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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 271 records · Page 15

Transformational Molecular Layer Deposition Tailor-Made Size-Sieving Sorbents for Post-Combustion CO 2 Capture

This report summarizes the carbon capture research and development conducted by The State University of New York at Buffalo (UB), University of South Carolina (USC), GTI Energy (GTI), and Rensselaer Polytechnic Institute (RPI) for U.S. Department of Energy (DOE) project DE-FE0031730 titled “Transformational Molecular Layer Deposition Tailor-made Size-Sieving Sorbents for Post-Combustion CO 2 capture.” The objective of this project was to develop a transformational molecular layer deposition (MLD) tailor-made size-sieving sorbent integrated with a pressure swing adsorption (PSA) cycle schedule that can be installed in new or retrofitted into existing pulverized coal (PC) power plants for CO 2 capture with a cost of electricity at least 30% lower than a supercritical PC power with CO 2 capture, or approximately $\$$30 per tonne of CO 2 captured, and with it being ready for demonstration by 2030.

20 FOSSIL-FUELED POWER PLANTS↗

Multilayer Silicon Carbide Composite Material Technology for High-Temperature Concentrated Solar-Thermal Power Components

In 2012, the U.S Department of Energy defined aggressive targets to achieve lower component costs and higher system efficiencies for concentrated solar-thermal power (CSP), and this, in turn, has led to the exploration of technology options that can operate at higher temperatures [1]. These next-generation CSP options, referred to as Generation 3 (a.k.a. Gen3), are targeting temperatures at or above 700 °C for the energy being delivered to the power cycle, and the more challenging plant conditions have necessitated a review and selection of alternative receiver heat transfer fluids as well as a search for materials that can meet the associated high-temperature component requirements. Nickel-based alloys are currently being considered, but these generally experience a significant drop in strength at temperatures > 775 °C [2] and may not be able to achieve corrosion and other lifetime requirements. Furthermore, these alloys are expensive, frequently have cost and schedule volatility, and offer little potential for lower cost at high production volumes. As an alternative, Ceramic Tubular Products, LLC (CTP) has developed a multilayer silicon carbide composite that can complement or replace alloys currently being considered for these Gen3 CSP applications.

14 SOLAR ENERGY↗

Magnetic Field Mapping Design for the MOLLER Spectrometer Magnets at Jefferson Lab

The Thomas Jefferson National Accelerator Facility (JLab) has developed a unique spectrometer system to study the weak interaction between electrons. The "Measurement of Lepton-Lepton Electroweak Reaction" (MOLLER) experiment, utilizing JLab's recent 12 GeV electron beam upgrade, is scheduled to operate for three years. Central to the MOLLER experiment are five water-cooled toroidal magnets, each with a unique geometry and seven-fold symmetry, designed to focus the particles. These magnets generate the magnetic field needed to separate incident beam electrons scattered from target electrons (Møller scattering) and protons (elastic e-p scattering) within a liquid hydrogen target. Here, this paper details the magnet field measuring technique developed to map all five MOLLER toroidal magnets at multiple locations inside and along the bore. It covers the design, mounting, and operation of the probe, along with the calibration procedure to determine the field and to prepare a field map for GEANT4 analysis. Additionally, the paper addresses the challenges of accurately measuring low magnetic fields.

Ghoshal, Probir K. [Thomas Jefferson National Acce↗

Queue wait time prediction in high performance computing (HPC) systems

High Performance Computing (HPC) systems are critical enablers for groundbreaking scientific research across various domains. Efficient resource allocation, facilitated by job scheduling, is paramount for maximizing the utilization of HPC systems. However, the variability in wait times for queued jobs poses challenges for users, necessitating accurate job wait time estimation. This paper explores the influence of job characteristics, including job size (the number of nodes requested and walltime), the queue to which the job is submitted and other resource requirements, on job wait times in leadership-class HPC systems. Focusing on the Theta Cray XC40 and Polaris machines at Argonne National Laboratory, the study evaluates the performance of different supervised learning algorithms in predicting job wait times. It also evaluates the impact of data preprocessing, including outlier detection, Principal Component Analysis (PCA), and feature selection, on the performance of wait time prediction models. The findings reveal insights into the relationship between job characteristics and wait times, offering a foundation for optimizing resource allocation and enhancing user experience. The methodologies and tools developed in this study are adaptable to other leadership-class HPC systems, providing a valuable contribution to the broader HPC community aiming to improve job scheduling efficiency and user satisfaction.

