Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical solver”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Physics-Informed Graph Neural Networks for Collaborative Dynamic Reconfiguration and Voltage Regulation in Unbalanced Distribution Systems

Network reconfiguration has long been employed as a strategic approach to minimize power distribution system losses and effectively regulate voltage levels. Tap-changing voltage regulators are also critical for controlling bus voltages, especially in accommodating the increasing integration of distributed energy resources (DERs) with intermittent outputs. This paper introduces novel methodologies to address the challenges of dynamic reconfiguration and optimal tap setting in unbalanced three-phase distribution systems. We propose an approximated mixed-integer quadratically constrained program (MIQCP) to model dynamic reconfiguration, along with a pioneering formulation for voltage regulator (VR) tap-setting based on Special Ordered Set type 1 (SOS1). To mitigate computational complexity, we propose a physics-informed spatial-temporal graph convolutional network (STGCN) with an integrated link classifier. The proposed approach enables efficient solution generation by fixing specific variables in the MIQCP instance and solving the simplified sub-MIP using an MIP solver. Numerical studies demonstrate the superior prediction accuracy of our STGCN model compared to baseline neural network models, resulting in reduced DER curtailment and voltage deviation with shorter computation time.

dynamic reconfiguration↗

SU-E-T-270: Diffusion Synthetic Acceleration for Linear Boltzmann Transport Equation

Purpose: Linear Boltzmann transport equation (LBTE) is as accurate as the Monte Carlo method (MC) for dose calculation in photon/particle therapy (LBTE is a deterministic and Eulerian formulation and MC is a statistical and Lagrangian description). An advantage of LBTE is that numerous acceleration techniques can be utilized for acceleration. This work is to explore the acceleration of LBTE via diffusion synthetic acceleration (DSA). Methods: For simplicity, two-dimensional, steady-state, and within-group LBTE is considered with two angular dimensions and two spatial dimensions. The discrete ordinate method is developed for solving this integro-differential equation. The angular variables are discretized using a level-symmetric quadrature set on the unit sphere. The spatial variables are discretized on the structured grid based on the diamond scheme. The source-iteration method (SI) is used to solve the discretized system.Since SI is slow in optically thick and highly scattering regime. DSA is developed to accelerate SI. The motivation for DSA is that diffusion equation (DE) is a good approximation of LBTE in the above regime. However, DE is much cheaper than LBTE computationally since DE only involves spatial variables. Thus, in each DSA iteration, DSA adds to the SI step a computationally-negligible DE step, i.e., to first solve DE with the SI residual as source term, and then compensate the SI solution with DE solution. Results: DSA was benchmarked and compared with SI. The difference between two methods was within 0.12% which verifies the accuracy of DSA, while DSA demonstrated the great advantage in speed, e.g., the reduction of iteration number to 6% and 4% respectively for cases with 100 and 1,000 scattering-absorption ratio that commonly occur in clinical dose calculation. Conclusion: DSA has been developed as one of many possible means for accelerating the numerical solver of LBTE for dose calculation. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.

97 MATHEMATICS AND COMPUTING↗

Atmospheric Profile Builder

APBuilder is a software tool designed to generate atmospheric profiles for use with AC2Dr by downloading weather model data and transforming it into 1D or 2D binary profiles. These binary profiles serve as required inputs for AC2Dr, an LLNL-developed, open source, two-dimensional numerical solver for the acoustic wave equation based on the finite difference method.

Kim, Keehoon [Lawrence Livermore National Laborato↗

Sunny.jl

Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for simulating spin dynamics both in and out of equilibrium. Uniquely, it features a broad generalization of classical and semiclassical approaches to SU(N) coherent states, which is useful for studying systems exhibiting strong spin-orbit coupling or local entanglement effects. Sunny also offers a well-developed framework for calculating the dynamical spin structure factor, enabling direct comparison with scattering experiments. Ease of use is a priority, with tools for symmetry-guided modeling and interactive visualization.

