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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗
DOE OSTI2025

Development of a River Dynamical Core for E3SM to simulate compound flooding on Exascale-class heterogeneous supercomputers

Flooding events pose significant risk to human life, property, and infrastructure. Physically-consistent quantification of altered flood risks in global models requires hyper-resolution (~1 km) or fine flood simulations using two-dimensional (2D) physics schemes, both of which are unavailable in the current generation Earth System Models. Here, in this work, we have developed the River Dynamical Core (RDycore), which is an open-source, 2D shallow water equation (SWE) library for the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). RDycore uses PETSc and libCEED libraries that allows it to run efficiently on CPUs and GPUs, as well as select a time-integration algorithm at runtime without requiring any code modifications. RDycore achieves spatial error convergence rates for problems with analytical and manufactured solutions similar to those reported previously in the literature, or consistent with the implemented first-order spatial discretization scheme. RDycore's accuracy in predicting flooding for a well-studied dam break problem is comparable to existing SWE models. For a problem with 471 million grid cells, RDycore achieves a speedup of 6.6x and 7.6x on GPUs compared to CPUs when using 320 compute nodes on DOE's Perlmutter and Frontier supercomputers, respectively. The one-way coupling of the RDycore library within E3SM is demonstrated by performing multiple 5-day flooding simulations during Hurricane Harvey driven by five precipitation datasets. The E3SM--RDycore simulations at 30 m spatial resolution accurately simulate maximum water height during the hurricane when benchmarked against a previously published study and achieve a speedup of 15x (Perlmutter) and 21x (Frontier) on GPUs relative to CPUs. The work presented here is the foundational step in providing hardware and algorithmic portability framework for simulating kilometer-scale river dynamics within E3SM.

Flood Simulation↗
DOE OSTI2024

A Verification Suite of Test Cases for the Barotropic Solver of Ocean Models

Abstract The development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs designed to verify the barotropic solver of atmosphere and ocean models. These include the non‐dispersive coastal Kelvin wave; the dispersive inertia‐gravity wave; the dispersive planetary and topographic Rossby waves; the barotropic tide; and a non‐linear manufactured solution. These TCs check the implementation of the linear pressure gradient term; the linear constant or variable‐coefficient Coriolis and bathymetry terms; and the non‐linear advection terms. Simulation results are presented for a variety of time‐stepping methods as well as two spatial discretizations: a mimetic finite volume method based on the TRiSK scheme, and a high‐order discontinuous Galerkin spectral element method. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Functional Nano-to-Microstructures by Jet Printing and Direct Ink Writing

Jet-based printing techniques and direct ink writing have emerged as complementary, convergent technologies serving as key platforms in additive manufacturing for functional nano- to microscale architectures. This review highlights how these approaches enable fine feature resolution and three-dimensional structures in advanced electronics and biointerfacing applications. The interplay of fluid mechanics, viscoelastic ink rheology, droplet–substrate interactions, and drying dynamics is examined as a critical determinant of printing fidelity. Application-focused case studies, from flexible thin-film transistors to bioprinted artificial tissues, demonstrate how precise structural control via printing translates to enhanced device performance and new functionality in electronic and biological systems. Finally, we discuss the challenges and future opportunities driving the evolution of these printing platforms toward autonomous, adaptive, and intelligent manufacturing systems.

Luo, Junchen [Sichuan Univ. of Arts and Science (C↗
DOE OSTI2023

Verification and validation of the open-source plasma fluid code: Zapdos

Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10 -2 to 10 -4 , while the convergence’s slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry and metastable density measurements by planar laser-induced fluorescence imaging. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Furthermore, probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at https://github.com/shannon-lab/zapdos.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Impact of lead on an axisymmetric, single bead blown powder DED overhung geometry

