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DOE OSTI2020

Motion Control of Hydraulic Actuators In the Presence of Discrete Pressure Rail Switching

Conventional off-highway mobile machines are hydraulically actuated and have poor energy efficiencies. The goal to increase system efficiency and to reap the benefits of electrification have led to the creation of a novel Hybrid Hydraulic-Electric Architecture (HHEA) which could significantly increase efficiency, decrease the sizes and cost of electrical components, and maintain control performance. The key concept is to utilize a set of common pressure rails to provide the majority of power via the power dense hydraulics and to modulate that power by small electric components, which are less power dense, for precise control. The paper presents the motion control strategy for this architecture. The architecture presents a distinct challenge in that as the energy minimization algorithm selects different pressure rails, the system could experience large discrete jumps in pressures that impact control performance, especially when the electric components are torque limited. To meet this challenge, a passivity based back-stepping controller is used as the nominal controller between pressure rail switching events and a separate transition controller is used to deal with the pressure rail switching events. Two transition controllers are proposed, one uses the electric motor torque as the input, and the other also uses valve timing as a second input. For both transition controllers, a least norm control approach is used to steer the system states to the exact desired states at the end of the short transition period (~ 40 ms). The transition controllers are able to reduce the tracking error and the required electric motor torque, and hence achieve better control performance even with smaller electric components.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

RLScheduler: An Automated HPC Batch Job Scheduler Using Reinforcement Learning

Today’s high-performance computing (HPC) platforms are still dominated by batch jobs. Accordingly, effective batch job scheduling is crucial to obtain high system efficiency. Existing HPC batch job schedulers typically leverage heuristic priority functions to prioritize and schedule jobs. But, once configured and deployed by the experts, such priority functions can hardly adapt to the changes of job loads, optimization goals, or system settings, potentially leading to degraded system efficiency when changes occur. To address this fundamental issue, we present RLScheduler, an automated HPC batch job scheduler built on reinforcement learning. RLScheduler relies on minimal manual interventions or expert knowledge, but can learn high-quality scheduling policies via its own continuous ‘trial and error’. We introduce a new kernel-based neural network structure and trajectory filtering mechanism in RLScheduler to improve and stabilize the learning process. Through extensive evaluations, we confirm that RLScheduler can learn high-quality scheduling policies towards various workloads and various optimization goals with relatively low computation cost. Moreover, we show that the learned models perform stably even when applied to unseen workloads, making them practical for production use.

Zhang, Di↗

DOE OSTI2025

Development and transferability of neural-network models for plasma-surface interactions

Plasma-surface interactions are increasingly critical to modern technologies; yet, accurate molecular dynamics simulations remain limited by the capabilities of interatomic potentials. Deep Potentials (DPs) promise to revolutionize the field by providing a systematic method for producing accurate interatomic potentials. The primary challenge of DP development is selecting a dataset, which efficiently spans the set of atomic environments one expects to encounter in the subsequent molecular dynamics simulations. The computational cost of density functional theory calculations, which are the typical basis for DP development, makes it impossible to directly verify the quality of a given DP. To address this challenge, we explore the development of a deep-learned interatomic potential, “DeepREBO,” trained to reproduce the behavior of the REBO2 empirical potential, enabling direct validation of training methodology and transferability. Using an active learning framework, we begin with a minimal dataset and iteratively expand it to train a Deep Potential-Smooth Edition model that faithfully reproduces REBO2 results for 25 eV hydrogen bombardment of diamond (001), a particularly challenging case. We show that small, carefully curated datasets can outperform large, unguided ones, with effective models requiring fewer than 15 000 snapshots. Subsequent transferability tests demonstrate that while DeepREBO generalizes well to diamond (111) surfaces, performance degrades for amorphous carbon or higher-energy impacts, highlighting the need for use-case-specific training data. We also evaluate methods to improve short-range repulsion. This study outlines best practices for training robust deep potentials and underscores the importance of dataset design for predictive plasma simulations.

