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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Improving Signal-to-Noise Ratio (SNR) for Readout Signals Using Adaptive Filters on Reconfigurable Controls Hardware

This study investigates the optimization of Signal-to-Noise Ratio (SNR) in superconducting quantum computing readout signals through adaptive filtering. Quantum computing technology has the potential to revolutionize various fields by delivering exponential speedup in solving certain computational problems. However, the technology's practical implementation is hindered by the difficulty of extracting clean, reliable signals during the readout phase, with various sources of noise presenting a significant barrier to clean signals. This noise, often present in readout profiles due to imperfect isolation, degrades the system's overall SNR, thus impeding the ability to extract the quantum state accurately. The research leverages the power of adaptive filtering to improve the SNR of quantum computing readout signals. Specifically, an adaptive filter is implemented in a PYNQ overlay on an FPGA, and eventually will be connected to a quantum computing system. The system models the noise with a Least Mean Squares (LMS) adaptive filter, and then subtracts the estimated noise from the received signal to improve the SNR. A Direct Memory Access (DMA) channel is used to handle the signal processing, delivering efficient, high-speed data transfer between the PYNQ system and the hardware. The study explores the benefits of this adaptive filtering technique, potentially providing a significant contribution to practical and fast quantum computing.

Johnson, Hans↗
DOE OSTI2022

Removable, Sequestration Coatings for Mitigating Hazardous Contaminants Related to Deactivation and Decommissioning Activities

This project is a collaborative effort between InnoSense LLC (ISL) and Oak Ridge National Laboratory (ORNL) aimed at mitigating the mercury (Hg) contamination problem at the Y-12 National Security Complex (NSC). The report summarizes the research and technology development work of the Phase IIB Project, led by Dr. Uma Sampathkumaran at ISL for the period of July 31, 2017–October 31, 2021. The Y-12 site cleanup includes technologies for safe and cost-effective facility demolition, soil remediation, and on-site treatment and disposal of mercury bearing wastes. One of the technology demonstration goals was a reactive strippable coating for targeted pre-demolition and de-contamination to limit Hg mobilization and the volume of debris requiring treatment for disposal. Toward this, ISL has developed a water-based reactive strippable coating (Trap & See-Hg™) to sequester elemental Hg(0) and mercuric Hg(II) species in the coating. The coating provides multiple benefits including (1) Hg vapor suppression, (2) sealing in the hazardous contaminants, (3) visually locating the contaminant through color changes, and (4) remediating the contaminated surfaces upon coating removal. Through collaboration between ORNL and ISL in Phase II work, the team successfully demonstrated the Trap & See-Hg technology to (1) visually locate the presence of Hg on concrete, soil and drywall surfaces, (2) effectively sequester all mercury species (elemental, soluble and insoluble Hg) from lab-generated and ex-situ soil and brick/rubble samples collected from the Y 12 site with 80 to 95% efficiency to capture/reduce Hg vapor concentration, (3) be applied by manual and robotic spray applicators and cure at room ambient, (4) remain a cohesive and peelable coating upon drying, and (5) sequester Hg0 from walls in the alpha-2 building basement at Y-12 during a small scale in-situ field trial. In Phase IIB, ISL’s effort was focused on refining the coating formulations with additives containing passive and reactive sorbents, colorimetric indicator, and thixotropic agents to achieve the desired performance. The paints were then evaluated at ORNL for applicability to metal and concrete surfaces of different sizes and shapes, and soil rubble, Hg-sorption capacity and achieving sag-free coating on surfaces when applied by a manual spray applicator. Ambient cure of the coating resulted in a dry thickness of 16–20 mil. The coatings were removed from smooth or rough surfaces with low to moderate force. Both lab-generated Hg-contaminated samples and soil and brick/rubble samples containing a range of Hg concentrations (collected from the Y-12 site by UCOR) were used in this project. Optimized formulations were applied to these samples and evaluated for ability to suppress Hg vapors, sequester Hg 0 and Hg(II) species and color mapping of mercury species on the test surface. The ORNL team initially identified three to four potential sites at Y-12 and ORNL for potential demonstration. However, the pandemic closed any possible avenues for on-site demonstration of the robotic spray applicator. The metal and concrete samples with low to high Hg content provided by UCOR from an ongoing demolition were subsequently used for ex-situ sample characterization and analysis at ORNL over a period of 25 days. The coatings suppressed Hg vapors with an efficiency of 95–99% from heavily contaminated metal and 60% from concrete substrate. Analysis of total Hg in the peeled paints indicates sorption capacities ranging from 12 µg Hg/g of paint from concrete to 1.2 mg Hg/g of paint from the metal substrates while peeled paints from soil samples could capture a total Hg from 2.3 mg Hg/g to 66 mg/g paint. Toxicity characteristic leaching procedure (TCLP) tests recovered total mercury leached at 0.15±0.0008 µg/L for concrete to 126.81±0.67 µg/L and 377.25±5.67 µg/L for the two metal substrates, to allow for informed decisions on downstream disposal considerations. Together, this Phase IIB demonstrated the potential value of the Trap & See-Hg for Hg uptake, vapor suppression, and color mapping, and may thus be used to enhance worker safety during site cleanup, facility demolition, and downstream waste disposal at Y-12 NSC.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Improving Signal-to-Noise Ratio (SNR) for Readout Signals Using Adaptive Filters on Reconfigurable Controls Hardware

