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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 73 records · Page 4

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗

FEW questions, many answers: using machine learning to assess how students connect food–energy–water (FEW) concepts

There is growing support and interest in postsecondary interdisciplinary environmental education which integrate concepts and disciplines in addition to providing varied perspectives. There is a need to assess student learning in these programs as well as rigorous evaluation of educational practices, especially of complex synthesis concepts. This work tests a text classification machine learning model as a tool to assess student systems thinking capabilities using two questions anchored by the Food-Energy-Water (FEW) Nexus phenomena by answering two questions (1) Can machine learning models be used to identify instructor-determined important concepts in student responses? (2) What do college students know about the interconnections between food, energy and water, and how have students assimilated systems thinking into their constructed responses about FEW? Reported here are a broad range of model performances across 26 text classification models associated with two different assessment items, with model accuracy ranging from 0.755 to 0.992. Expert-like responses were infrequent in our dataset compared to responses providing simpler, incomplete explanations of the systems presented in the question. For those students moving from describing individual effects to multiple effects, their reasoning about the mechanism behind the system indicates advanced systems thinking ability. Specifically, students exhibit higher expertise for explaining changing water usage than discussing tradeoffs for such changing usage. This research represents one of the first attempts to assess the links between foundational, discipline-specific concepts and systems thinking ability. These text classification approaches to scoring student FEW Nexus Constructed Responses (CR) indicate how these approaches can be used, in addition to several future research priorities for interdisciplinary, practice-based education research. Development of further complex question items using machine learning would allow evaluation of the relationship between foundational concept understanding and integration of those concepts as well as more nuanced understanding of student comprehension of complex interdisciplinary concepts.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Visibility-enhanced model-free deep reinforcement learning algorithm for voltage control in realistic distribution systems using smart inverters

Increasing integration of distributed solar photovoltaic (PV) into distribution networks could result in adverse effects on grid operation. Traditional model-based control algorithms require accurate model information that is difficult to acquire and thus are challenging to implement in practice. Here, this paper proposes a surrogate model-enabled grid visibility scheme to empower deep reinforcement learning (DRL) approach for distribution network voltage regulation using PV inverters with minimal system knowledge. In contrast to existing DRL methods, this paper presents and corroborates the adverse impact of missing load information on DRL performance and, based on this finding, proposes a surrogate model methodology to impute load information utilizing observable data. Additionally, a multi-fidelity neural network is utilized to construct the DRL training environment, chosen for its efficient data utilization and enhanced robustness to data uncertainty. The feasibility and effectiveness of the proposed algorithm are assessed by considering DRL testing across varying degrees of observable load information and diverse training environments on a realistic power system.

14 SOLAR ENERGY↗

An Advanced Cooling Device for Concentrated Photovoltaic Systems

Concentrated photovoltaics (CPV) have the potential to significantly enhance the energy conversion utilization of solar panels and reduce solar generation costs, making them a crucial area of advancement in solar power generation technology. However, the concentration of sunlight can lead to overheating of solar panels, resulting in a notable reduction in both the efficiency of solar power generation and the lifespan of the panels. This challenge remains the predominant technical hurdle that hinders the application of concentrated photovoltaic power generation technology. In this study, we propose a new cooling method for concentrated photovoltaic power generation systems via an integrated approach of incorporating Phase-Change Thermal Storage (PCTS) and Thermoelectric Generator (TEG) technology. This new method not only enhances the overall system's electricity generation efficiency but also effectively resolves the technical challenge of concentrated photovoltaic panel overheating issues, ensuring the continuity of concentrated photovoltaic power generation and extending the lifespan of solar panels and their components. In order to make full use of the wasted heat generated by photovoltaic power generation and effectively improve the power generation efficiency of the system, this work developed a phase change heat storage device based on a phase change material. This device uses the temperature difference between day and night to recover wasted heat from photovoltaic power generation. Through integration with the thermoelectric power generation system, thermal energy can be converted into electrical energy. In addition, the Peltier effect of thermoelectric materials is used to construct a photovoltaic panel overheating protection system, which significantly improves the reliability and service life of the system.