Ab-initio molecular dynamics↗

DOE OSTI2021

Opportunities for Treatment and Reuse of Agricultural Drainage in the United States

Irrigation accounts for 42% of the total freshwater withdrawals in the United States. Climate change, the pressure of a growing population, degrading water quality, and increased competition from other sectors could constrain continuous supply to meet future agricultural water demand. This study presents an evaluation framework to assess the potential reuse of agricultural drainage water for crop irrigation. Using a regional approach, we review the current state of agricultural drainage treatment and reuse and the institutional, economic, and other barriers that can influence the reuse decision. In the 31 eastern states, agricultural drainage contains valuable nutrients that can be reused for irrigation with minimal treatment, while the 17 western states struggle with large volumes of saline drainage that can contain constituents of concern (e.g., selenium), preventing reuse without treatment. Using a new decision-support tool called WaterTAP3, a potential treatment train for saline agricultural drainage was analyzed to identify treatment challenges, research needs, and the potential implementation at a larger scale. As demonstrated by our case study, desalination of agricultural drainage is costly and energy intensive and will require sizable investments to fully develop and optimize technologies as well as manage the generated waste and brine.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Photonic curing for innovative fabrication of flexible metal oxide optoelectronics

Abstract Flexible optoelectronics, based on non-planar substrates, hold promise for diverse applications such as wearables, health monitors, and displays due to their cost-effective manufacturing methods. Despite the superior properties of metal oxides, the challenge of processing them at high temperatures incompatible with plastic substrates necessitates innovative annealing approaches. Photonic curing, which delivers microsecond to millisecond broadband (200–1500 nm) light pulses on a sample, emerges as a viable solution. Depending on the optical properties, the targeted film absorbs the radiant energy resulting in rapid heating while the transparent substrate absorbs a minimal amount of light and remains at ambient temperature. The light intensity can be high, but since the light pulse is short, the total energy absorbed by the sample remains low and will not damage the plastic substrate. This perspective explores the innovative application of photonic curing to fabricate flexible metal oxide optoelectronics, including thin-film transistors, metal–insulator–metal devices, solar cells, transparent conductors, and Li batteries, emphasizing the conversion of sol–gel precursors to metal oxides. However, this technique was initially developed for sintering metal nanoparticles to conductive patterns and poses intriguing challenges in explaining its mechanism for metal oxide conversion, especially considering the limited absorption of visible light by most sol–gel precursors. The review delves into UV-induced photochemistry, common flexible metal-oxide optoelectronic components, and non-intuitive distinctions between photonic curing and thermal annealing. By elucidating the distinctive role of photonic curing in overcoming temperature-related challenges and advancing the fabrication of flexible metal oxide optoelectronics, this perspective offers valuable insights that could shape the future of flexible optoelectronics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A Scalable Compact Additively Manufactured Molten Salt to Supercritical Carbon Dioxide Heat Exchanger for Solar Thermal Application

Design of an additively manufactured molten salt (MS) to supercritical carbon dioxide (sCO 2 ) primary heat exchanger (PHE) for solar thermal power generation is presented. The PHE is designed to handle temperatures up to 720 °C on the MS side and an internal pressure of 200 bar on the sCO 2 side. In the core, MS flows through a three-dimensional periodic lattice network, while sCO 2 flows within pin arrays. The design includes integrated sCO 2 headers located within the MS flow, allowing for a counterflow design of the PHE. The sCO 2 headers are configured to enable uniform flow distribution into each sCO 2 plate while withstanding an internal pressure of 200 bar and minimizing obstruction to the flow of MS around it. The structural integrity of the design is verified on additively manufactured (AM) 316 stainless steel sub-scale specimens. An experimentally validated, correlation-based sectional PHE core thermofluidic model is developed to study the impact of flow and geometrical parameters on the PHE performance, with varied parameters including the mass flowrate, surface roughness, and PHE dimensions. A process-based cost model is used to determine the impact of parameter variation on build cost. The model results show that a heat exchanger with a power density of 18.6 MW/m 3 (including sCO 2 header volume) and effectiveness of 0.88 can be achieved at a heat capacity rate ratio of 0.8. As a result, the impact of design and AM machine parameters on the cost of the PHE are assessed.

14 SOLAR ENERGY↗

DOE OSTI2025

Feasibility Assessment of Using Electrical Impedance Tomography for Damage Localization in Graphite Microreactor Components

Microreactors have great potential to decrease capital costs and construction timelines, reducing the barriers to implementing advanced nuclear reactor technologies. However, the lower power output of these microreactors introduces economic challenges if the operation and maintenance costs cannot be reduced sufficiently. Many microreactor concepts use graphite materials for in-core moderator and structural purposes, which will require periodic inspection or, ideally, in situ structural health monitoring. This work describes an initial evaluation of the feasibility of leveraging graphite’s semiconducting properties to perform electrical impedance tomography (EIT) for defect localization. First, a study was performed to identify the best methods for bonding electrical contacts to minimize the effects of contact resistance that interfere with impedance measurements of the graphite. After determining the best bonding approach, electrodes were attached to multiple graphite components with varying geometries (e.g., simple block and more representative microreactor hexagonal block). In parallel, finite element analysis approaches were developed and implemented to analyze the impact of defects and contact resistances and to inform an iterative inverse model for reconstructing the conductivity distribution. The results of this study show that defect localization in graphite components is possible using EIT if a sufficient number of electrodes (to improve spatial resolution) can be bonded using a technique with very low contact resistance and those contact resistances remain stable during reactor operation. If the reactor core and vessel design do not allow electrodes to be bonded during reactor operation, then it may be possible to detach/reattach electrodes between reactor operation and outages if a suitable mechanical connection that offers repeatable contact resistance can be identified. Alternatively, future work could focus on identifying contacts that can survive the harsh reactor operating environment so that contacts do not need to be removed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Scaling Building Energy Audits through Machine Learning Methods on Novel Drone Image Data

