Results for “multiple solutions” — Page 68

NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗

NASA NTRS2004

Textbook Multigrid Efficiency for Leading Edge Stagnation

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Diskin, Boris↗

NASA NTRS2004

Textbook Multigrid Efficiency for Leading Edge Stagnation

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading-edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (FAS) cycle per grid. Asymptotic convergence rates of the FAS cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Diskin, Boris↗

NASA NTRS2007

Distributed Traffic Complexity Management by Preserving Trajectory Flexibility

In order to handle the expected increase in air traffic volume, the next generation air transportation system is moving towards a distributed control architecture, in which groundbased service providers such as controllers and traffic managers and air-based users such as pilots share responsibility for aircraft trajectory generation and management. This paper presents preliminary research investigating a distributed trajectory-oriented approach to manage traffic complexity, based on preserving trajectory flexibility. The underlying hypotheses are that preserving trajectory flexibility autonomously by aircraft naturally achieves the aggregate objective of avoiding excessive traffic complexity, and that trajectory flexibility is increased by collaboratively minimizing trajectory constraints without jeopardizing the intended air traffic management objectives. This paper presents an analytical framework in which flexibility is defined in terms of robustness and adaptability to disturbances and preliminary metrics are proposed that can be used to preserve trajectory flexibility. The hypothesized impacts are illustrated through analyzing a trajectory solution space in a simple scenario with only speed as a degree of freedom, and in constraint situations involving meeting multiple times of arrival and resolving conflicts.

Idris, Husni↗

NASA NTRS2009

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

NASA NTRS2012

General Methodology for Designing Spacecraft Trajectories

A methodology for designing spacecraft trajectories in any gravitational environment within the solar system has been developed. The methodology facilitates modeling and optimization for problems ranging from that of a single spacecraft orbiting a single celestial body to that of a mission involving multiple spacecraft and multiple propulsion systems operating in gravitational fields of multiple celestial bodies. The methodology consolidates almost all spacecraft trajectory design and optimization problems into a single conceptual framework requiring solution of either a system of nonlinear equations or a parameter-optimization problem with equality and/or inequality constraints.

Condon, Gerald↗

NASA NTRS2013

Development of a High Reliability Compact Air Independent PEMFC Power System

Autonomous Underwater Vehicles (AUV's) have received increasing attention in recent years as military and commercial users look for means to maintain a mobile and persistent presence in the undersea world. Compact, neutrally buoyant power systems are needed for both small and large vehicles. Historically, batteries have been employed in these applications, but the energy density and therefore mission duration are limited with current battery technologies. Vehicles with stored energy requirements greater than approximately 10 kWh have an alternate means to get long duration power. High efficiency Proton Exchange Membrane (PEM) fuel cell systems utilizing pure hydrogen and oxygen reactants show the potential for an order of magnitude energy density improvement over batteries as long as the subsystems are compact. One key aspect to achieving a compact and energy dense system is the design of the fuel cell balance of plant (BOP). Recent fuel cell work, initially focused on NASA applications requiring high reliability, has developed systems that can meet target power and energy densities. Passive flow through systems using ejector driven reactant (EDR) circulation have been developed to provide high reactant flow and water management within the stack, with minimal parasitic losses compared to blowers. The ejectors and recirculation loops, along with valves and other BOP instrumentation, have been incorporated within the stack end plate. In addition, components for water management and reactant conditioning have been incorporated within the stack to further minimize the BOP. These BOP systems are thermally and functionally integrated into the stack hardware and fit into the small volumes required for AUV and future NASA applications to maximize the volume available for reactants. These integrated systems provide a compact solution for the fuel cell BOP and maximize the efficiency and reliability of the system. Designs have been developed for multiple applications ranging from less than 1 kWe to 70 kWe. These systems occupy a very small portion of the overall energy system, allowing most of the system volume to be used for reactants. The fuel cell systems have been optimized to use reactants efficiently with high stack efficiency and low parasitic losses. The resulting compact, highly efficient fuel cell system provides exceptional reactant utilization and energy density. Key design variables and supporting test data are presented. Future development activities are described.

