded thresholds of 12%. Variance thresholds averaged 17% of nominal except for the (3sec,0.2) process in which they were 32%. Detection times for suprathreshold changes in the parameters may be roughly described by the changes in RMS velocity of the process. A more complex model is presented which consists of a Kalman filter designed for the nominal process using velocity as the input, and a modified Wald sequential test for changes in the variance of the residual. The model predictions agree moderately well with the experimental data. Models using heuristics, e.g. level crossing counters, were also examined and are found to be descriptive but do not afford the unification of the Kalman filter/sequential test model used for changes in mean.

Curry, R. E.↗
NASA NTRS1990

Metabolic and morphologic properties of single muscle fibers in the rat after spaceflight, Cosmos 1887

The adaptation of a slow (soleus, Sol) and a fast (medial gastrocnemius, MG) skeletal muscle to spaceflight was studied in five young male rats. The flight period was 12.5 days and the rats were killed approximately 48 h after returning to 1 g. Five other rats that were housed in cages similar to those used by the flight rats were maintained at 1 g for the same period of time to serve as ground-based controls. Fibers were classified as dark or light staining for myosin adenosine triphosphatase (ATPase). On the average, the fibers in the Sol of the flight rats atrophied twice as much as those in the MG. Further, the fibers located in the deep (close to the bone and having the highest percentage of light ATPase and high oxidative fibers in the muscle cross section) region of the MG atrophied more than the fibers located in the superficial (away from the bone and having the lowest percentage of light ATPase and high oxidative fibers in the muscle cross-section) region of the muscle. Based on quantitative histochemical assays of single muscle fibers, succinate dehydrogenase (SDH) activity per unit volume was unchanged in fibers of the Sol and MG. However, in the Sol, but not the MG, the total amount of SDH activity in a 10-microns-thick section of a fiber decreased significantly in response to spaceflight. Based on population distributions, it appears that the alpha-glycerophosphate dehydrogenase (GPD) activities were elevated in the dark ATPase fibers in the Sol, whereas the light fibers in the Sol and both fiber types in the MG did not appear to change. The ratio of GPD to SDH activities increased in the dark (but not light) fibers of the Sol and was unaffected in the MG. Immunohistochemical analyses indicate that approximately 40% of the fibers in the Sol of flight rats expressed a fast myosin heavy chain compared with 22% in control rats. Further, 31% of the fibers in the Sol of flight rats expressed both fast and slow myosin heavy chains compared with 8% in control rats. Immunohistochemical changes in the MG were minimal. These data suggest that the magnitude and direction of enzymatic activity and cell volume changes are dependent on the muscle, the region of the muscle, and the type of myosin expressed in the fibers. Further, the ability of fibers to maintain normal or even elevated activities per unit volume of some metabolic enzymes is remarkable considering the marked and rapid decrease in fiber volume.

NASA Experiment Number COS 1887-26↗
DOE OSTI2020

Correlation-based network analysis combined with machine learning techniques highlight the role of the GABA shunt in Brachypodium sylvaticum freezing tolerance

Perennial grasses will account for approximately 16 billion gallons of renewable fuels by the year 2022, contributing significantly to carbon and nitrogen sequestration. However, perennial grasses productivity can be limited by severe freezing conditions in some geographical areas, although these risks could decrease with the advance of climate warming, the possibility of unpredictable early cold events cannot be discarded. We conducted a study on the model perennial grass Brachypodium sylvaticum to investigate the molecular mechanisms that contribute to cold and freezing adaption. The study was performed on two different B. sylvaticum accessions, Ain1 and Osl1, typical to warm and cold climates, respectively. Both accessions were grown under controlled conditions with subsequent cold acclimation followed by freezing stress. For each treatment a set of morphological parameters, transcription, metabolite, and lipid profiles were measured. State-of-the-art algorithms were employed to analyze cross-component relationships. Phenotypic analysis revealed higher adaption of Osl1 to freezing stress. Our analysis highlighted the differential regulation of the TCA cycle and the GABA shunt between Ain1 and Osl1. Osl1 adapted to freezing stress by repressing the GABA shunt activity, avoiding the detrimental reduction in fatty acid biosynthesis and the concomitant detrimental effects on membrane integrity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1987