Building energy audits are time-consuming and labor-intensive. This paper describes a new method using machine learning (ML) techniques on novel data sources (drone images) to improve the identification of building characteristics and retrofit opportunities, and thereby reduce the effort for audits. The new ML method includes: (1) Building footprint extraction using line extraction, polygonization, and polygon-merging, (2) Building envelope extraction using PIX4d modeling software to reconstruct a building 3D model, (3) Visualization tool for viewing images from the 3D model, (4) Window-to-wall ratio (WWR) using state-of-art deep neural network semantic segmentation, (5) Envelope thermal anomaly detection using an unsupervised machine learning clustering algorithm, and (6) Rooftop energy equipment detection based on an object detection algorithm. The testing of this method involved a comparison of additional ML-generated information overlaid on current ‘state-of-practice’ audit and remote assessment baselines using evaluation metrics: labor time and associated cost, marginal benefits of using ML-generated information in workflows for audits and remote assessments, integration potential with existing processes and tools, and replicability/scalability of the method. In two test buildings in California that had comprehensive drawings and meter data available, the ML method effectively generated a building footprint, envelope, rooftop equipment, WWR, and locations of envelope thermal anomalies. Projected target segments of the ML method are sites with minimal drawings and energy data, and underserved sectors such as multistoried housing, disadvantaged communities, and schools for which the ML method can enable identification of building asset characteristics and prioritization of envelope retrofits and decentralized energy equipment retrofits.

Singh, Reshma↗

DOE OSTI2023

EVs@Scale Next-Gen Profiles - Fleet Utilization 2023

As U.S. fleet operators begin transitioning to electric vehicles (EVs), critical questions arise regarding how to manage this shift without disrupting fleet operations or placing undue stress on the electric grid. A major challenge for fleets is maintaining effective operational schedules while accommodating charging requirements, particularly with high-power charging (HPC) infrastructure, which presents grid stability concerns for utilities. Proposed solutions such as charging substations, megawatt charging systems (MCS), and smart charge management systems (SCMS) offer potential pathways forward, but their effectiveness depends on alignment with real-world fleet behavior and operational constraints. This report investigates the charging and utilization behavior of EV and EVSE fleets actively employing HPC technologies by conducting detailed case study analyses based on telematics data. A suite of predefined metrics—covering charging, routing, and other operational behaviors—is developed to evaluate the impact of fleet activities on grid infrastructure and identify opportunities for optimization. Results highlight variations in charging behavior across fleets, such as weekday versus weekend usage, diurnal charging trends, and the role of operational predictability in enabling SCMS effectiveness. While SCMS can help lower costs and improve energy efficiency for fleets with stable schedules, they may be insufficient for fleets with highly variable or long-haul operations, which may require more robust solutions like MCS. Visualization of aggregated hourly energy metrics reveals that while fleet behaviors are diverse, there are common temporal patterns that could inform infrastructure planning and energy management. These insights emphasize the need for fleet-specific charging strategies that minimize grid impact while supporting reliable fleet operations. Additionally, the report underscores the broader economic stakes of electrification, particularly in high-value markets such as freight, where misaligned transitions could stall EV adoption. By examining current EV and EVSE fleet deployments using predetermined standardized metrics, this study offers a foundation for developing technologies and operational frameworks that support scalable, grid-compatible electrification across a variety of fleet types while establishing a baseline understanding of operational behaviors. In doing so, we aim to ensure that future charging solutions reflect actual fleet needs and grid constraints—an essential step toward maintaining operational continuity and achieving a successful transition to electric fleet operations.