This study investigates the optimization of Signal-to-Noise Ratio (SNR) in superconducting quantum computing readout signals through adaptive filtering. Quantum computing technology has the potential to revolutionize various fields by delivering exponential speedup in solving certain computational problems. However, the technology's practical implementation is hindered by the difficulty of extracting clean, reliable signals during the readout phase, with various sources of noise presenting a significant barrier to clean signals. This noise, often present in readout profiles due to imperfect isolation, degrades the system's overall SNR, thus impeding the ability to extract the quantum state accurately. The research leverages the power of adaptive filtering to improve the SNR of quantum computing readout signals. Specifically, an adaptive filter is implemented in a PYNQ overlay on an FPGA, and eventually will be connected to a quantum computing system. The system models the n oise with a Least Mean Squares (LMS) adaptive filter, and then subtracts the estimated noise from the received signal to improve the SNR. A Direct Memory Access (DMA) channel is used to handle the signal processing, delivering efficient, high-speed data transfer between the PYNQ system and the hardware. The study explores the benefits of this adaptive filtering technique, potentially providing a significant contribution to practical and fast quantum computing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Neutrino Beam Monitoring

Accelerator facilities produce neutrino beams from meson decays in a decay volume. Experiments measure event rates that depend on flux, cross sections, and detector response, so the flux is predicted using hadron production and beamline modeling and constrained by beam instrumentation, since near detectors alone cannot separate flux from cross section. Proton, hadron, and muon monitors can track the parent particle distributions and beam conditions, providing the inputs needed for flux predictions in long-baseline experiments such as NOvA, T2K, and DUNE. This talk reviews how beam monitors are used in practice to understand neutrino flux. Proton beam monitors tell where the beam hits the target and how stable it is. Farther downstream, hadron and muon monitors sample particles produced in meson decays. Because those muons come from the same parents as the neutrinos, their profiles reveal focusing, alignment shifts, and other changes in the beam, and they are routinely used to detect problems and guide flux predictions. The muon information can be used more quantitatively; for example, to infer the parent meson phase space, and fast radiation-hard timing detectors can add sensitivity to the momentum dependence of the focusing. These developments show both how tightly beam measurements can constrain the flux and where the current limits still lie. These approaches complement monitored-beam concepts, in which the decay region is instrumented to detect charged leptons from meson decays and to measure the neutrino flux directly.

Ganguly, Sudeshna [Fermilab] (ORCID:00000003163482↗
DOE OSTI2026

Neutrino Beam Monitoring

Accelerator facilities produce neutrino beams from meson decays in a decay volume. Experiments measure event rates that depend on flux, cross sections, and detector response, so the flux is predicted using hadron production and beamline modeling and constrained by beam instrumentation, since near detectors alone cannot separate flux from cross section. Proton, hadron, and muon monitors can track the parent particle distributions and beam conditions, providing the inputs needed for flux predictions in long-baseline experiments such as NOvA, T2K, and DUNE. This talk reviews how beam monitors are used in practice to understand neutrino flux. Proton beam monitors tell where the beam hits the target and how stable it is. Farther downstream, hadron and muon monitors sample particles produced in meson decays. Because those muons come from the same parents as the neutrinos, their profiles reveal focusing, alignment shifts, and other changes in the beam, and they are routinely used to detect problems and guide flux predictions. The muon information can be used more quantitatively; for example, to infer the parent meson phase space, and fast radiation-hard timing detectors can add sensitivity to the momentum dependence of the focusing. These developments show both how tightly beam measurements can constrain the flux and where the current limits still lie. These approaches complement monitored-beam concepts, in which the decay region is instrumented to detect charged leptons from meson decays and to measure the neutrino flux directly.