A new methodology for free wake analysis using curved vortex elements

A method using curved vortex elements was developed for helicopter rotor free wake calculations. The Basic Curve Vortex Element (BCVE) is derived from the approximate Biot-Savart integration for a parabolic arc filament. When used in conjunction with a scheme to fit the elements along a vortex filament contour, this method has a significant advantage in overall accuracy and efficiency when compared to the traditional straight-line element approach. A theoretical and numerical analysis shows that free wake flows involving close interactions between filaments should utilize curved vortex elements in order to guarantee a consistent level of accuracy. The curved element method was implemented into a forward flight free wake analysis, featuring an adaptive far wake model that utilizes free wake information to extend the vortex filaments beyond the free wake regions. The curved vortex element free wake, coupled with this far wake model, exhibited rapid convergence, even in regions where the free wake and far wake turns are interlaced. Sample calculations are presented for tip vortex motion at various advance ratios for single and multiple blade rotors. Cross-flow plots reveal that the overall downstream wake flow resembles a trailing vortex pair. A preliminary assessment shows that the rotor downwash field is insensitive to element size, even for relatively large curved elements.

Bliss, Donald B.↗
NASA NTRSDate not supplied

Mitigating Headward Fluid Shifts with Venoconstrictive Thigh Cuffs during Spaceflight

Venoconstrictive thigh cuffs (VTC) are a mechanical countermeasure capable of attenuating the spaceflight induced headward fluid shift, and thus may be a viable spaceflight associated neuro-ocular syndrome (SANS) countermeasure. Crewmembers can use VTC to mitigate the headward fluid shift to aid in adapting to spaceflight. However, data are needed to determine if VTC affect ocular structures. PURPOSE The purpose of this study is to determine the efficacy of long duration use of VTC application to mitigate the spaceflight-induced headward fluid shift. We hypothesize that a VTC countermeasure will temporarily reverse the headward fluid shift and attenuate spaceflight-induced changes of internal jugular vein (IJV) cross-sectional area, IJV pressure, stroke volume, cardiac output, intraocular pressure (IOP), and optic nerve head and retinal morphology. METHODS This study will evaluate the effectiveness of VTC countermeasure application on the headward fluid shift, as well as cardiovascular and ocular variables. VTC during spaceflight will be worn for an extended duration (up to 6 hours) with data collected at three time points (30 minutes, 3 hours, and 6 hours) to characterize the temporal profile of key fluid shift outcome measures of the vascular fluid shift, IOP, and ocular structure changes. Ten astronauts will be recruited to participate and will be studied before and during approximately 180-day International Space Station (ISS) spaceflight missions. Baseline data collection will occur approximately 90-days before launch (Figure). Preflight, each leg of the crewmember will be measured to determine the VTC cuff size and a cuff fit check session will occur prior to the preflight baseline ground imaging to verify the appropriate fit measured via a surface contact pressure. Prior to donning the VTC, baseline measures without VTC will be collected seated, supine, and supine followed by data collection with the VTC. The baseline data collection will include ultrasound (IJV area and pressure, stroke volume and cardiac output), brachial blood pressure and heart rate, optical coherence tomography (OCT) imaging (total retinal thickness and choroid thickness), and IOP. An inflight cuff fit check session, same as the preflight fit check, will occur prior to VTC use on ISS. The inflight VTC experiment will be conducted early (FD45) and late (R-45) to determine if mission duration affects VTC fit and the efficacy of fluid redistribution. A system usability scale comfort questionnaire will be included in each VTC session to capture feedback from crewmembers regarding the comfort and usability of the VTC. SCIENTIFIC & MISSION IMPACT Results will narrow knowledge gaps described in the Human Research Roadmap to mitigate the headward fluid shift during spaceflight and help NASA to 1) determine the efficacy of extended use VTC application to mitigate the spaceflight-induced headward fluid shift and 2) further the understanding of the use of VTC on vascular fluid shifts, IOP, and ocular structure during spaceflight. Supported by NASA Human Research Program Directed Research. Figure. Detailed Testing Schedule. Baseline data collection at L-90 will be performed in a randomized order of position.