Charging↗

DOE OSTI2020

Water-Based Electrode Manufacturing and Direct Recycling of Lithium-Ion Battery Electrodes—A Green and Sustainable Manufacturing System

It is critical to develop a low-cost and environmentally friendly system to manufacture and recycle lithium-ion batteries (LIBs) as the demand on LIBs keeps increasing dramatically. Conventional LIB cathodes are manufactured using N-methyl-2-pyrrolidone as the solvent, which is expensive, highly toxic, flammable, and energy intensive to produce and recover. Ideally, a close-loop industrial supply chain should be built, in which the batteries are manufactured, market harvested, and recycled with minimal external toxic solvent through the whole system. This work demonstrates a green and more sustainable manufacturing method for LIBs where no hazardous organic solvent is used during electrode manufacturing and recycling. The electrodes fabricated via water-based processing demonstrate comparable rate performance and cycle life to the ones from conventional solvent-based processing. Utilization of a water-soluble binder enables recovering the cathode compound from spent electrodes using water, which is successfully regenerated to deliver comparable electrochemical performance to the pristine one.

25 ENERGY STORAGE↗

DOE OSTI2020

Research and Development Priorities for Silicon Photovoltaic Module Recycling to Support a Circular Economy

Large-scale deployment of photovoltaic (PV) modules has considerably increased in recent decades. Given an estimated lifetime of 30 years, the challenge of how to handle large volumes of end-of-life PV modules is starting to emerge. In this Perspective, we assess the global status of practice and knowledge for end-of-life management for crystalline silicon PV modules. We focus in particular on module recycling, a key aspect in the circular economy of photovoltaic panels. We recommend research and development to reduce recycling costs and environmental impacts compared to disposal while maximizing material recovery. We suggest that the recovery of high-value silicon is more advantageous than the recovery of intact silicon wafers. This approach requires the identification of contaminants and the design of purification processes for recovered silicon. The environmental and economic impacts of recycling practices should be explored with techno–economic analyses and life-cycle assessments to optimize solutions and minimize trade-offs. As photovoltaic technology advances rapidly, it is important for the recycling industry to plan adaptable recycling infrastructure.

c-Si↗

DOE OSTI2020

Generation of ionic liquid tolerant Pseudomonas putida KT2440 strains via adaptive laboratory evolution

Although the use of ionic liquids (ILs) for the pretreatment of lignocellulosic biomass has been limited due to high costs, recent efforts to develop low-cost protic ILs show promise for achieving cost-effectiveness for biorefineries. However, an additional challenge remains in that ILs present in biomass hydrolysates are toxic to most microbial hosts, resulting in poor growth phenotypes. To address this issue, we applied an adaptive laboratory evolution (ALE) approach for tolerizing Pseudomonas putida KT2440, an industrially relevant bacterial host, to two low-cost ILs (triethanolammonium acetate [TEOH][OAc] and triethylammonium hydrogen sulfate [TEA][HS]). After continuous cultivations with gradually increased IL levels, we obtained evolved strains showing significant improvements in their growth performance under high concentrations of the ILs (maximum 4% [TEOH][OAc] and 8% [TEA][HS], in w/v) at which the wild-type strain cannot grow. Sequencing of evolved strains revealed multiple regions where mutations were associated with improved performance in minimal media conditions (relA, gacS, oprB/PP_1446, fleQ, tktA, and uvrY/PP_4100) and in IL-specific conditions (PP_5350, PP_4929/emrE, oprD, and PP_5324). We further validated the causality of the PP_5350 and emrE genes for improved IL tolerance via reverse engineering and transcriptomic analysis. Here, a common mutation in the PP_5350 gene, encoding a RpiR family transcriptional regulator, was shown to significantly upregulate the glyoxylate cycle for efficient acetate catabolism. In addition, it was suggested that the emrE gene encodes an efflux pump which can export [TEA][HS]. Finally, the cultivation of two of the best performing evolved strains with IL-treated biomass hydrolysates demonstrated their considerable potential to be used as platform strains. Taken as a whole, this work provides strains for utilization of IL-treated biomass and a mechanistic understanding that could be further leveraged to develop efficient microbial bioprocesses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

High‐Performance Low‐Emissivity Paints Enabled by N‐Doped Poly(benzodifurandione) (n‐PBDF) for Energy‐Efficient Buildings

Abstract Low‐emissivity (low‐e) paints reduce radiative heat exchange between buildings and the environment, stabilizing indoor climates and lowering air conditioning demand. However, low‐cost, durable, and colored low‐e paints have yet to be demonstrated. Here, an approach is proposed using n‐doped poly(benzodifurandione) (n‐PBDF), a transparent organic conducting polymer, coated over colored commercial paints. This achieves a low thermal emissivity of 0.19 in the mid‐infrared spectrum, attributed to the efficient charge transport of delocalized π‐electrons in n‐PBDF structure. The reduction in thermal emissivity aids in regulating building temperatures by minimizing heat transfer between buildings and their surroundings across diverse climate zones and seasons. The n‐PBDF coating preserves the underlying paint's color due to its high visible transparency, meeting aesthetic requirements. It also shows strong stability in accelerated indoor weathering tests, ensuring long‐term performance. Simulations estimate annual HVAC energy savings of over 10,800 kWh in San Francisco and 5,500 kWh in Chicago for the typical mid‐rise apartments. The paint's versatility, scalability, and durability make it suitable for buildings, vehicles, and greenhouses, aiding urban heat island mitigation.