Metal additive manufacturing can be utilized for the near net-shape manufacture of components in a layer wise technique. Traditionally, the buildup process is conducted in the direction of gravity or bottom to top in the vertical orientation; however, with the availability of commercial systems with additive heads or fixturing that can index from vertical, and the need to manufacture larger parts without modifying available systems, the limitation of manufacturing from bottom to top is removed enabling the buildup of larger components printed at an angle from vertical. The effect of gravity on the melt pool and as-deposited component quality when printing off vertical is unknown in literature, especially for axisymmetric components. This understanding is critical for the advancement of manufacturing components of increased size in 4 and 5-axis additive systems. This investigation utilizes blown powder directed energy deposition to evaluate the change in as-printed geometry when the start point is altered in relation to gravity while the part rotates to manufacture an axisymmetric component. The objectives of this work are to determine the impact of the deposition location on the geometric variability on axisymmetric components. This investigation tests the hypothesis that differences in layer height exist due to a change in catchment efficiency when the deposition location is moved to a tangent of the round geometry due to a change in the melt pool dynamics. It was found the ideal deposition location when printing at 26.6-degrees from vertical was at −90-degrees from the top center point of the component, along the tangent, where gravity was pushing the melt pool down, but the rotation of the part was pulling the deposited material towards the top center of the component. This work provides an understanding of layer height stability and catchment efficiency to guide print orientation strategy for high-aspect ratio components. It was found the −90-degree lead deposition had the best layer height stability at 0.6 % as compared to the top-center at 6.3 % and +90-degree deposition location at 9.2 % for the nominal programmed layer height. The change in layer height also effected the final diameter the greatest for the top center deposition location where the diameter diverged by 2.5 % during the overbuild condition and converged by 0.6 %. In conclusion, this finding will increase the manufacturing efficiency of axisymmetric components by increasing the passive stability of the printing process for the successful manufacture of parts without the need for perfectly calibrated manufacturing parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Fully consistent Eulerian Monte Carlo fields method for solving probability density function transport equations in turbulence modeling

The probability density function (PDF) transport equation method is a sophisticated model for the closure of turbulent mixing and turbulent reactive flows. An efficient solution approach for solving the PDF transport equation has been vital for the method to be widely used in applications. The Eulerian Monte Carlo fields (EMCF) method has been developed to solve the PDF transport equation efficiently for decades. A recent work by Wang et al. revealed a serious issue of the EMCF method for not being fully consistent with the PDF transport equation for which the method is designed to solve. This work advances the state of the art by introducing fully consistent EMCF methods for solving the PDF transport equation. The fully consistent EMCF formulations are derived for two different PDF equation forms. The consistency of the EMCF formulations is mathematically confirmed by examining the derived moment transport equations from the EMCF formulations and from the PDF transport equation. The method of manufactured solutions is employed to further verify the consistency and convergence of the different EMCF formulations numerically. The newly introduced EMCF formulations bring the EMCF method to full consistency with the PDF transport equations for the first time.

42 ENGINEERING↗
DOE OSTI2020

Process optimization of complex geometries using feed forward control for laser powder bed fusion additive manufacturing

Additive manufacturing (AM) enables the fabrication of complex designs that are difficult to create by other means. Metal parts manufactured by laser powder bed fusion (LPBF) can incorporate intricate design features and demonstrate desirable mechanical properties. However, printing a part that is qualified for its intended application often involves reprinting and discarding many parts to eliminate defects, improve dimensional accuracy, and increase repeatability. The process of iteratively converging on the appropriate build parameters increases the time and cost of creating functional LPBF manufactured parts. This work describes a fast, scalable method for part-scale process optimization of arbitrary geometries. Additionally, the computational approach uses feature extraction to identify scan vectors in need of parameter adaptation and applies results from simulation-based feed forward control models. This method provides a framework to quickly optimize complex parts through the targeted application of models with a range of fidelity and by automating the transfer of optimization strategies to new part designs. The computational approach and algorithmic framework are described, a software package is implemented, the method is applied to parts with complex features, and parts are printed on a customized open architecture LPBF machine.

