Numerical residual perturbation solution applied to an earth satellite including luni-solar effects
Mathematical model and computer program for numerical solution of earth orbit differential equations of motion
MATHEMATICAL MODEL↗
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Results for “Mathematical Computing”
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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A laboratory breadboard system for dual-arm teleoperation
The computing architecture of a novel dual-arm teleoperation system is described. The novelty of this system is that: (1) the master arm is not a replica of the slave arm; it is unspecific to any manipulator and can be used for the control of various robot arms with software modifications; and (2) the force feedback to the general purpose master arm is derived from force-torque sensor data originating from the slave hand. The computing architecture of this breadboard system is a fully synchronized pipeline with unique methods for data handling, communication and mathematical transformations. The computing system is modular, thus inherently extendable. The local control loops at both sites operate at 100 Hz rate, and the end-to-end bilateral (force-reflecting) control loop operates at 200 Hz rate, each loop without interpolation. This provides high-fidelity control. This end-to-end system elevates teleoperation to a new level of capabilities via the use of sensors, microprocessors, novel electronics, and real-time graphics displays. A description is given of a graphic simulation system connected to the dual-arm teleoperation breadboard system. High-fidelity graphic simulation of a telerobot (called Phantom Robot) is used for preview and predictive displays for planning and for real-time control under several seconds communication time delay conditions. High fidelity graphic simulation is obtained by using appropriate calibration techniques.
Bejczy, A. K.↗
Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization
Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.
Wilson, Jeffrey D.↗
Towards a Theory for Integration of Mathematical Verification and Empirical Testing
From the viewpoint of a project manager responsible for the V&V (verification and validation) of a software system, mathematical verification techniques provide a possibly useful orthogonal dimension to otherwise standard empirical testing. However, the value they add to an empirical testing regime both in terms of coverage and in fault detection has been difficult to quantify. Furthermore, potential cost savings from replacing testing with mathematical verification techniques cannot be realized until the tradeoffs and synergies can be formulated. Integration of formal verification with empirical testing is also difficult because the idealized view of mathematical verification providing a correctness proof with total coverage is unrealistic and does not reflect the limitations imposed by computational complexity of mathematical techniques. This paper first describes a framework based on software reliability and formalized fault models for a theory of software design fault detection - and hence the utility of various tools for debugging. It then describes a utility model for integrating mathematical and empirical techniques with respect to fault detection and coverage analysis. It then considers the optimal combination of black-box testing, white-box (structural) testing, and formal methods in V&V of a software system. Using case studies from NASA software systems, it then demonstrates how this utility model can be used in practice.
Lowry, Michael↗
Acceleration of Thermochemistry Solves in MOOSE and Pronghorn
This work focuses on the development and implementation of strategies to accelerate thermochemical calculations within MOOSE-based multiphysics simulations, particularly for applications in MSRs. We highlight the inherent complexity of nuclear materials, which require a multiscale approach to accurately model their behavior across various physical domains, including mechanical, chemical, and thermal phenomena. Thermochemical equilibrium calculations are crucial for predicting material properties and enhancing the fidelity of these simulations. The integration of Thermochimica, a Gibbs energy minimizer, into MOOSE allows for the direct minimization of Gibbs energy at every point on the mesh. However, the computational cost of such integration is significant. To address this, we explored acceleration strategies such as multi-threading support and the use of a thermodynamic ValueCache to reduce redundant calculations. Additionally, we investigated modifications to Thermochimica to enable phase constraints and improve its coupling with phase-field models, which are essential for simulating microstructural evolution and corrosion in MSR. These efforts aim to optimize the computational efficiency and accuracy of multiphysics simulations, thereby supporting the development of reliable and efficient nuclear materials for next-generation reactor technologies.