Vasquez, Arturo↗

NASA NTRS2014

Hybrid Data Assimilation without Ensemble Filtering

The Global Modeling and Assimilation Office is preparing to upgrade its three-dimensional variational system to a hybrid approach in which the ensemble is generated using a square-root ensemble Kalman filter (EnKF) and the variational problem is solved using the Grid-point Statistical Interpolation system. As in most EnKF applications, we found it necessary to employ a combination of multiplicative and additive inflations, to compensate for sampling and modeling errors, respectively and, to maintain the small-member ensemble solution close to the variational solution; we also found it necessary to re-center the members of the ensemble about the variational analysis. During tuning of the filter we have found re-centering and additive inflation to play a considerably larger role than expected, particularly in a dual-resolution context when the variational analysis is ran at larger resolution than the ensemble. This led us to consider a hybrid strategy in which the members of the ensemble are generated by simply converting the variational analysis to the resolution of the ensemble and applying additive inflation, thus bypassing the EnKF. Comparisons of this, so-called, filter-free hybrid procedure with an EnKF-based hybrid procedure and a control non-hybrid, traditional, scheme show both hybrid strategies to provide equally significant improvement over the control; more interestingly, the filter-free procedure was found to give qualitatively similar results to the EnKF-based procedure.

Kalman Filter↗

NASA NTRSDate not supplied

TPSAS-NF1676L-32060-DND

All previous PSP testing done in the Unitary Plan Wind Tunnel (UPWT) have required a significant amount of manual operation of the system. This has resulted in decreased testing efficiency and precluded the ability to provide near real-time data analysis to the customer. The overall goal of this project is to integrate the PSP data acquisition system into the supersonic UPWT data acquisition system (DAS) and create an adaptive software platform from which PSP data acquisition can be triggered by the tunnel and critical testing conditions can be recorded in real time for rapid analysis of the PSP data. This analysis includes the mapping of up to eight camera views onto a surface grid for analysis and converting to pressure using parameters supplied by the DAS. To fully implement this solution, communication must first be established between the Unitary DAS and the PSP DAS. This will be done by employing multiple scripts written in Python and C++ and implemented on a Linux cluster. These will be demonstrated and refined on an upcoming test (December 2018), and the successful completion will result in the ability to have automatic collection of PSP images and near real-time analysis capabilities.

Juliette Eddins↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The Role of Radiation-Induced Non-Equilibrium Plutonium Oxidation States in Solution

Plutonium plays a key role in global actinide research and nuclear fuel cycle technologies, and yet, our fundamental understanding of its inherent radiation-induced chemical behavior is limited. These radiation-induced processes cannot simply be switched off, as they are as fundamentally inherent to plutonium as the impact of relativistic effects on its f-electrons. In less chemically complex actinide systems, such as aqueous solutions of neptunium and americium, both steady-state and transient radiolysis products play a significant role in the redox cycling of their oxidation states, which ultimately impacts their chemistry and transport. However, plutonium's multiple, coexisting, and chemically active oxidation states, which comprise of bare ions and dioxo cations, provide additional redox pathways that complicate the aforementioned radiation-induced competition kinetics. Mechanistically understanding the response of these multiple oxidation states, both equilibrium and non-equilibrium, to intense ionizing radiation fields is essential for predicting the behavior of plutonium under a host of conditions that support technological innovation in global nuclear energy and non-proliferation efforts. Here, advances in radiation-induced plutonium solution chemistry will be presented, including new results from time-resolved electron pulse and steady-state gamma and alpha irradiations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

NASA NTRS1991

Multiple vs single scattering - Assessment of magnitudes

All orders of scattering are analyzed for two artifical canopies. The SHL canopy consists of Small Horizontal Leaves that are much smaller than the leaf-to-leaf spacing. The IHL canopy consists of Infinite Horizontal Layers, where each leaf is of infinite extent (a horizontal plane). Hemispheric leaf reflectances and transmittances independent of the direction of illumination lead to exact solutions for these models. Sunlight that penetrates to a given leaf area index level is much stronger in an SHL canopy than that in IHL; but the difference becomes muted when leaf transmittance is large. Multiple scattering enhances the hemispheric canopy reflectance more strongly in SHL than it does in IHL. The enhancement depends linearly on leaf transmittance in SHL and on the transmittance squared in IHL. Comparison with measured reflectances indicates that IHL model grossly underestimates multiple scattering in soybean canopies.

Otterman, Joseph↗

NASA NTRS1986

A survey of the state of the art and focused research in range systems, task 2

Many communication, control, and information processing subsystems are modeled by linear systems incorporating tapped delay lines (TDL). Such optimized subsystems result in full precision multiplications in the TDL. In order to reduce complexity and cost in a microprocessor implementation, these multiplications can be replaced by single-shift instructions which are equivalent to powers of two multiplications. Since, in general, the obvious operation of rounding the infinite precision TDL coefficients to the nearest powers of two usually yield quite poor system performance, the optimum powers of two coefficient solution was considered. Detailed explanations on the use of branch-and-bound algorithms for finding the optimum powers of two solutions are given. Specific demonstration of this methodology to the design of a linear data equalizer and its implementation in assembly language on a 8080 microprocessor with a 12 bit A/D converter are reported. This simple microprocessor implementation with optimized TDL coefficients achieves a system performance comparable to the optimum linear equalization with full precision multiplications for an input data rate of 300 baud. The philosophy demonstrated in this implementation is dully applicable to many other microprocessor controlled information processing systems.