3D printing↗
DOE OSTI2022

Code Verification and Solution Verification framework in pin-resolved neutron transport code MPACT

Program verification in scientific computing encompasses the application of formal and mathematical techniques to a scientific computing code for its credibility, accuracy, and validity. Code Verification identifies bugs and performance issues in the software development stage. Solution Verification assesses the applicability of the code and the accuracy of the solution to problems of interest. Both activities utilize application cases and quantify the error against prescribed acceptance criteria. However, simply executing more application cases does not guarantee stronger or more comprehensive credibility. Here, we establish a verification framework that involves Code Verification and Solution Verification, both of which work together such that the overarching goal of “converge to the correct answer for the intended application” can be reasonably inferred. The application of such a verification framework is demonstrated using the pin-resolved neutron transport code MPACT, where standard unit tests and regression tests are covered, and where the Method of Exact Solutions and the Method of Manufactured Solutions are successfully used. Additionally, the applicability of Method of Manufactured Solutions is extended to the OECD/NEA C5G7 benchmark problems of practical material and geometric configurations. Solution Verification activities are demonstrated on a practical hierarchy of application models of increasing complexity ranging from 2D pin cell problems to 3D assembly problems. The convergence behavior and rate of convergence with respect to each individual variable are studied and provided. This framework can be adapted broadly to other fields involving scientific computing codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
DOE OSTI2021

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore (Computional Evaluation of Thermal Response of Open-Cell Foam with Circular Pore)

The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Here, two-dimensional, steady state analyses were performed on unit cells with centered, circular pores using a second order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Microchannel-based Membrane-less Extraction of Li from Unconventional Lithium Sources & the Separation of REE

This final report provides an overview of the Project's entire duration, covering July 1, 2021 to December 31, 2023. It primarily focuses on the achievements, technological developments, and unique challenges the team faced while working on separating and extracting Lithium from produced waters. The project's primary aim was to create an integrated, high-throughput, membrane-less, and modular microfluidic platform that could extract Lithium from unconventional sources. We have successfully met all goals and milestones envisioned in the SOPO document. The most critical primary milestones, including the Go-No-Go milestone (refer to the Gantt chart in the Appendices), were successfully accomplished. We demonstrated phase separation (>90%) and extraction (>85%) performance in the MPSE using synthetic, and representative produced water composition feed at 50 ml/min total flow through MPSE 36. We have also performed a parametric study of the MPSE operations, beyond the scope of SOPO, exploring operating conditions of current and broader interest. The extended investigation of operational parameters is concurrent with our efforts to seek further development of the MPSE technology beyond the scope of the Project. Along these lines of development, we have made efforts to be responsive to DOE calls for technological developments of other types of resources (beyond PW) for the recovery of Critical Materials and higher TRL development (beyond TRL 4). During the work on this Project, we developed and implemented three innovative technical approaches that emerged from our efforts to successfully meet the Project milestones. The innovative & original technical approaches developed and implemented in this Project are now the contributions to process engineering that could be clearly credited to the Project. First, Convergent Design Approach is a comprehensive feedforward & feedback loop of four design phases: i) design for functionality, ii) design for manufacturing, iii) design for sustainability, and iv) design for market. Next was Process Intensification. A major aim of this Project was to create an innovative phase separation & extraction microscale-based technology for Li separation – thus the words microchannel-based in the Project title. A microscale-based technology is intrinsically in the center of the Process Intensification domain as defined by its unique principles. Therefore, Process Intensification was implicitly envisioned in the Project’s SOPO. Lastly, Time Scale Analysis is a novel tool for discovering the needs and directions of Process Intensification implementations in any process technology. This Project is fully credited for developing and implementing the three novel technical approaches mentioned above. These are general contributions to process engineering that emerged from this Project. Beyond the original SOPO scope, the OSU-U.Pitt research group utilized a Convergent Design methodology, integrating first-principles mathematical modeling with experimental validation on the Minimum Development Vehicle. By creating these Digital Twins, the team rapidly assessed manufacturing iterations to support TEA analysis. This framework further enabled the development of advanced Surface Modification Techniques, where hydrophobic and oleophobic coating strategies were optimized via Digital Twin tools and validated through rigorous 100-hour longevity testing. TEA Analysis: The closing efforts of this Project were focused on the TEA analysis. TEA analysis had two primary functions: i) enabling critical assessments of design variations withing 10 the Concurrent Design Approach, thus enabling evolution of the MPSE design to reach faster- better-cheaper alternatives; and ii) to create a bridge between the accomplishments of this Project and future projects of higher TRL, beyond TRL 6 level. It is important to note that the TEA model created in the Project stirred the technological solutions for the recovery of critical materials toward a vision of a very profitable modular plant that has unique zero-waste water discharge signature. More importantly, thanks to our experimental performance data and conservative assumptions, the TEA model predicts minimal technological and investment risks. Low cost of a modular unit of a nominal capacity of [1000 tons of Li 2 CO 3 /year] positions the MPSE based technology within the reach of community investors, thus offering a paradigm shift in the development of critical technologies. The project successfully navigated two primary challenges: solvent selection and manufacturing adaptation. Restricted by the SOPO to existing literature for lithium recovery, the team identified a critical need for a "material excellence program" to develop next-generation solvents, eventually concluding with a preliminary investigation into promising Ionic Liquids (ILs). Simultaneously, COVID-19 supply chain disruptions forced a pivot from traditional manufacturing to advanced additive methods at ATAMI-OSU. By transitioning from stainless steel to 3D-printed polymer substrates, the team achieved a transformative three-order-of- magnitude reduction in manufacturing costs and compressed prototyping timelines from several months to just two days. The MPSE technology offers significant energy, environmental, and economic advantages by overcoming the traditional bottlenecks of phase-separation hardware and contactor size. Unlike conventional mixer-settlers or membrane-based systems, MPSE operates without moving parts or fouling-prone membranes, achieving robust performance even with challenging, viscous, or particulate-heavy feeds. Key performance metrics include an energy intensity reduction of 5–50x (3–40 kJ/m 3 ) compared to incumbent technologies and a dramatic reduction of processing time to under 60 seconds, which drastically reduces the physical plant footprint. These technical efficiencies translate into superior economic outcomes; for a 100 t/year Li 2 CO 3 facility, implementing MPSE is projected to nearly halve contactor CAPEX (from $\$$6.08M to $\$$3.01M) and significantly increase the project's Net Present Value (NPV), derisking new investment and enabling distributed critical-mineral processing configurations. The commercialization of MPSE technology is being spearheaded by Vigsur Dynamics Inc., which has adopted a structured, parallel approach to technical and business development since its formation in January 2026. Following extensive customer discovery and engagement with the Oregon State University accelerator, Vigsur Dynamics is working to establish a business model that transitions from pilot demonstrations to modular hardware sales, ultimately aiming for a "build-own-operate" service strategy. Current technical milestones—including 100 hours of continuous operation, superior energy efficiency, and successful 6-unit modular scale-up— provide a foundation for this transition. Backed by ongoing IP licensing and a growing network of industrial and venture advisors, the company is actively de-risking the platform to replace conventional mixer-settler systems in the critical minerals market.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