Okafor, Nwamaka↗

SMART-COM – Scalable Multi-Agent Adaptive Resolution Tools for Collaborative Outage Management

The purpose of this grant was to conduct scientific research and prototype applications to support NPP outage staff in their adaptive decision-making in efficient scheduling and resource allocation while preventing violation of safety technical specifications. The project contributed to scientific knowledge and engineering methods in (1) user interface design, (2) scheduling optimization and risk estimation, and (2) natural language processing that would benefit the nuclear power plants in minimizing schedule overruns and even unexpected shutdowns. The research team conducted site visits at a test reactor facility and an operating nuclear power plant to gather necessary information and inputs for research and development of a software application to support NPP staff in executing their outages. The final software application consisted of three modules. First, the natural language processing module supports interactive processing of technical documentation to build a database for outage staff to query non-permissible actions on system components. This module can alleviate outage staff from reviewing extensive documentation and minimize violation of technical specifications, especially in time-sensitive situations. Second, the schedule optimization module schedules outage activities and compute risk indices that outperform existing software and current practice. This module can reduce completion time of an outage that typically have too many activities for human to optimize based on current practice that does not apply the latest operations research. Finally, the visualization module presents progress and risk information of the overall outage and individual activities, as well as enabling access to the natural language processing and schedule optimization modules. This module can provide outage staff with situation awareness that are necessary to make risk-informed decisions in response to unexpected events during the execution of an outage.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Affordable and Scalable Modular Multifamily Housing: A Case Study on Cost, Construction Time Savings, and Waste Reduction in California: Preprint

Modular construction can significantly reduce waste when compared to traditional methods. This case study evaluates cost, construction time, and waste metrics for a 195-unit stick-built project and for a 66-unit modular project both based in Los Angeles, CA. We partner with SoLa Impact (real estate developer) and Model/Z (modular manufacturer) to evaluate the impact of Model/Z's 1-bedroom modular unit which is produced in a 160,000 sq ft local factory in South Los Angeles. We compare them to similar stick-built/site-built multifamily construction by the same developer in Los Angeles. This study finds that modular production reduced construction waste through precise prefabrication, concentrated workforce expertise, and streamlined logistics while cutting transportation needs, improving project efficiency and lowering associated timelines and costs. Economies of scale are being realized as Model/Z has produced over 500 affordable housing units and supplied for projects up to 188 units, shortening schedules and lowering per-unit costs and supporting affordable housing goals in income-challenged South Los Angeles. Modular methods offer a scalable, resource-efficient pathway to increasing affordable housing supply while reducing total development costs by 10-15% and project timelines by 50%, while simultaneously creating local jobs and training opportunities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Application of Banking Scoring and Rating for Coherent Risk Measures in Electricity Systems ABSCORES

This project developed a framework for asset and system risk management that can be incorporated into current electricity system operations to improve economic efficiency and establish an Electric Assets Risk Bureau. We leveraged scoring and ratings from banking and financial institutions alongside current optimization methods in dispatching power systems to help system operators and electricity markets schedule resources. This approach is based on the observation that there are major discrepancies between the power scheduled by a system operator and the actual power generated/consumed. These discrepancies—exacerbated by unplanned contingencies (e.g., natural disasters)—are caused by multiple factors, including the different financial, environmental and risk preferences of power producers, consumers, and aggregators. We developed a framework that counteracts two failures in electricity system operations: imperfect information and missing markets for products. The technical approach included five tasks. Tasks 1 and 2 supported the development of risk scores at the asset level with historical data collected for this project. Tasks 3, 4, and 5 incorporated scoring into decision-making at the system level. The proposed effort achieved PERFORM's Program Objectives because the proposed outputs and algorithms do not exist in the electricity industry and are an innovative approach to managing risk. Since the acknowledged need to better assess and act upon risk profiles for grid assets has not been met by the industry, this project will also impact ARPA-E's Mission Areas, including improving energy efficiency and giving the U.S. a technological lead in advanced energy technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Framework for Extensible, Asynchronous Task Scheduling (FEATS) in Fortran

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP, explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI), or compiler-specific language extensions such as those provided by CUDA. By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models. Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data-parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. The paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task-scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

Richardson, Brad↗

On the Feasibility of Simulation-Driven Portfolio Scheduling for Cyberinfrastructure Runtime Systems