Ganguly, Sudeshna [Fermilab] (ORCID:00000003163482↗
DOE OSTI2026

Heavy Element Spectroscopy in the Gas Phase

Actinides are inherently unstable and undergo nuclear decay processes with a concurrent release of energy. Consequently, they are used for nuclear power generation, nuclear weapons, and nuclear medicine. However, the radioactive decay processes also pose significant technological problems for the safe treatment and storage of spent nuclear materials. Cost-effective extraction of the actinides is the key first step in the remediation of nuclear waste, but the appropriate chemical means have yet to be determined. Our present understanding of the chemistry of actinides is limited, with the role of the 5f electrons posing a set of particularly challenging questions. The work reported here is focused on the use of electronic spectroscopy to probe the bonding of small molecules in the gas phase that contains thorium or uranium. Analyses of these data, carried out within the framework of ligand field theory, reveal clear evidence that the 5f electrons are spectators that retain their atomic metal ion character.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Bilayer Hubbard model: Analysis based on the fermionic sign problem

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its phase diagram in the interplane hopping t ⊥ versus on-site interaction U parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small U. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our paper demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin-piston problem for a ferromagnetic thin film: Shock waves and solitons

In this report the unsteady, nonlinear magnetization dynamics induced by spin injection in an easy-plane ferromagnetic channel subject to an external magnetic field are studied analytically. Leveraging a dispersive hydrodynamic description, the Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for the magnetization's perpendicular component (spin density) and azimuthal phase gradient (fluid velocity). Spin injection acts as a moving piston that generates nonlinear, dynamical spin textures in the ferromagnetic channel with downstream quiescent spin density set by the external field. In contrast to the classical problem of a piston accelerating a compressible gas, here, variable spin injection and field lead to a rich variety of nonlinear wave phenomena from oscillatory spin shocks to solitons and rarefaction (expansion) waves. A full classification of solutions is provided using nonlinear wave modulation theory by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the classical piston problem such as rarefaction waves and shocks manifest in their spin-based counterparts as smooth and highly oscillatory transitions, respectively, between two distinct magnetic states. The spin shock is an example of a dispersive shock wave, which arises in many physical systems. New features without a gas dynamics counterpart include composite wave complexes with “contact” spin shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced piston edge behaviors including a stationary soliton and an oscillatory wave train. These coherent wave structures have physical implications for the generation of high frequency spin waves from pulsed injection and persistent, stable stationary and/or propagating solitons in the presence of magnetic damping. The analytical results are favorably compared with numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Competing polar phases in 2D ferroelectric transition metal thio- and selenophosphates

The aim of this Perspective is to provide an in-depth discussion of a certain class of 2D ferroelectrics that feature a van der Waals gap where more than one polar phase can exist energetically close to the ground state. Polar phases of interest can include different ferroelectric, antiferroelectric, and paraelectric phases, which can be transformed into each other through external stimuli, offering unprecedented control over polar material properties. With this level of control, important size limitations and integration problems can be overcome, and material platforms with tunable polar properties for multi-functional devices and sensors can be developed for the next generation of information and energy technologies. We highlight the co-existence of polar properties that have been found on local scales using advanced local characterization techniques as well as methods to control polar properties in transition metal thio-/selenophosphates. In conclusion, we give an overview of future challenges and opportunities in this emerging field of energetically close polar phases.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A mass–momentum consistent coupling for mesh-adaptive two-phase flow simulations