Yao, K.↗

NASA NTRS2019

Star Tracker Accuracy Improvement and Optimization for Attitude Measurement in Three-Axis

High precision attitude measurement systems obviate the need for the beacon from the receiver making it possible for the spacecraft to beam a laser communications signal to a ground station without the ground station advertising its location. The research presented targets new detection and estimation methods to improve the accuracy in locating stars on a focal plane detector, and an understanding of the effects of changes in the optics design parameters and aberration, including defocus, on the navigation solution itself. This understanding can lead to an optimization of the attitude solution with respect to those optics realm parameter changes. The methodology discussed includes the development of a model of a current star tracker system. Using this model, multiple algorithms are implemented, including a multi-hypothesis method (MHT), to detect and estimate the position of the stars on the focal plane detector. It will be shown that using the MHT for detection and estimation, a greater accuracy can be found for each star estimation from more traditional detection and estimation algorithms. The approach then uses the model to develop statistics of the star tracker and the attitude estimation outputs to understand the accuracy, or variance, of the system's attitude solution. This solution is repeated for a range of defocus aberration, and a lower limit to the variance of the attitude solution is shown. A Cramer Rao lower bound solution is derived for the star tracker system and the results are compared to the Monte Carlo analysis from the model and shown to correlate very well. The approach uses a star image not as a Gaussian spot on the focal plane as done in previous work, and use of an image that includes the effects of aberrations of the optic system, and the effects of under-sampling and noise from the focal plane detector as well. Analysis includes exploring a star tracker's accuracy improvement through the combination of focus error and under-sampling effects alone, possibly contradicting conventional wisdom and approaches.

Lichter, Michael J.↗

DOE OSTI2023

Projected Multi-Agent Consensus Equilibrium (PMACE) With Application to Ptychography

Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image. In this article, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications. We describe PMACE in terms of an equilibrium problem and an equivalent fixed-point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem. To demonstrate the value of PMACE, we apply it to the problem of ptychography, in which a sample is reconstructed from the diffraction patterns resulting from coherent X-ray illumination at multiple overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. In conclusion, our results demonstrate that the PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms when the spots are sparsely sampled.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

Integrated NTP Vehicle Radiation Design

The development of a nuclear thermal propulsion stage requires consideration for radiation emitted from the nuclear reactor core. Applying shielding mass is an effective mitigating solution, but a better alternative is to incorporate some mitigation strategies into the propulsion stage and crew habitat. In this way, the required additional mass is minimized and the mass that must be applied may in some cases be able to serve multiple purposes. Strategies for crew compartment shielding are discussed that reduce dose from both engine and cosmic sources, and in some cases may also serve to reduce life support risks by permitting abundant water reserves. Early consideration for integrated mitigation solutions in a crewed nuclear thermal propulsion (NTP) vehicle will enable reduced radiation burden from both cosmic and nuclear sources, improved thrust-to-weight ratio or payload capacity by reducing 'dead mass' of shielding, and generally support a more robust risk posture for a NTP-powered Mars mission by permitting shorter trip times and increased water reserves

Caffrey, Jarvis↗

NASA NTRS2018

Integrated NTP Vehicle Radiation Design

The development of a nuclear thermal propulsion stage requires consideration for radiation emitted from the nuclear reactor core. Applying shielding mass is an effective mitigating solution, but a better alternative is to incorporate some mitigation strategies into the propulsion stage and crew habitat. In this way, the required additional mass is minimized and the mass that must be applied may in some cases be able to serve multiple purposes. Strategies for crew compartment shielding are discussed that reduce dose from both engine and cosmic sources, and in some cases may also serve to reduce life support risks by permitting abundant water reserves. Early consideration for integrated mitigation solutions in a crewed nuclear thermal propulsion (NTP) vehicle will enable reduced radiation burden from both cosmic and nuclear sources, improved thrust-to-weight ratio or payload capacity by reducing 'dead mass' of shielding, and generally support a more robust risk posture for a NTP-powered Mars mission by permitting shorter trip times and increased water reserves.

Caffrey, Jarvis A.↗