Runtime systems that automate the execution of applications on distributed cyberinfrastructures need to make scheduling decisions. Researchers have proposed many scheduling algorithms, but most of them are designed based on analytical models and assumptions that may not hold in practice. The literature is thus rife with algorithms that have been evaluated only within the scope of their underlying assumptions but whose practical effectiveness is unclear. It is thus difficult for developers to decide which algorithm to implement in their runtime systems.To obviate the above difficulty, we propose an approach by which the runtime system executes, throughout application execution, simulations of this very execution. Each simulation is for a different algorithm in a scheduling algorithm portfolio, and the best algorithm is selected based on simulation results. The main objective of this work is to evaluate the feasibility and potential merit of this portfolio scheduling approach, even in the presence of simulation inaccuracy, when compared to the traditional one-algorithm approach. We perform this evaluation via a case study in the context of scientific workflows. Our main finding is that portfolio scheduling can outperform the best one-algorithm approach even in the presence of relatively large simulation inaccuracies.

Casanova, Henri↗

Evaluating Economic Impact: An Investment Tool for Large Language Model Integration in Workweek Management

This paper explores the development and application of an investment tool designed to quantify the costs and potential savings associated with integrating large language models (LLMs) into work week management optimization (WMO) within the nuclear industry. LLMs, with their advanced natural language processing capabilities, can significantly enhance various aspects of work management, such as problem identification, prioritization, planning, scheduling, information retrieval, and information summary. Our investment tool focuses on evaluating the return on investment (ROI) for LLM applications in WMO by considering four pivotal decision factors: model selection, application, user training, and hosting options. This paper details the development and implementation of the ROI model and illustrates its application through multiple case studies, analyzing the impact of different variables, such as work time saved, number of requests, and model performance, on the computed ROI over two years. The computed ROI is also compared over different hosting solutions. Our findings indicate that ROI increases with enhanced work time savings and optimal request load but can decline with high request volumes or increased model costs. This model aids decision-makers in the nuclear industry by providing a structured approach to assessing the economic viability and potential savings from integrating LLMs into WMO processes.

97 - MATHEMATICS AND COMPUTING↗

Evaluating Economic Impact: An Investment Tool for Large Language Model Integration in Workweek Management

This paper explores the development and application of an investment tool designed to quantify the costs and potential savings associated with integrating large language models (LLMs) into work week management optimization (WMO) within the nuclear industry. LLMs, with their advanced natural language processing capabilities, can significantly enhance various aspects of work management, such as problem identification, prioritization, planning, scheduling, information retrieval, and information summary. Our investment tool focuses on evaluating the return on investment (ROI) for LLM applications in WMO by considering four pivotal decision factors: model selection, application, user training, and hosting options. This paper details the development and implementation of the ROI model and illustrates its application through multiple case studies, analyzing the impact of different variables, such as work time saved, number of requests, and model performance, on the computed ROI over two years. The computed ROI is also compared over different hosting solutions. Our findings indicate that ROI increases with enhanced work time savings and optimal request load but can decline with high request volumes or increased model costs. This model aids decision-makers in the nuclear industry by providing a structured approach to assessing the economic viability and potential savings from integrating LLMs into WMO processes.

99 - GENERAL AND MISCELLANEOUS↗

AC Power Flow Based DLMP Calculation and Decomposition Method to Smooth Power Fluctuation of Distributed Renewable Energy Sources

As the penetration of renewable energy sources increases, the growing renewable power variability brings ramping issues to power systems. Meanwhile, the development of distributed energy resources (DERs) makes the distribution systems to provide both energy and ancillary services. To incentivise individual resources and customers to alleviate ramping issues on the demand side, a two-stage distribution locational marginal price (DLMP) calculation and decomposition method is developed to formulate the marginal power ramping price for DERs. In the first stage of the proposed method, a distribution system operator market scheduling model based on AC optimal power flow is designed to estimate the optimal operating point of the distribution system. Subsequently, the voltage and power flow constraints are linearised in stage two to calculate DLMP. Finally, based on the Lagrange function and sensitivity factors, DLMP is decomposed to the marginal costs for active/reactive power, voltage management, power loss and power variability. Case studies demonstrate that the proposed model can effectively smooth the power fluctuation and reduce the ramping flexibility requirements of distribution systems.