Dahlbom, David↗

Sunny.jl: A Julia Package for Spin Dynamics

Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for simulating spin dynamics both in and out of equilibrium. Uniquely, it features a broad generalization of classical and semiclassical approaches to SU(N) coherent states, which is useful for studying systems exhibiting strong spin-orbit coupling or local entanglement effects. Sunny also offers a well-developed framework for calculating the dynamical spin structure factor, enabling direct comparison with scattering experiments. Ease of use is a priority, with tools for symmetry-guided modeling and interactive visualization.

97 MATHEMATICS AND COMPUTING↗

Plan to Verify and Validate Multi-Hazard Risk-Informed Margin Management Methods and Tools

This report describes the development plan for verification and validation (V&V) of multihazard risk informed margin management (RIMM) methods and tools. The plan will include using new INL developed tool sets coupled with the new multi-partner External Hazards Experimental Group (EHEG) coordinated by the Idaho National Laboratory (INL) within the Risk-Informed Safety Margin Characterization (RISMC) technical pathway of the Light Water Reactor Sustainability Program. The RISMC pathway is developing a suite of new tools and methods for advanced evaluation of facility risk. The RISMC toolkit, includes tools and methods focused on evaluation of risk from external hazards (e.g, seismic and flooding events), which have been shown to be dominant risk contributors in probabilistic risk assessments performed for operating nuclear power plants (NPPs). The external events activity (EEA) within the RISMC pathway is tasked with developing tools and methods focused on evaluation of multi-hazard external risk (e.g, seismic and flooding events). The EHEG will provide technical expertise and experimental large-scale testing data needed for development and validation of tools and methods in the RISMC toolkit for external hazard safety evaluations. The EEA within RISMC has two key elements: (1) an organizational and research framework provided by INL and (2) a coordinated group of university and national laboratory partners with the complementary expertise and experimental capabilities needed to conduct large-scale external hazard-focused experiments. This cooperative group will allow INL to leverage a range of existing capabilities to meet the unique needs of RISMC tool and method development. In addition, the capabilities of the EHEG could be used to address needs of other national laboratories. Currently, there is limited data available for development and validation of the tools and methods being developed in the RISMC Toolkit. The EHEG is being developed to obtain high quality, large-scale experimental data validation of RISMC tools and methods in a timely and cost-effective way. The group of universities and national laboratories that will eventually form the EHEG (which is ultimately expected to include both the initial participants and other universities and national laboratories that have been identified) have the expertise and experimental capabilities needed to both obtain and compile existing data archives and perform additional seismic and flooding experiments. The data developed by EHEG will be stored in databases within RISMC. These databases will be used to validate the advanced external hazard tools and methods. The numerical tools under development in RISMC are used to evaluate the impacts that external hazards have on nuclear power plants. These analysis tools will be used to advanced current risk calculation processes and reduce uncertainty in these calculations. To have confidence in the predictive capability of these numerical tools it is important to verify and validate them. To verify and validate numerical tools the user must understand what physics is being used to represent the problem (i.e. constitutive models used to represent the soil and structure), the numerical solver approach used (i.e. finite element), what data already exists that could be used to validate the tools, and what data is needed for validation.

31274↗

Five years of ForTrilinos ECP

The ForTrilinos subproject of the Exascale Computing Project (ECP) was initiated to bring the capabilities and scalability of the Trilinos numerical solver collection to Fortran scientific application codes. A novel Fortran extension to the Simplified Wrapper and Interface Generator (SWIG) tool, which automatically generates Fortran bindings from existing C/C++ library code, has been applied to key Trilinos solver libraries to generate the new ForTrilinos libraries. SWIG-Fortran has additionally been used to generate new Fortran compatibility layers for additional scientific libraries and applications. This report summarizes the products and impact of the ForTrilinos subproject.