J V Jasien↗
NASA NTRSDate not supplied

Ground Tests on the BOLT Geometry at Mach 7: Cross-Facility Comparison and Stability Analysis

Transition measurements have been obtained through two experimental campaigns conducted independently by the German Aerospace Center and the French Aerospace Lab with the French Alternative Energies and Atomic Energy Commission on subscale models of the BOLT-1 flight experiment geometry. This paper details a cross-facility comparison of measurements obtained at Mach 7, as well as subsequent computational analysis. Infrared (IR) thermography measurements obtained by both campaigns have facilitated a global comparison of the transition front across facilities at analagous conditions, which are found to be in good agreement. High-frequency surface pressure fluctuation data demonstrate significant amplification of instabilities with Mack-mode characteristics in the outboard regions of the acreage. These measurements are compared to stability analyses of varying fidelity. The computational methods employed to characterize the boundary-layer transition phenomena include the traditional line-marching implementation of the Parabolized Stability Equations (PSE), 2D eigenvalue analysis coupled with PSE, and Adaptive Mesh Refinement Wavepacket Tracking. While the 2D eigenvalue analysis is found to predict instabilities, which correlate in terms of frequency and acreage location to the experimental measurements, the predicted amplification for these instabilities is lower than would typically be expected for transition. Line-marching results for traveling crossflow produce the best match to the experimental transition front, with a consistent transition N factor of approximately 3-3.5.

Boundary Layer Transition↗
DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The underappreciated importance of solar radiation in constraining spring phenology of temperate ecosystems in the Northern and Eastern United States

Spring phenology of temperate ecosystems is highly sensitive to climate change, generating various impacts on many important terrestrial surface biophysical processes. Although various prognostic models relying on environmental variables of temperature and photoperiod have been developed for spring phenology, comprehensive ecosystem-scale evaluations over large landscapes and long-time periods remain lacking. Further, environmental variables other than temperature and photoperiod might also importantly constrain spring phenology modelling but remain under-investigation. To address these issues, we leveraged around 20-years datasets of environmental variables (from Daymet and GLDAS products) and the spring phenology metric (i.e., the greenup date) respectively derived from MODIS and PhenoCams across 108 sites in the Northern and Eastern United States. We firstly cross-compared MODIS-derived greenup date with official PhenoCams product with high accuracy (R 2 = 0.70). Then, we evaluated the three prognostic models (i.e., Growing Degree Date (GDD), Sequential (SEQ) and optimality-based (OPT)) with MODIS-derived spring phenology, assessed the model residuals and their associations with soil moisture, rainfall, and solar radiation, and revised the two photoperiod-relevant models (SEQ, OPT) by replacing the daylength variable with solar radiation, which was found to contribute the most to model residuals. We found that 1) all models demonstrated good capability in characterizing spring phenology, with OPT performing the best (RMSE = 8.04 ± 5.05 days), followed by SEQ (RMSE = 10.57 ± 7.77 days) and GDD (RMSE = 10.84 ± 8.42 days), 2) all models displayed high model residuals showing tight correlation with solar radiation (r = 0.45–0.75), and 3) the revised models that included solar radiation significantly performed better with an RMSE reduction by 22.08%. Such results are likely because solar radiation better constrains early growing season plant photosynthesis than photoperiod, supporting the hypothesis of spring phenology as an adaptive strategy to maximize photosynthetic carbon gain (approximated by solar radiation) while minimizing frost damage risk (captured by temperature). Collectively, our study here reveals the underappreciated importance of solar radiation in constraining spring phenology of temperate ecosystems, and suggests ways to improve spring phenology modelling and other phenology-related ecological processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Enamel nanocrystal misorientation increased with meat-eating and agriculture