14 SOLAR ENERGY↗

Methods in PES-Learn: Direct-Fit Machine Learning of Born–Oppenheimer Potential Energy Surfaces

The release of PES-L EARN version 1.0 as an open-source software package for the automatic construction of machine learning models of semi-global molecular potential energy surfaces (PESs) is presented. Improvements to PES-L EARN ’s interoperability are stressed with new Python API that simplifies workflows for PES construction via interaction with QCSchema input and output infrastructure. In addition, a new machine learning method is introduced to PES-L EARN : kernel ridge regression (KRR). The capabilities of KRR are emphasized with examination of select semi-global PESs. All machine learning methods available in PES-L EARN are benchmarked with benzene and ethanol datasets from the rMD17 database to illustrate PES-L EARN ’s performance ability. Fitting performance and timings are assessed for both systems. Finally, the ability to predict gradients with neural network models is presented and benchmarked with ethanol and benzene. PES-L EARN is an active project and welcomes community suggestions and contributions.

kernel ridge regression↗

Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗

An Advanced Cooling Device for Concentrated Photovoltaic Systems

Concentrated photovoltaics (CPV) have the potential to significantly enhance the energy conversion utilization of solar panels and reduce solar generation costs, making them a crucial area of advancement in solar power generation technology. However, the concentration of sunlight can lead to overheating of solar panels, resulting in a notable reduction in both the efficiency of solar power generation and the lifespan of the panels. This challenge remains the predominant technical hurdle that hinders the application of concentrated photovoltaic power generation technology. In this study, we propose a new cooling method for concentrated photovoltaic power generation systems via an integrated approach of incorporating Phase-Change Thermal Storage (PCTS) and Thermoelectric Generator (TEG) technology. This new method not only enhances the overall system's electricity generation efficiency but also effectively resolves the technical challenge of concentrated photovoltaic panel overheating issues, ensuring the continuity of concentrated photovoltaic power generation and extending the lifespan of solar panels and their components. In order to make full use of the wasted heat generated by photovoltaic power generation and effectively improve the power generation efficiency of the system, this work developed a phase change heat storage device based on a phase change material. This device uses the temperature difference between day and night to recover wasted heat from photovoltaic power generation. Through integration with the thermoelectric power generation system, thermal energy can be converted into electrical energy. In addition, the Peltier effect of thermoelectric materials is used to construct a photovoltaic panel overheating protection system, which significantly improves the reliability and service life of the system.

Gou, Yimeng↗

The role of an intramolecular hydrogen bond in the redox properties of carboxylic acid naphthoquinones

A bioinspired naphthoquinone model of the quinones in photosynthetic reaction centers but bearing an intramolecular hydrogen-bonded carboxylic acid has been synthesized and characterized electrochemically, spectroscopically, and computationally to provide mechanistic insight into the role of proton-coupled electron transfer (PCET) of quinone reduction in photosynthesis. The reduction potential of this construct is 370 mV more positive than the unsubstituted naphthoquinone. In addition to the reversible cyclic voltammetry, infrared spectroelectrochemistry confirms that the naphthoquinone/naphthoquinone radical anion couple is fully reversible. Calculated redox potentials agree with the experimental trends arising from the intramolecular hydrogen bond. Molecular electrostatic potentials illustrate the reversible proton transfer driving forces, and analysis of the computed vibrational spectra supports the possibility of a combination of electron transfer and PCET processes. The significance of PCET, reversibility, and redox potential management relevant to the design of artificial photosynthetic assemblies involving PCET processes is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cryogen-free modular scanning tunneling microscope operating at 4-K in high magnetic field on a compact ultra-high vacuum platform

One of the daunting challenges in modern low temperature scanning tunneling microscopy (STM) is the difficulty of combining atomic resolution with cryogen-free cooling. Further functionality needs, such as ultra-high vacuum (UHV), high magnetic field (HF), and compatibility with μm-sized samples, pose additional challenges to an already ambitious build. We present the design, construction, and performance of a cryogen-free, UHV, low temperature, and high magnetic field system for modular STM operation. An internal vibration isolator reduces vibrations in this system, allowing for atomic resolution STM imaging while maintaining a low base temperature of ∼4 K and magnetic fields up to 9 T. Samples and tips can be conditioned in situ utilizing a heating stage, an ion sputtering gun, an e-beam evaporator, a tip treater, and sample exfoliation. In situ sample and tip exchange and alignment are performed in a connected UHV room temperature stage with optical access. Multisite operation without breaking vacuum is enabled by a unique quick-connect STM head design. A novel low-profile vertical transfer mechanism permits transferring the STM between room temperature and the low temperature cryostat.