AC optimal power flow↗

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development and Demonstration of a Fuel-Efficient, Class 8 Tractor & Trailer Engine System (SuperTruck II)

Navistar presents the SuperTruck II (ST II) Final Report to the Unites States Department of Energy (US DOE), which covers the five Budget Periods (BPs) from 10-1-2016 through 6-30-2022. For ST II, Navistar built on the achievements of the SuperTruck I (ST I) Program as a catalyst to continue critical research, design and development, testing, and operations to reach the ambitious goals of the ST II project. This approach allowed Navistar to continue contributing to the essential needs of our nation for safe, efficient, and cost-effective delivery of goods and services, as we reduced negative environmental effects and improved operational productivity. This document contains information specified in DOE F 4600.2, Final Scientific/Technical Report DOE F 241.3, B. SCIENTIFIC/TECHNICAL REPORTS, explaining how we met and exceeded program requirements. Throughout this Final Report, Navistar extracted information from documents prepared during the project that represent our management, design and development, building, and testing efforts to meet and exceed SuperTruck II project goals. Navistar followed Plan requirements to achieve / exceed Project Objectives: a) >100% improvement in vehicle freight efficiency (FE) (on ton-MPG basis) relative to 2009 baseline with stretch goal of 140% improvement [actual: 170%); b) >55% engine brake thermal efficiency (BTE) demonstrated in operational engine at a 65-mph cruise point on a dynamometer – ≥31% increase from 2009 baseline [actual: 55.20% of combined BTE) ; and c) development and implementation of commercially cost effective technologies (in terms of a simple payback). Technology selection / development path focused on developing technologies applicable for production within 3-year approach, while ensuring technology readiness and cost of ownership for end users. The Program was organized into five budget periods: Requirements / Technology Assessment and Initial Hardware Testing; Technology Development and Concept Readiness Demonstration; Technology Finalization and Validation Tractor / Trailer Fabrication, Integration and Commissioning Demonstration; and Fuel Economy (FE) and Brake Thermal Efficiency (BTE) and Program Completion. Leadership was provided by DOE, with tasks performed by laboratories (Argonne National Laboratory, Lawrence Livermore National Laboratory); partners at Bosch, TPI, Dana, and J.B. Hunt; , and support from University of Michigan and Clemson University. Navistar lead this team with Principal Investigator / Contracting Officer; Project Manager (PM); Vehicle, Engine, and Aftertreatment Engineers; Finance Manager, Technical Program Leads, and Legal/IP; and other key personnel. Work also included personnel in risk management; funding / budget / finance. Work involved analysis, development, testing, and down selection of individual/system engine, aftertreatment, and vehicle technologies, with integration of selected technologies into a prototype vehicle for demonstration of fuel-efficiency gain. Work also included component/integrated system level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. As ST II progressed, Navistar performed computer-based modeling / simulations of technologies focused on the primary operational areas: Engine, Aftertreatment, and Vehicle. During the ST II Program, the COVID Virus outbreak unexpectedly challenged by the effects of, which affected staffing, scheduling, design, supplies, availability of materials, production procedures, and testing. The DOE responded by extending the program by three quarters to ensure that project tasks were completed for this vital project. Focus continued on analyzing, developing, testing, and down selecting individual-/system-level engine and vehicle technologies for integration of the final selected technologies into a prototype vehicle that would demonstrate fuel-efficiency gains made possible through these technologies. This included component/integrated system-level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, solar power, distributed and intelligent vehicle power, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. Throughout the program, function, reliability, and performance at all levels were ensured through testing. Proof of this approach was demonstrated in multiple, on-road demonstrations: Scenario A (Flatland) Fuel Economy, Scenario B (Hilly) Fuel Economy, and City Cycle Tests. Other benefits derived from ST II included new/improved products, publications, patents, and next-step capabilities related to electric/hydrogen vehicles and autonomous driving.

Zukouski, Russ↗

Safety-Related Instrumentation and Control Pilot Upgrade (Initial Scoping Phase Implementation Report)

This research report (1) describes the process followed and products developed during the SR I&C Pilot Project Initial Scoping Phase, and (2) captures lessons learned. Exelon Generation and LWRS collaborated to develop a Digital Transformation Strategy as part of a larger Advanced Concept of Operations. The proposed SR I&C Pilot Upgrade provides a foundation stone for this Digital Transformation that will improve plant safety, reliability, and operational performance while lowering plant Total Cost of Ownership (TCO). Initial Scoping Phase activities for this Pilot Project have been performed in accordance with industry processes that have been adapted to better support digital upgrades. These processes include IP-ENG-001, Standard Design Process (SDP), NISP-EN-04, Standard Digital Engineering Process (SDEP), and Electric Power Research Institute (EPRI) Report 3002011816, Digital Engineering Guide (DEG). Completing Initial Scoping Phase Engineering and Operations, Licensing, and Project Management Activities was necessary to sufficiently bound the scope, schedule, and estimated cost of the Project to enable utility management to authorize moving into the Conceptual Design Phase. A significant finding of the Business Case Analysis (BCA) methodology developed and applied as part of this effort was that the growth rate of material costs for sustaining the operation of obsolete SR I&C equipment is accelerating. This directly contributed to the Project Economic Analysis created to justify continuing the Project. Project Initial Scoping Phase lessons learned have also been captured to assist the larger industry in understanding the Digital Transformation Strategy and SR I&C Pilot Project Initial Scoping Phase efforts. This is in keeping with the public/private partnership that has been established between the Department of Energy (DOE) and Exelon for this effort with engagement from the NRC. By addressing first-of-a-kind (FOAK) risks and capturing lessons learned, the SR I&C Pilot Upgrade Project addresses technical, regulatory, and business risks to enable subsequent implementers of similar upgrade.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Safety-Related Instrumentation & Control Pilot Upgrade Initiation Phase Implementation Report