36 - MATERIALS SCIENCE↗
Total Effective Dose from Radiologic Emissions from INL Facilities for Calculation of Population Dose for the INL 2024 Annual Site Environmental Report
Total effective radiation dose from airborne releases was calculated using air dispersion modeling performed by the National Oceanic and Atmospheric Administration (NOAA) Idaho Falls Office using their HYSPLIT computer model (Stein et al. 2015; Draxler et al. 2013), and the Dose Multi-Media (DOSEMM) dose assessment model (Rood 2019) . The objective of these calculations was to provide a grid of total effective dose across a model domain that encompasses a 50-mile (80-km) radius from any Idaho National Laboratory (INL) Site source. In addition to INL Site sources, releases from the Radiological and Environmental Sciences Laboratory (RESL) (IF-683) and IF-603 located at the INL Research Center (IRC) within the Idaho Falls city limits were also included. Due to tracking limitations, radionuclides released from IF-611 and IF-603 are modeled as released from IF-603. The dose results will be combined with GIS software to compute a total population dose for the calendar year (CY) 2024 and will be reported in the INL Annual Site Environmental Report (ASER). This report does not cover the population dose calculation and only documents generation of the gridded dose file.
42 - ENGINEERING↗
SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations
Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.
97 MATHEMATICS AND COMPUTING↗
Performance Improvements of the Griffin Solvers in FY24
The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Systems-To-Atoms (S2A): enabling hydrogen for climate security
The project addresses a critical gap in hydrogen infrastructure by integrating system-level energy models with atomic-scale material simulations in a unified Systems-to-Atoms (S2A) framework. The motivation stems from the need to develop efficient, cost-effective, and durable hydrogen transport and utilization technologies to support decarbonization of hard-to-electrify sectors such as heavy-duty transportation. Current system models lack awareness of material performance mechanisms, while material-scale models do not account for system-level usage and variability. To bridge this divide, the team developed a co-simulation capability linking techno-economic analyses, reactor/process-flow modeling, and molecular-scale catalysis simulations. Applied to hydrogen delivery in California, the framework enabled comparative evaluations of compressed, cryogenic, and liquid organic hydrogen carrier (LOHC) pathways, highlighting how catalyst operation and unit process efficiency influence overall performance. The results demonstrate that no single material or transport mode is universally optimal; instead, heterogeneous solutions tuned to specific operational contexts deliver better performance. The project delivers a new capability for cross-scale material co-design, advancing hydrogen infrastructure readiness and informing DOE and LLNL missions in climate and energy resilience.
organic↗
An on-line system for hand-printed input
The capability of graphic input/output systems is described. Topics considered are a character recognizer and dictionary building program, an initial flow chart element input program, and a system entitled The Assistant Mathematician, which uses ordinary mathematics to specify numeric computation. All three parts are necessary to allow a user to carry on a mathematical dialogue with the computer in the language and notation of his discipline or problem domain.
Williams, T. G.↗
A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications
Our work on the DOE-sponsored project “A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications,” was an effort to address critical challenges in nu merical computing and its applications to optimization. The increasing demand for robust and scalable solutions to large-scale linear algebra problems has highlighted the limitations of traditional approaches, particularly in heterogeneous and extreme-scale computing environments. Randomized Numerical Linear Algebra (RandNLA) offers a promising framework to address these challenges, and this proposal builds on this foundation by introducing innovations in sensitivity analysis and computational adaptability.
97 MATHEMATICS AND COMPUTING↗
Quantification and Utilization of Subjectively Determined Data in the Construction of Mathematical Models
Quantification and utilization of subjectively determined data in construction of mathematical models
COMPUTER METHOD↗
Accelerating magnonic simulations with the pseudospectral Landau-Lifshitz equation
The pseudospectral Landau-Lifshitz (PS-LL) model can describe atomic-scale magnetic exchange interactions within a continuum framework. This is achieved by employing a convolution kernel that models the nonlocal interaction in a grid-independent manner. Even though the PS-LL was originally introduced to address atomic exchange, any nonlocal kernel can be modeled. In the field of magnonics, the dipole field is fundamental to describe the dispersion relation of magnons, the quasiparticle representation of angular momentum. Because dipole-dipole interactions are long-range, numerical approaches typically rely on convolutions. Here, we demonstrate that the PS-LL model can be used to perform magnonic simulations with a single convolution kernel derived from analytical solutions. We demonstrate a twofold increase in computational speed compared with the full dipole calculation. This approach is valid insofar as the excitations are linear, which is typically the case for magnons. Our results have the potential to accelerate magnonic research, particularly for the inverse design method, where several simulations must be performed to achieve the desired outcome.