Instruments & Instrumentation↗

Neuro-Spark: A Submicrosecond Spiking Neural Networks Architecture for In-Sensor Filtering

Neuro-Spark, which is a new neuromorphic architecture with a field-programmable gate array (FPGA) implementation for ultrafast spiking neural network (SNN) inference at the edge, facilitates smart-pixel in-sensor filtering for high-energy physics experiments at the Large Hadron Collider (LHC). Utilizing the evolutionary optimization for neuromorphic systems (EONS) training method, we generate compact SNN models with 91% signal efficiency, akin to convolutional neural networks but with half the parameters. However, deploying near the detector poses a challenge because the SNN must handle a sustained input data rate exceeding 1013 GB/s. To overcome this, we propose a novel hardware architecture that uses high-level synthesis to construct a tuned architecture for the EONS-trained SNN. In addition to the analysis and validation with an AMD Xilinx Artix-A7 FPGA, our solution consumes only ç24% of FPGA LUT and flipflops. We also introduce an innovative quantization method that reduces FPGA resource utilization by ç15% without compromising accuracy. Our FPGA implementation achieves computing latency of ç10 ns for smart-pixel application inference on an edge FPGA.

Miniskar, Narasinga Rao↗

Building on success in systems design of high yielding low‐input energycanes for marginal lands

Energycane and Miscanthus are highly sustainable and productive perennial grasses that produce a large annual crop of shoot biomass. Theoretical analysis of metabolism has suggested that these crops could be engineered to accumulate 20% of their harvestable biomass as oil. Given their much higher biomass yields than soybean and canola, this would yield several times more oil per acre. This could be converted to biodiesel or sustainable aviation fuel (SAF) by well‐established technologies. Energycane is well suited to the southeast quarter of the contiguous 48 states and Miscanthus to the northeast quarter. The objective of this award was to provide the foundation for converting these crops to oilcanes from DNA constructs and transformation to field trials and pilot plant development of oil extraction. Genetic engineering focused on development and implementation of improved constructs to increase oil levels, and increased photosynthesis to support the additional energy needed for oil production. The specific progress in each of our subtasks follows together with the products arising.

09 BIOMASS FUELS↗

Nuclear Materials Packaging, Transportation, and Systems Analysis Group Software Quality Assurance Plan: ANSYS Mechanical Finite Element Analysis Software Version 2023R1

ANSYS Inc. develops and markets engineering simulation software and services used in the aerospace, automotive, manufacturing, electronics, biomedical, energy, defense, and many other industries. ANSYS is dedicated to engineering simulation and is the world’s leading software provider. ANSYS was founded in 1970 and is headquartered in Canonsburg, Pennsylvania. ANSYS provides an engineering analysis tool combining structural, thermal, computational fluid dynamics, acoustic, and electromagnetic simulation capabilities. ANSYS has two main programs, which use the same solvers: (1) Mechanical APDL (ANSYS Design Parametric Language), a Fortran-based coding platform, and (2) ANSYS Workbench, which uses a graphical user interface to aid in finite element analysis implementation. This plan covers both APDL and Workbench. The ANSYS computer program is a large-scale, multipurpose finite element program that can be used to solve several classes of engineering analyses. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses, and various types of field and coupled-field applications. The program contains many special features that allow nonlinearities or secondary effects such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation to be included in the solution. As ANSYS has been developed, other special capabilities such as substructuring, submodeling, random vibration, kinetostatics, kinetodynamics, free convection fluid analysis, acoustics, magnetics, piezoelectrics, coupled-field analysis, and design optimization have been added to the program. These capabilities contribute further to making ANSYS a multipurpose analysis tool for varied engineering disciplines. The ANSYS program has been in commercial use for over 50 years and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil, and steel industries. Additionally, many consulting firms and hundreds of universities have used ANSYS for analysis, research, and educational purposes. ANSYS is recognized worldwide as one of the most widely used and capable programs of its type. Ansys design analysis software is the first created within a quality system with ISO 9001 certification, the internationally accepted quality standard. Product development, testing, maintenance and support processes also meet the United States Nuclear Regulatory Commission's quality requirements, as they have for nearly four decades. The Quality Assurance Service Agreement is suitable for the customers working in the nuclear industry who need to meet specific federal regulations including 10CRF50 Appendix B and provisions of 10CFR21. ANSYS has retained its original International Organization for Standardization (ISO) 9001 accreditation certificate since1995-05-04, It’s current certificate is valid until 2027-05-29.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Directed energy deposition of functionally graded V-4Cr-4Ti to Fe-9Cr transition for fusion power systems