97 MATHEMATICS AND COMPUTING↗

Engineering Computational Practices (Rev. 1)

This manual will attempt to motivate the use of an automated build system for the purposes of computational science and engineering. As part of this motivation, the surrounding computational practices of version control, documen tation, compute environment management, and regression testing will also be addressed as applied to the practice of computational engineering. Specifically, this manual intends to motivate the adoption of these traditional software engineering practices for use in research and production engineering simulation projects. This manual is not the first such effort in the greater scientific computing community. In fact, the authors relied heavily on the lesson plans of the Software Carpentry, established to teach computing skills to researchers in 1998. As the intention for this manual is to lay out fundamental practices of engineering computing, it will not attempt to fully teach the underlying concepts and will instead reference the well designed lesson plans of the Software Carpentry. Where possible, this manual will explain to general computing practices and concepts and limit discussion of specific software implementations to examples or vehicles for practice in concrete application. The specific software taught by the Software Carpentry curriculum is an excellent starting point to learn the core concepts of computational engi neering. However, the authors have found that applications to engineering simulation and analysis require translation of these software development concepts into the language and workflows of computational engineers. Adopting these computational tools may require engineers to re-imagine their workflows in some combination of traditional engineer ing and software concepts. It has also been necessary to extend existing software build systems for engineering practices beyond the simple wrap ping of engineering software execution. Where necessary, examples of specific software and their method of extension to engineering simulations will be given, with reference to the User Manual for recommended practical use. Where this manual relies on specific implementation examples, it should be understood that the practicing engineer may find that different software is more amenable to their specific work. It is always the overall collection of computational practices is more important than any specific software implementation. The ability to recognize which concepts are implemented by a software package will make a practicing engineer agile to changing project needs, computing resources, numeric solvers, programming languages, and even available funding.

42 ENGINEERING↗

Electromagnetic Field Simulation Utilizing VERTEX

The understanding of electromagnetic fields is essential for many core applications at Oak Ridge National Laboratory (ORNL). Electromagnetic fields play an important role in particle accelerators, antennas, electric motors, power grids, and are principal part of nuclear fusion. We develop a numerical solver called able to treat the Maxwell system utilizing ORNL's VERTEX framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SVD Orbit Correction in Zgoubi And Examples: SATURNE, RHIC, EIC RCS

This Tech. Note describes the SVD technique in the Lorentz force numerical solver zgoubi. It has been used as a tool to study the effect of vertical orbit perturbation on polarization transmission in RHIC, and for the study of the compensation of orbit defects resulting from stray fields in the EIC RCS.

43 PARTICLE ACCELERATORS↗

A Physics-Informed Deep Learning Description of Knudsen Layer Reactivity Reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

GCAM Regional Tuning: A framework to tune GCAM parameters

GCAM assumptions typically generate scenarios that are designed to be internally consistent and globally coherent. The gcamdata tool which facilitates the compilation of data sets and user assumptions is not well suited to tailoring to specific country or regional realities, sponsor requirements, or perform harmonization for model intercomparison needs. As described in this report, the GCAM Regional Tuning project develops a computational framework that enables users to adjust GCAM parameters, so model outputs match targeted outcomes at user-defined spatial, temporal, and sectoral resolutions. The framework integrates GCAM, gcamdata, and gcamwrapper with a set of flexible “tuning directives” and an iterative numerical solver. Users can define targets (e.g., technology shares in power generation, BEV uptake, sectoral service demands), select tuners that manipulate relevant GCAM parameters (e.g., share weights, cost adders, elasticities), and export tuned parameters as reusable GCAM XML inputs for future runs. We demonstrate the approach and document usage, diagnostics, and known limitations, and we outline potential future directions.

97 MATHEMATICS AND COMPUTING↗

A Continuous-Discontinuous Galerkin Method for Electromagnetic Simulations Based on an All-Frequency Stable Formulation

In this paper, a potential-based partial-differential formulation, called the all-frequency stable formulation, is presented for the accurate and robust simulation of electromagnetic problems at all frequencies. Due to its stability from (near) dc to microwave frequencies, this formulation can be applied to simulate wide-band and multiscale problems without encountering the infamous low-frequency breakdown issue or applying basis function decompositions such as the tree-cotree splitting technique. To provide both efficient and flexible numerical solutions to the electromagnetic formulation, a mixed continuous-discontinuous Galerkin (CDG) method is proposed and implemented. In regions with homogeneous media, the continuous Galerkin method is employed to avoid the introduction of duplicated degrees of freedom (DoFs) on the elemental interfaces, while on the interfaces of two different media, the discontinuous Galerkin method is applied to permit the jump of the normal components of the electromagnetic fields. Numerical examples are provided to validate and demonstrate the proposed numerical solver for problems in a wide electromagnetic spectrum.