Mathematics and computing↗
Surrogate Model Integration with MOOSE XFEM for Creep Crack Growth
Ferritic-martensitic steels are key structural materials for advanced reactors but experience time-dependent deformation and damage under prolonged high temperature and irradiation, leading to creep-driven crack initiation and growth. High-fidelity models—crystal plasticity with irradiation mechanisms, phase-field for microstructural evolution, and continuum-damage viscoplasticity—capture the underlying physics but are too computationally intensive for broad design-space exploration and uncertainty quantification. This milestone advances a scalable alternative by integrating a microstructure-sensitive surrogate creep model into the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework and extending it to fracture via the extended finite element method (XFEM). The surrogate model, developed with collaborators at Sandia and Los Alamos National Laboratories, maps relevant microstructural descriptors to the viscoplastic response of HT9. We embed this surrogate within a coupled deformation-damage workflow in MOOSE/XFEM to simulate creep-driven crack initiation and propagation. Implementation enhancements include updates to the material interface, a plastic correction phase involving microstructure evolution, and fracture criteria to ensure numerical robustness and compatibility with the surrogate structure. Demonstrations on canonical creep benchmarks spanning uniaxial and multiaxial states show that the surrogate reproduces key trends of high-fidelity models while substantially reducing computational cost. The resulting capability bridges physics fidelity and performance, providing a practical path to a predictive, microstructure-aware assessment of creep and fracture in reactor materials.
36 - MATERIALS SCIENCE↗
Automatic computation of data-set definitions
Mathematical method for the construction of a computer program data set description from a computer program contains detailed declarative information. Cartesian products and disjoint-union operators are used to yield a series of recursive group equations.
Reynolds, J. C.↗
On The Incorporation of Both Function-Driven Requirements and Topology Optimization in The Development of Lunar Launch & Landing Pads
In the design of additively manufactured structures, there can be a constant battle between focusing on function-driven design and topology optimization in an attempt to improve a products ability to meet all requirements. Function-driven optimization is defined as the process of identifying the best design parameters that satisfy project functionality requirements. Function-driven optimization is typically implemented by a designer(s) who, instead of computational limitations, has human bias for the input or inputs determined. On the other hand, topology optimization is defined as a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions, and constraints with the goal of maximizing the performance of the system. In topology optimization, the work is defined by the limited mathematical inputs and computationally available goals/restraints. If not evaluated simultaneously, these two approaches can result in fundamentally different design concepts meant to address the same requirements. NASA’s Artemis program includes the development of a base camp near the lunar South Pole. After site selection is made, one of the first infrastructure elements needed will be a launch and landing pad (LLP). The construction of such a pad will prevent damage to nearby structures from plume-surface interaction (PSI) while also providing a stable platform for the lander. These benefits reduce the required distance between the established landing zones and other settlement infrastructure. In this paper, the authors evaluate the requirements associated with lunar LLP development, application of both functional and topological optimization techniques, methodologies to combine the two techniques, and potential impacts on final design of such a pad.
In-situ↗
Data Compilation and Analysis from the Sirius-1 Experiment at TREAT for Transient Simulation Validation
This report assembles comprehensive data from the Sirius-1 experiment conducted by Idaho National Laboratory in collaboration with the National Aeronautics and Space Administration. The primary goal is to provide a robust data set that external users can utilize for the validation of computational methods for transient multiphysics simulations. By compiling all relevant data, including experiment design calculations, detailed engineering drawings for the experiment and data from reactor and fuel specimen measurement, this report is intended to serves as a reference for researchers and engineers working on the development and validation of computational models for transient nuclear behavior.
21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
Accelerating Innovative Energy Solutions Using Combustion Simulations
Combustion-based transportation, electricity generation, and industrial heating in manufacturing constitute the three largest sectors of energy demand. Some of the recent technology development in these sectors are: switching to low-carbon fuels for the transportation sector, increasing energy efficiency in the power sector, and capturing carbon emissions from conventional power generators. Several teams at the National Renewable Energy Laboratory have been actively advancing research in these areas by leveraging computational modeling of combustion processes across the heavy-duty land based transportation, aviation, and power generation sectors. This article summarizes some of these efforts, demonstrating the potential of advanced computational techniques to generate technological solutions that will transform the global energy system.
08 HYDROGEN↗