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

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The future of computing beyond Moore’s Law

Moore’s Law is a techno-economic model that has enabled the information technology industry to double the performance and functionality of digital electronics roughly every 2 years within a fixed cost, power and area. Advances in silicon lithography have enabled this exponential miniaturization of electronics, but, as transistors reach atomic scale and fabrication costs continue to rise, the classical technological driver that has underpinned Moore’s Law for 50 years is failing and is anticipated to flatten by 2025. Here, this article provides an updated view of what a post-exascale system will look like and the challenges ahead, based on our most recent understanding of technology roadmaps. It also discusses the tapering of historical improvements, and how it affects options available to continue scaling of successors to the first exascale machine. Lastly, this article covers the many different opportunities and strategies available to continue computing performance improvements in the absence of historical technology drivers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Superconvergence of Online Optimization for Model Predictive Control

We develop a one-Newton-step-per-horizon, online, lag-L, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, while the algorithmic error, determined by Newton’s method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of L. In conclusion, numerical experiments validate our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power densities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

SINDA - Systems Improved Numerical Differencing Analyzer

Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.

Damico, Steve J.↗
DOE OSTI2020

A Nonlinear Regression Method for Composite Protection Modeling of Induction Motor Loads

Protection equipment are used to prevent damages to induction motor loads by isolating those from the power network in the event of severe faults. Modeling the response of induction motor loads and their protection is vital for power system planning and operation, especially in understanding system's response moments after a fault has occurred. This article proposes an optimization based framework to generate composite protection models for commercial building motor loads. Introducing a mathematical abstraction, the task of finding a suitable (simplified) model of the composite protection scheme is formulated as a nonlinear regression problem. Numerical examples are provided to illustrate the application of the framework.

Kundu, Soumya↗
DOE OSTI2023

Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. Here, we demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Coupling of Transport and Chemical Processes in Catalytic Combustion

Catalytic combustors have demonstrated the ability to operate efficiently over a much wider range of fuel air ratios than are imposed by the flammability limits of conventional combustors. Extensive commercial use however needs the following: (1) the design of a catalyst with low ignition temperature and high temperature stability, (2) reducing fatigue due to thermal stresses during transient operation, and (3) the development of mathematical models that can be used as design optimization tools to isolate promising operating ranges for the numerous operating parameters. The current program of research involves the development of a two dimensional transient catalytic combustion model and the development of a new catalyst with low temperature light-off and high temperature stablity characteristics.

Bracco, F. V.↗
NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗
NASA NTRS1986

The mathematical modeling of rapid solidification processing

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Gutierrez-Miravete, E.↗
NASA NTRS1989

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗
NASA NTRS2006

Inspiring the Next Generation: Student Experiments and Educational Activities on the International Space Station, 2000-2006

One important objective of NASA has always been to inspire the next generation. NASA and human space flight have a unique ability to capture the imaginations of both students and teachers. The presence of humans onboard the International Space Station (ISS) for more than five years now has provided a foundation for numerous educational activities aimed at capturing the interest and motivating study in the sciences, technology, engineering, and mathematics. Yet even before the Expedition 1 crew arrived at station in November 2000, experiments with student participation were being conducted onboard ISS in support of NASA missions. One of NASA's protein crystal growth experiments had been delivered to station by the shuttle Atlantis during STS-106 in September 2000 and was returned to Earth six weeks later aboard the shuttle Discovery during the STS-92 mission. From very early on it was recognized that students would have a strong interest in the ISS, and that this would provide a unique opportunity for them to get involved and participate in science and engineering projects on ISS. It should be noted that participation is not limited to U.S. students but involves the 16 International Partner countries and various other countries under special commercial agree

Thomas, Donald A.↗
NASA NTRS2012

The International Space Station (ISS) Education Accomplishments and Opportunities