This study proposes a graded structure via additive manufacturing for divertor and first wall blanket applications in fusion reactors. Materials were selected based on thermodynamic calculations to operate from 1100 °C at the plasma-facing level to 550 °C at the structural steel level. Conventional joining methods often lead to failures due to discrete reaction layers with significant mechanical property differences. Using laser beam-directed energy deposition (LB-DED), this study demonstrates the fabrication of a VCrTi-Gr91 steel functionally graded component through a novel process parameter optimization framework. A systematic approach included powder characterization, single-track depositions, and construction of printability maps. Near full-density specimens of each interlayer were additively manufactured, and a transition from V-based alloys to reduced activation ferritic martensitic steels was achieved. Computational material selection of interlayer alloys and thermodynamic/diffusion kinetics simulations prevented most interface incompatibilities. A brittle intermetallic formed at one interface, causing cracking, which was not predicted by current thermodynamic models. Transition alloy design approach was updated with a more recent database and a mitigation strategy has been proposed to eliminate the formation of deleterious intermetallic phases. Ultimately, LB-DED has proven effective for producing multi-material graded systems for fusion applications, with the demonstrated process parameter optimization framework applicable to various materials.

Additive manufacturing↗

Surface roughness and dimensional evaluation of laser powder bed fusion additively manufactured shell and tube heat exchangers

The growing interest in additively manufactured (AM) heat exchangers drove the need to understand how this construction technique impacts heat exchanger performance. Two primary factors driven by AM that influence heat exchanger performance are surface roughness and geometry. To better understand these parameters, a range of shell and tube heat exchangers constructed using laser powder bed fusion were evaluated. Of those evaluated, the surface roughness throughout a fourteen-tube, zero-baffle heat exchanger was measured using computed tomography. Between the inner and outer tubes, the inner tube surfaces had a greater surface roughness than the outer by 8.07 μm, while the surfaces at the top of the build volume had higher surface roughness values than the bottom. Dimensionally, the inner tube diameters of this heat exchanger were 0.15% different from the design value, while the outer diameters were within a 0.84 % difference. Manual measurements across seven other heat exchangers yielded a maximum 1.15% difference between the design and measured diameters. Across the build volume for all heat exchangers studied, the tube diameters at the top were larger than at the bottom by a maximum of 1.24% difference. Inconsistent melting throughout the individual parts and the build volume, as well as particle splatter and thermal gradient variation were attributed to the surface roughness and dimensional changes seen. These results strengthen the knowledge of dimensional and surface roughness considerations when designing AM heat exchangers.