This research report (1) describes the process followed and products developed during the SR I&C Pilot Project Initial Scoping Phase, and (2) captures lessons learned. Exelon Generation and LWRS collaborated to develop a Digital Transformation Strategy as part of a larger Advanced Concept of Operations. The proposed SR I&C Pilot Upgrade provides a foundation stone for this Digital Transformation that will improve plant safety, reliability, and operational performance while lowering plant Total Cost of Ownership (TCO). Initial Scoping Phase activities for this Pilot Project have been performed in accordance with industry processes that have been adapted to better support digital upgrades. These processes include IP-ENG-001, Standard Design Process (SDP) [Reference 2], NISP-EN-04, Standard Digital Engineering Process (SDEP) [Reference 3], and Electric Power Research Institute (EPRI) Report 3002011816, Digital Engineering Guide (DEG). Completing Initial Scoping Phase Engineering and Operations, Licensing, and Project Management Activities was necessary to sufficiently bound the scope, schedule, and estimated cost of the Project to enable utility management to authorize moving into the Conceptual Design Phase. A significant finding of the Business Case Analysis (BCA) methodology developed and applied as part of this effort was that the growth rate of material costs for sustaining the operation of obsolete SR I&C equipment is accelerating. This directly contributed to the Project Economic Analysis created to justify continuing the Project. Project Initial Scoping Phase lessons learned have also been captured to assist the larger industry in understanding the Digital Transformation Strategy and SR I&C Pilot Project Initial Scoping Phase efforts. This is in keeping with the public/private partnership that has been established between the Department of Energy (DOE) and Exelon for this effort with engagement from the NRC. By addressing first-of-a-kind (FOAK) risks and capturing lessons learned, the SR I&C Pilot Upgrade Project addresses technical, regulatory, and business risks to enable subsequent implementers of similar upgrades.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Enabling Seamless Transitions from Experimental to Production HPC for Interactive Workflows

The evolving landscape of scientific computing requires seamless transitions from experimental to production HPC environments for interactive workflows. This paper presents a structured transition pathway developed at OLCF that bridges the gap between development testbeds and production systems. We address both technological and policy challenges, introducing frameworks for data streaming architectures, secure service interfaces, and adaptive resource scheduling for time-sensitive workloads and improved HPC interactivity. Our approach transforms traditional batch-oriented HPC into a more dynamic ecosystem capable of supporting modern scientific workflows that require near real-time data analysis, experimental steering, and cross-facility integration.

Etz, Brian [ORNL] (ORCID:0000000208554863)↗

Optimal checkpointing for adjoint multistage time-stepping schemes

Here, we consider checkpointing strategies that minimize the number of recomputations needed when performing discrete adjoint computations using multistage time-stepping schemes that require computing several substeps within one complete time step. Specifically, we propose two algorithms that can generate optimal checkpoint-ing schedules under weak assumptions. The first is an extension of the seminal Revolve algorithm adapted to multistage schemes. The second algorithm, named CAMS, is developed based on dynamic programming, and it requires the least number of recomputations when compared with other algorithms. The CAMS algorithm is made publicly available in a library with bindings to C and Python. Numerical results show that the proposed algorithms can deliver up to two times the speedup compared with that of classical Revolve. Moreover, we discuss the utilization of the CAMS library in mature scientific computing libraries and demonstrate the ease of using it in an adjoint workflow. The proposed algorithms have been adopted by the PETSc TSAdjoint library. Their performance has been demonstrated with a large-scale PDE-constrained optimization problem on a leadership-class supercomputer. This work is a significant extension of the authors' conference paper.

97 MATHEMATICS AND COMPUTING↗