The International Space Station (ISS) has the unique ability to capture the imaginations of both students and teachers worldwide and thus stands as an invaluable learning platform for the advancement of proficiency in research and development and education. The presence of humans on board ISS for the past ten years has provided a foundation for numerous educational activities aimed at capturing that interest and motivating study in the sciences, technology, engineering and mathematics (STEM) disciplines which will lead to an increase in quality of teachers, advancements in research and development, an increase in the global reputation for intellectual achievement, and an expanded ability to pursue unchartered avenues towards a brighter future. Over 41 million students around the world have participated in ISS-related activities since the year 2000. Projects such as the Amateur Radio on International Space Station (ARISS) and Earth Knowledge Acquired by Middle School Students (EarthKAM), among others, have allowed for global student, teacher, and public access to space through radio contacts with crewmembers and student image acquisition respectively. . With planned ISS operations at least until 2020, projects like the aforementioned and their accompanying educational materials will be available to enable increased STEM literacy around the world. Since the launch of the first ISS element, a wide range of student experiments and educational activities have been performed by each of the international partner agencies: National Aeronautics and Space Administration (NASA), Canadian Space Agency (CSA), European Space Agency (ESA), Japan Aerospace Exploration Agency (JAXA) and Russian Federal Space Agency (Roscosmos). Additionally, a number of non-participating countries, some under commercial agreements, have also participated in Station-related activities. Many of these programs still continue while others are being developed and added to the station crewmembers tasks on a regular basis. These diverse student experiments and programs fall into one of the following categories: student-developed experiments; students performing classroom versions of ISS experiments; students participating in ISS investigator experiments; students participating in ISS engineering education; education demonstrations and cultural activities. This paper summarizes some of the main student experiments and educational activities that have been conducted on the ISS. It also highlights some upcoming projects.

Alleyne, Camille W.↗
NASA NTRS2014

Inspiring the Next Generation: The International Space Station Education Accomplishments

The International Space Station (ISS) has a unique ability to capture the imagination of both students and teachers worldwide. Since 2000, the presence of humans onboard ISS has provided a foundation for numerous educational activities aimed at capturing that interest and motivating study in the sciences, technology, engineering and mathematics (STEM). Over 43 million students around the world have participated in ISS-related educational activities. Projects such as YouTube Space Lab, Sally Ride Earth Knowledge-based Acquired by Middle Schools (EarthKAM), SPHERES (Synchronized Position Hold Engage and Reorient Experimental Satellites) Zero-Robotics, Tomatosphere, and MAI-75 events among others have allowed for global student, teacher and public access to space through student classroom investigations and real-time audio and video contacts with crewmembers. Educational activities are not limited to STEM but encompass all aspects of the human condition. This is well illustrated in the Uchu Renshi project, a chain poem initiated by an astronaut while in space and continued and completed by people on Earth. With ISS operations now extended to 2024, projects like these and their accompanying educational materials are available to more students around the world. From very early on in the program's history, students have been provided with a unique opportunity to get involved and participate in science and engineering projects. Many of these projects support inquiry-based learning that allows students to ask questions, develop hypothesis-derived experiments, obtain supporting evidence and identify solutions or explanations. This approach to learning is well-published as one of the most effective ways to inspire students to pursue careers in scientific and technology fields. Ever since the first space station element was launched, a wide range of student experiments and educational activities have been performed, both individually and collaboratively, by all the international partner agencies, National Aeronautics and Space Administration (NASA), Canadian Space Agency (CSA), European Space Agency, (ESA), Japan Aerospace Exploration Agency (JAXA) and Russian Federal Space Agency (Roscosmos), and a number of non-participating countries, some under commercial agreements. Many of these programs still continue, and others are being developed and added to the stations tasks on a regular basis. These diverse student experiments and programs fall into one of the following categories: student-developed experiments; students performing classroom versions of ISS experiments; students participating in ISS investigator experiments; education competitions; students participating in ISS Engineering Education; Education Demonstrations and Cultural Activities. This paper summarizes some of the main student experiments and educational activities that have been conducted on the space station.

Alleyne, Camille W.↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