Enamel covers teeth, is the hardest tissue in the vertebrate body and has a complex multiscale structure from nanometres to millimetres. The structure comprises thin, long hydroxyapatite (Ca 5 (PO 4 ) 3 OH) nanocrystals, 50–70 nm wide, many micrometres long, parallel and bundled into approximately 5-µm-wide rods. The rods undulate and cross into a microscale ‘decussation pattern’ that toughens enamel by deflecting cracks. However, the crystallographic orientation of enamel nanocrystals is poorly understood. Here we show that the misorientation angle of adjacent nanocrystals varies markedly across 12 primate teeth spanning 9 species, 17.8 million years of evolution and diverse diets. Using a method called Polarization Enabled Large Input of Crystal Angles at the Nanoscale (PELICAN), we compare nanocrystals in the same (pre)molar locations and show that misorientation increases with food hardness in extant and fossil non-human apes and monkeys. We compare misorientation across three major dietary shifts in human evolution: the transition to meat-eating about 2.0–1.5 million years before present, to agriculture (about 12,000 years before present), and the Industrial Revolution (about 250 years before present). We show that over the past 1.6 million years, in the human lineage misorientation increased with time, especially when meat and stone-ground grains were introduced into human diets, but not with the Industrial Revolution. Thus, besides macro-changes, teeth adapted to dietary change at the nanoscale and crystallographically. This observation suggests that misorientation may contribute to enamel’s resilience; thus, bioinspired materials may consider small misorientation angles for added resilience.

biomaterials↗
NASA NTRS1996

Three-Dimensional Multiscale MHD Model of Cometary Plasma Environments

First results of a three-dimensional multiscale MHD model of the interaction of an expanding cometary atmosphere with the magnetized solar wind are presented. The model starts with a supersonic and super-Alfvenic solar wind far upstream of the comet (25 Gm upstream of the nucleus) with arbitrary interplanetary magnetic field orientation. The solar wind is continuously mass loaded with cometary ions originating from a 10-km size nucleus. The effects of photoionization, electron impact ionization, recombination, and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our new multiscale upwind scalar conservation laws-type numerical technique (MUSCL). We have named this the multiscale adaptive upwind scheme for MHD (MAUS-MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. The main findings are the following: (1) Mass loading decelerates the solar wind flow upstream of the weak cometary shock wave (M approximately equals 2, M(sub A) approximately equals 2), which forms at a subsolar standoff distance of about 0.35 Gm. (2) A cometary plasma cavity is formed at around 3 x 10(exp 3) km from the nucleus. Inside this cavity the plasma expands outward due to the frictional interaction between ions and neutrals. On the nightside this plasma cavity considerably narrows and a relatively fast and dense cometary plasma beam is ejected into the tail. (3) Inside the plasma cavity a teardrop-shaped inner shock is formed, which is terminated by a Mach disk on the nightside. Only the region inside the inner shock is the 'true' diamagnetic cavity. (4) The model predicts four distinct current systems in the inner coma: the density peak current, the cavity boundary current, the inner shock current, and finally the cross-tail current. (5) The calculated plasma parameters (magnetic field, plasma density, speed, and temperature) are in very good agreement with published Giotto observations.

Gombosi, Tamas I.↗
NASA NTRS2007

Simulation of a Periodic Jet in a Crossflow with a RANS Solver Using an Unstructured Grid

A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

Atkins, H. L.↗
NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗
NASA NTRS2009

Highly Scalable Matching Pursuit Signal Decomposition Algorithm

Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.

Christensen, Daniel↗
NASA NTRS1991

Hierarchic models for laminated plates

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Actis, Ricardo Luis↗