Liu, Xiaojie [School of Mechanical Engineering and↗

DOE OSTI2023

Enhancing flexibility for climate change using seasonal energy storage (aquifer thermal energy storage) in distributed energy systems

Long-term energy storage is expected to play a vital role in the deep decarbonization of building energy sectors, while enhancing the flexibility of buildings to withstand future climate variations. However, it is challenging to design distributed multi-energy systems (DMES) while taking into account the uncertainties introduced by climate change, since stochastic optimization of such systems is difficult. The present study introduces a stochastic optimization model to address this bottleneck, taking into account DMES including aquifer thermal energy storage (ATES) as the long-term thermal storage. For the first time, a novel optimization algorithm links ATES with the DMES optimization model with the support of a simplified geotechnical model. Subsequently, a case study was conducted, focusing on a residential district in Chicago where the impact of future climate condition, energy demand, and solar and wind energy potentials were evaluated using Weather Research and Forecasting (WRF) data (up to 2080) and the EnergyPlus model. The study revealed that ATES is an attractive way to improve the renewable energy penetration level and minimize the dependence on fossil fuels with reasonable support from the grid to assist the fluctuations in both demand and generation. Furthermore, ATES notably reduces fuel consumption and dependence while greatly enhancing the flexibility of the energy system to withstand fluctuations in demand and renewable energy generation brought by future climate variations. These qualities will make ATES an important part of distributed energy systems, even though it is not currently the lowest cost alternative due to lack of technology maturity. Furthermore, the design platform introduced in the present study can be used to design DMES enhancing flexibility to accommodate future climate variations.

25 ENERGY STORAGE↗

DOE OSTI2022

Thermal conductivity evaluation of ion irradiated Si 3 N 4 and ZrN ceramics using spatial domain thermoreflectance

Nitride ceramics have been investigated for different applications in the nuclear industry, such as space nuclear power, fusion reactor diagnostics and plasma heating, inert matrix fuels, and accident tolerant fuels. Although thermal conductivity remains one of the most important properties to track following irradiation, traditional techniques such as laser flash and xenon flash are limited to bulk sample characterization, which requires lengthy and cost-consuming neutron irradiation. This work used spatial domain thermoreflectance (SDTR) for the micrometer-scale measurement of thermal conductivity in 15 MeV Ni ion-irradiated silicon nitride and zirconium nitride from 1 to 50 dpa and 300 to 700 °C. Here, the SDTR-measured unirradiated thermal conductivity was found to be consistent with the published data on bulk samples. Electrically conductive ZrN exhibits modest reduction after irradiation which is minimal at the highest irradiation temperatures. In electrically insulating Si 3 N 4 , the reduction is more significant and unlike ZrN, the reduction remains significant even at a higher irradiation temperature. The thermal resistance evolution following irradiation was compared with lattice swelling, which was determined using grazing incidence x-ray diffraction, and radiation-induced defects were observed using transmission electron microscopy. A saturation value was observed between 15 and 50 dpa for thermal conductivity degradation in both nitride ceramics and a direct correlation with high-temperature defect recombination was observed, as well as the potential presence of additional carrier scattering mechanisms.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Replication of x-ray blazed gratings by nano-inscribing.

A nano-inscribing technique was tested as a method of cost-effective replication of blazed diffraction gratings for x-rays. A saw-tooth mold for the nano-inscribing was fabricated by a double-replication process from a master blazed grating. The nano-inscribing was performed using a UV-curable resist of low viscosity to provide a small thickness of the resist replicas, required for a following transfer process. The nano-inscribing process was optimized to minimize surface relaxation and preserve the saw-tooth shape of the grooves, required for high diffraction efficiency. The quality of the replica gratings was evaluated via diffraction efficiency simulations. The simulations demonstrated that near theoretical efficiency can be achieved for the x-ray gratings made by the nano-inscribing approach.

blazed grating↗

DOE OSTI2025

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

coupled problems↗