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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

NASA NTRS1992

Design concepts for the development of cooperative problem-solving systems

There are many problem-solving tasks that are too complex to fully automate given the current state of technology. Nevertheless, significant improvements in overall system performance could result from the introduction of well-designed computer aids. We have been studying the development of cognitive tools for one such problem-solving task, enroute flight path planning for commercial airlines. Our goal was two-fold. First, we were developing specific systems designs to help with this important practical problem. Second, we are using this context to explore general design concepts to guide in the development of cooperative problem-solving systems. These designs concepts are described.

Smith, Philip J.↗

NASA NTRS1995

Enroute flight planning: Evaluating design concepts for the development of cooperative problem-solving systems

There are many problem-solving tasks that are too complex to fully automate given the current state of technology. Nevertheless, significant improvements in overall system performance could result from the introduction of well-designed computer aids. We have been studying the development of cognitive tools for one such problem-solving task, enroute flight path planning for commercial airlines. Our goal has been two-fold. First, we have been developing specific system designs to help with this important practical problem. Second, we have been using this context to explore general design concepts to guide in the development of cooperative problem-solving systems. These design concepts are described below, along with illustrations of their application.

Smith, Philip J.↗

NASA NTRS1994

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 3: Illustrative test problems

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 3 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 3 explains the kinetics and kinetics-plus-sensitivity analysis problems supplied with LSENS and presents sample results. These problems illustrate the various capabilities of, and reaction models that can be solved by, the code and may provide a convenient starting point for the user to construct the problem data file required to execute LSENS. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Bittker, David A.↗

NASA NTRS1971

Equicontrollability and its application to model-following and decoupling.

Discussion of 'model following,' a term used to describe a class of problems characterized by having two dynamic systems, generically known as the 'plant' and the 'model,' it being required to find a controller to attach to the plant so as to make the resultant compensated system behave, in an input/output sense, in the same way as the model. The approach presented to the problem takes a structural point of view. The result is a complex but informative definition which solves the problem as posed. The application of both the algorithm and its basis, equicontrollability, to the decoupling problem is considered.

Curran, R. T.↗

NASA NTRS1979

Spectral methods for problems in complex geometries

Techniques that permit the efficient application of spectral methods to solve problems in nearly arbitrary geometries are presented. These methods were found to be viable alternatives to finite difference and finite element processes. The spectral methods applied are extensions of the standard techniques of separation of variables to the solution of arbitrarily complicated problems.

Orszag, S. A.↗

NASA NTRS2002

Computing the Envelope for Stepwise-Constant Resource Allocations

Computing tight resource-level bounds is a fundamental problem in the construction of flexible plans with resource utilization. In this paper we describe an efficient algorithm that builds a resource envelope, the tightest possible such bound. The algorithm is based on transforming the temporal network of resource consuming and producing events into a flow network with nodes equal to the events and edges equal to the necessary predecessor links between events. A staged maximum flow problem on the network is then used to compute the time of occurrence and the height of each step of the resource envelope profile. Each stage has the same computational complexity of solving a maximum flow problem on the entire flow network. This makes this method computationally feasible and promising for use in the inner loop of flexible-time scheduling algorithms.

Muscettola, Nicola↗

NASA NTRS2001

Computing the Envelope for Stepwise Constant Resource Allocations

Estimating tight resource level is a fundamental problem in the construction of flexible plans with resource utilization. In this paper we describe an efficient algorithm that builds a resource envelope, the tightest possible such bound. The algorithm is based on transforming the temporal network of resource consuming and producing events into a flow network with noises equal to the events and edges equal to the necessary predecessor links between events. The incremental solution of a staged maximum flow problem on the network is then used to compute the time of occurrence and the height of each step of the resource envelope profile. The staged algorithm has the same computational complexity of solving a maximum flow problem on the entire flow network. This makes this method computationally feasible for use in the inner loop of search-based scheduling algorithms.

Muscettola, Nicola↗

DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗

DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

NASA NTRS1990

A tool for modeling concurrent real-time computation

Real-time computation is a significant area of research in general, and in AI in particular. The complexity of practical real-time problems demands use of knowledge-based problem solving techniques while satisfying real-time performance constraints. Since the demands of a complex real-time problem cannot be predicted (owing to the dynamic nature of the environment) powerful dynamic resource control techniques are needed to monitor and control the performance. A real-time computation model for a real-time tool, an implementation of the QP-Net simulator on a Symbolics machine, and an implementation on a Butterfly multiprocessor machine are briefly described.