36 MATERIALS SCIENCE↗

A Bottom-Up Cost Estimation Tool for Nuclear Microreactors

The rising interest in nuclear microreactors has highlighted the need for comprehensive technoeconomic assessments. However, the scarcity of publicly available designs and cost data has posed significant challenges. To address this issue, the Microreactor Optimization Using Simulation and Economics (MOUSE) tool is developed. MOUSE is a tool that integrates nuclear microreactor design with reactor economics. The design calculations encompass core simulations using the OpenMC Monte Carlo Particle Transport Code [romano2015], along with simplified balance of plant calculations. On the economic side, MOUSE provides detailed bottom-up cost estimates, calculating both the total capital cost and the levelized cost of energy for first-of-a-kind and nth-of-a-kind microreactors. The cost estimation correlations are developed using data from the MARVEL project and additional literature sources. MOUSE has released as an open-source tool on GitHub (MOUSE Tool). By combining design calculations with cost equations, MOUSE enables users to evaluate the impact of various technological consideration, advanced moderators, design changes, material/fuel changes, and geometry modifications—as well as economic parameters like interest rates and construction duration. This comprehensive framework can guide stakeholders towards technological solutions that enhance microreactor competitiveness. Additionally, powered by the WATTS toolkit [romano2022], MOUSE supports optimization studies, parametric analyses, and uncertainty calculations/propagation. Currently, preconceptual designs of three microreactor types are included in MOUSE: a liquid metal thermal microreactor (LTMR), gas cooled TRISO-fueled microreactor (GCMR) and heat-pipe TRISO fueled microreactor (HPMR). To showcase its ability, MOUSE was used to conduct detailed bottom-up cost estimates for the first of a kind (FOAK) and Nth of a kind (NOAK) of the following microreactors • A 20MWt LTMR that is built on the ongoing MARVEL demonstration at Idaho National Laboratory (INL) • A 15 MWt GCMR that was designed to be more representative of the typical commercial microreactor • A 7 MWt HPMR that was built on previous work (Choi 2024) The The reader should note that these three designs and corresponding cost estimates are examples to demonstrate the MOUSE capability. The designs are pre-conceptual, the reactor designs were not optimized, and the cost estimates were developed with incomplete information. Additionally, stakeholders might be interested in a variety of designs that may differ from the examples provided in this report. The MOUSE tool can also be used to study how design choices affect economics. To demonstrate its capability, MOUSE was used conduct parametric studies such as examining the economic impact of the reflector's material and thickness, the moderator's booster material and dimensions, fuel composition and enrichment, core size, and power level. Several insights were gained from these parametric studies.

Hanna, Botros↗

The Schwinger-Keldysh coset construction

The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modernizing the Nuclear Industry and New Ways of Working

Nuclear energy is recognized as the most feasible energy source towards achieving nation-wide net-zero goals (COP 208, MIT). Additionally, the demand for reliable, consistent energy supply is soaring with the construction of energy hungry data centers and AI tools. This means the construction of new nuclear and the continuation of current nuclear are a high national priority. However, this leaves the nuclear industry with a workforce challenge. The rising demand for nuclear power is threatened by an underpopulated workforce. There exist a few contributors to the decreased workforce such as skewed workforce demographics resulting in large-scale workforce retirement. Also, some plants have observed difficulty hiring and retaining skill sets that typically comprise the nuclear power workforce – specifically skilled craftsman. Those who are graduating with desirable skills are seeking employment in sectors that are more modern and culturally more aligned with younger generational values. Lastly, within the nuclear sector, skilled employees will be a competitive commodity as advanced plants come online offering work environments that incorporate modern technologies, skill sets, and opportunities for career advancement. These factors emphasize the need for legacy plants to modernize with a focus on the workplace environment and culture that meets younger generations’ skills, cultural expectations, and desire for advancement opportunities. Nuclear plants are actively engaged in deploying advancements that improve the management of systems, structures, and components as well as process improvements and technologies that can reduce the costs of operation and maintenance. However, the advancements must also be analyzed, reviewed and deployed in a manner that considers the impact on how people within the organization collaborate, communicate, make decisions, and solve problems. Neglecting to consider the cultural impact of modernization risks poor adoption, unrealized opportunities, or insignificant change toward helping attract new employees. The traditional way of working is not necessarily the way new generations want to engage with their employer. For instance, in a survey performed by North American Young Generation in Nuclear the top three reasons for younger nuclear employees to seek other job opportunities was seeking better work-life balance, a lack of advancement opportunities, and work culture and leadership style differences (Smyth et al. 2022). Integrated Operations for Nuclear (ION) is an approach for the nuclear industry to create long-term strategic modernization plans and analyze each advancement for the impact on people and processes and measure how those impacts flow up to support high-level, long-term plant goals and requirements. One principle of ION is to replace the current labor-centric operation style in legacy nuclear plants with data-centric collaborative operation styles. This paper will explain how transitioning operations to leverage centralized skills and responsibility, multi-skilled teams, and collaborative decision making can flatten the hierarchical structure in plants, enable greater individual efficacy while also offering more experiences and advancement opportunities to staff. Adopting the ION way of working shifts the industry mind-set towards more networked, collaborative, and modern way of working that will attract skilled, next-generation workers to operate the legacy nuclear fleet.

99 - GENERAL AND MISCELLANEOUS↗

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