Yan, Su↗

Tycho: Realistically Simulating Exoplanets within Stellar Clusters. I. Improving the Monte Carlo Approach

To fully understand the diverse population of exoplanets, we must study their early lives within open clusters, the birthplace of most stars with masses >0.5M {sub ⊙} (including those currently in the field). Indeed, when we observe planets within clustered environments, we notice highly eccentric and odd systems that suggest the importance of dynamical pathways created by interactions with additional bodies (as in the case of HD 285507b). However, it has proven difficult to investigate these effects, as many current numerical solvers for the multi-scale N-body problem are simplified and limited in scope. To remedy this, we aim to create a physically complete computational solution to explore the role of stellar close encounters and interplanetary interactions in producing the observed exoplanet populations for both open cluster stars and field stars. We present a new code, Tycho, which employs a variety of different computational techniques, including multiple N-body integration methods, close encounter handling, modified Monte Carlo scattering experiments, and a variety of empirically informed initial conditions. We discuss the methodology in detail, and its implementation within the AMUSE software framework. Approximately 1% of our systems are promptly disrupted by star-star encounters contributing to the rogue planets occurrence rate. Additionally, we find that close encounters which that perturb long-period planets lead to 38.3% of solar-system-like planetary systems becoming long-term unstable.

79 ASTRONOMY AND ASTROPHYSICS↗

HIS-TORIC: Extending core ICRF wave simulation to include realistic SOL plasmas

This paper presents a novel approach to incorporating an arbitrarily shaped edge scrape-off-layer (SOL) plasma and an ion cyclotron range of frequency (ICRF) antenna structure into existing core ICRF wave simulation models. We partition the entire computation domain into two sub-domains: a core and an edge region. Simulations in each domain are performed separately with appropriate numerical solvers. For the core, the TORIC ICRF solver [M. Brambilla, Plasma Phys. Contrl. Fusion 41, 1 (1999)] was modified to impose an essential (Dirichlet) boundary condition at its interface with the edge domain. In the edge, a finite element method (FEM) is used to solve a cold collisional plasma model. The domains are then joined together using the continuity boundary condition for the tangential electric and magnetic fields at their interfaces (Hybrid Integration of SOL to TORIC: HIS-TORIC). The model developed here was tested using an ICRH H minority heating scenario on the Alcator C-Mod tokamak [I. Hutchinson et. al., Phys. Plasmas 1, 1511 (1994)]. The simulated pattern of core wave propagation agrees well with a standard TORIC simulation. This approach opens the possibility of using a realistic diverted SOL plasma and a complicated 3D RF antenna together with a rigorous hot core plasma model, while requiring only minimal modification to existing RF codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma response to the injection of an electron beam

The results of Vlasov-Poisson-solver numerical simulations of the detailed temporal response of a Maxwellian plasma to the sudden injection of an electron beam are presented in graphs and maps and discussed. Phenomena characterized include ion bursts, electron shocks and holes, plasma heating and expulsion, density gradients; cavitons, deep-density-front and solitary-pulse propagation down the density gradient, and Bunemann-mode excitation leading to formation of a virtual cathode and double layers which are at first monotonic or have low-potential-side dips or high-potential-side bumps and become strong as the electron-current density decreases. The strength of the double layer is found to be roughly proportional to the beam energy.

Singh, N.↗

A theoretical investigation of laser-sustained plasma thruster

A numerical code has been successfully developed for the investigation of thruster performance using a laser-sustained hydrogen plasma as the propellant. The plasma was sustained using a 10.6-micron CO2 laser beam focused at different positions within the thruster. The physical model assumed that plasma is in thermodynamical equilibrium (LTE), and geometric ray tracing was adopted to describe the laser beam. The steady-state, axisymmetric, Navier-Stokes equations coupled with the laser power absorption process have been solved numerically. A pressure based Navier-Stokes numerical solver using body-fitted coordinates was used to calculate the laser-supported rocket flow which includes both subsonic and supersonic flow regions. From the limited parametric study, which did not try to optimize the rocket performance, it was found that better performance was obtained when the laser beam was focused closer to the rocket throat.

Jeng, San-Mou↗