Sharma, D. D.↗

NASA NTRS1991

Challenges in building intelligent systems for space mission operations

The purpose here is to provide a top-level look at the stewardship functions performed in space operations, and to identify the major issues and challenges that must be addressed to build intelligent systems that can realistically support operations functions. The focus is on decision support activities involving monitoring, state assessment, goal generation, plan generation, and plan execution. The bottom line is that problem solving in the space operations domain is a very complex process. A variety of knowledge constructs, representations, and reasoning processes are necessary to support effective human problem solving. Emulating these kinds of capabilities in intelligent systems offers major technical challenges that the artificial intelligence community is only beginning to address.

Hartman, Wayne↗

NASA NTRS1980

A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

Wang, S. S.↗

NASA NTRSDate not supplied

Automated Unstructured Grid Adaptation on a Strut Fuel Injector at Hypervelocity Flow Conditions

Computational fluid dynamics (CFD) analysis is presented with the use of an automated unstructured grid adaptation tool on a strut fuel injector at hypervelocity flow conditions. The analysis was carried out with the VULCAN-CFD solver using Reynolds-averaged simulations (RAS). The hypervelocity flow conditions match the high Mach number flow of the experiments conducted as part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center (LaRC). The current work uses an automated grid adaptation tool recently implemented in VULCAN-CFD, and explores this tool’s ability to solve highspeed mixing problems. Simulation results obtained using the unstructured adaptive grid approach are compared to those on a user-generated structured grid. These results are evaluated by analyzing how efficiently comparable fidelity results are obtained from both adapted and structured simulations. In addition, two adaptation strategies were used to explore the impact on the final solution. In the current work, the unstructured grid adaptation tool automatically generates unstructured grids and performs adaptation of the grid based on a Hessian error estimate of a specified flowfield parameter. Multiple adaptations were executed using each run strategy with the one-dimensional values of the mixing efficiency used to determine grid convergence and for comparison with the structured grid simulation results. It was found that the unstructured adaptive grid simulations were able to produce results that matched closely with those on structured grids using far fewer grid cells, and thus, requiring far less computational time to reach the solution. It was also discovered that the adaptation run strategy influenced the total number of grid cells and the efficiency with which a final grid-adapted solution was reached. Furthermore, motivated by the grid convergence index (GCI) used for structured grid simulations, a grid convergence estimate (GCE) was developed and demonstrated for the grid adaptation. Overall, the investigation demonstrated that the automated unstructured grid adaptation tool implemented in VULCAN-CFD is capable of accurately and efficiently solving complex high-speed mixing problems with only a fraction of the grid cells required to obtain comparable results on a user-generated structured grid.

hypersonics↗

NASA NTRSDate not supplied

Automated Unstructured Grid Adaptation on a Strut Fuel Injector at Hypervelocity Flow Conditions

hypersonics↗

NASA NTRS2014

Engineering Antifragile Systems: A Change In Design Philosophy

While technology has made astounding advances in the last century, problems are confronting the engineering community that must be solved. Cost and schedule of producing large systems are increasing at an unsustainable rate and these systems often do not perform as intended. New systems are required that may not be achieved by current methods. To solve these problems, NASA is working to infuse concepts from Complexity Science into the engineering process. Some of these problems may be solved by a change in design philosophy. Instead of designing systems to meet known requirements that will always lead to fragile systems at some degree, systems should be designed wherever possible to be antifragile: designing cognitive cyberphysical systems that can learn from their experience, adapt to unforeseen events they face in their environment, and grow stronger in the face of adversity. Several examples are presented of on ongoing research efforts to employ this philosophy.

Jones, Kennie H.↗

DOE OSTI2023

Computational Science at Los Alamos National Laboratory (Rev. 1) [Slides]

High Performance Computing (HPC) enables problem solving at the grandest scales, on the most complex challenges that face humanity. The problems often tackled by scientific computing are: Very complex; Cool; Using the fastest, most powerful supercomputers on the planet; Often important, impactful, effecting real lives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Solving disorder in (3D) real space: a comparative study of the three-dimensional difference pair distribution function and atomic resolution holography reconstructions

The quantitative analysis of local ordering principles in disordered crystalline systems has gained much attention over the past few years, as it is often considered crucial for optimizing material functionality. This development has been driven by significant advancements in computational and experimental methods, which have led to the establishment and widespread use of various analytical techniques. In this study, we perform model calculations to compare the effectiveness of atomic resolution holography and three-dimensional difference pair distribution function analysis (3D-ΔPDF). Using Cu 3 Au as a model system, we demonstrate an approach to derive local order parameters quantitatively and show that both techniques are well suited to quantifying chemical short-range order correlations and local bond-distance variations. By evaluating the strengths and limitations of both techniques, we advocate for their combined use to solve complex short-range order problems accurately.

3D-ΔPDF↗