LLMs for Mfg.—On the State of Large Language Models and Applications to Manufacturing

Additive Manufacturing (AM), referred to as 3D printing, has emerged as a key pillar of Industry 4.0 enabling layer-by-layer fabrication of intricate geometries from CAD models. In parallel, Large Language Models (LLMs), deep learning models for natural language generation trained on vast text corpora, have demonstrated unprecedented capabilities in understanding and generating human-like text. The convergence of these trends opens new opportunities at the intersection of AM and AI/ML, where LLMs can assist engineers and researchers in design, manufacture planning, and knowledge discovery. Recent academic work has begun to explore LLM applications in AM and adjacent fields, such as material science, mechanical engineering, and design for additive manufacturing. This exploration ranges from intelligent process planning to domain-specific knowledge retrieval. This survey provides a comprehensive review of current developments, focusing on peer-reviewed literature contributions that apply, adapt, and advance LLMs in general and domain-specific domains. We analyze state-of-the-art (SOTA) techniques, such as fine-tuning foundational models for specific domains, retrieval-augmented generation (RAG) pipelines, knowledge graph integration, and delve into the architectures and evaluation methods employed. The goal of this survey is to inform researchers and practitioners of the current capabilities and limitations of LLMs in general and in domain-specific applications, and to outline how these models are being tailored to meet the requirements of these applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