Here, we present a novel mass-momentum consistent coupling between a geometric volume-of-fluid scheme and an incompressible flow solver with differing directional-splitting approaches. The advection of the volume fraction is performed using a direction-split algorithm, whereas the momentum advection algorithm uses a traditional unsplit, fractional-step approach. Both algorithms employ finite-volume discretizations based on Cartesian meshes. In solving the mass-momentum consistency problem, momentum fluxes at the cell faces are weighted by the density fluxes based on the already advected volume fraction. The success of our approach lies on introducing a Favre-averaged velocity interpolation at the liquid/gas interface along with a minmod slope limiter. Mesh-convergence studies show that when the minmod slope limiter is used, the two-phase solver retains an accuracy between first and second order, but when a purely upwind scheme is considered, its accuracy drops to first order. Finally, after considering several validation problems, the solver is shown to agree well with reference numerical and experimental data while retaining its robustness and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Variant Nelson-Barr mechanism with minimal flavor violation

Within the general framework of using spontaneous CP violation to solve the strong CP problem, we construct a variant Nelson-Barr model in which the Standard Model (SM) quark contribution to the strong CP phase is cancelled by new heavy QCD-charged fermions. This cancellation is ensured by choosing conjugate representations for the new colored states under the same global flavor symmetry of SM quarks. Choosing the global flavor symmetry to be that of minimal flavor violation, we suppress higher-order corrections to the strong CP phase to well below current experimental constraints. More than two dozen massless Goldstone bosons emerge from spontaneous flavor symmetry breaking, which yield strong astrophysical constraints on the symmetry breaking scale. In the early universe, the Goldstone bosons can be thermally produced from their interactions with the heavy colored fermions and contribute to ΔN eff at a measurable level. As a function of reheating temperature, the predicted ΔN eff shows an interesting plateau behavior we dub the “flavor stairway”, which encodes information about the SM quark flavor structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A microstructural signature of the coesite-quartz transformation: New insights from high-pressure experiments and EBSD

Ultra-high pressure (UHP) metamorphism is difficult to identify in continental crust as few petrological barometers are suitable for dominantly felsic lithologies. In such cases, burial to extreme depths is commonly identified through the preservation of coesite, a high-pressure polymorph of SiO 2 that typically forms at depths exceeding ∼ 100 km (i.e., > 2 GPa pressure). Unfortunately, coesite readily transforms to quartz upon exhumation, meaning that UHP terranes may often be overlooked. While some studies have suggested that quartz may inherit an orientation signature indicative of former coesite, both the specific nature of this signature and the conditions favouring its development remain uncertain. Here, to address this problem, we combine electron backscatter diffraction analysis of natural and experimental samples to explore microstructural evolution across the coesite-quartz phase transformation. We demonstrate that neighbouring domains of quartz commonly feature an 84 ± 4° rotation of [c] axes around the pole of a common {m} plane. This orientation relationship is a product of epitaxy, whereby the {$11\bar{2}2$} Japan twin plane in quartz nucleates on the (010) plane in coesite. In supercell simulations, the nucleation of Japan twins can be explained by the energetically favourable alignment of quartz tetrahedra on parental coesite tetrahedra. Through experiments, we demonstrate that this signature emerges over a broad range of conditions, regardless of the availability of nucleation sites (e.g., grain boundaries) or the density of crystal lattice defects (e.g., dislocations). Overall, our work provides a quantitative and unambiguous tool for identifying UHP terranes from quartz in isolation.

Coesite↗
DOE OSTI2024

Calibration of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation with Machine Learning Surrogate Models

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory is one of the most powerful accelerator-driven neutron sources in the world. The intense protons strike on SNS's mercury target to provide bright neutron beams, which also leads to severe fluid-structure interactions inside the target. Prediction of resultant loading on the target is difficult particularly when helium gas is injected into mercury to reduce the loading and mitigate the pitting damage on vessel walls. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this multi-physics problem. However, several uncertain parameters in the R-P model require intensive simulations to determine their optimal values. With the help of machine learning and the measured target strain, we have studied the major uncertain parameters in this R-P model and developed a framework to identify optimal parameters that significantly reduce the discrepancy between simulations and experimental strains. The preliminary results show the possibility of using this mercury/helium mixture and surrogate models to predict a better match of target strain response when the helium gas is injected.

Lin, Lianshan↗
DOE OSTI2024

Training models using forces computed by stochastic electronic structure methods

Abstract Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.

Ceperley, David M. (ORCID:0000000150826271)↗
DOE OSTI2026

Modeling Multi-View Impedance-Based Cross-Geometry SOH Estimator for Li-ion Batteries

Abstract: Accurately estimating battery’s State of Health (SOH) remains challenging when models must generalize across cell designs and operating conditions. Most Electrochemical Impedance Spectroscopy (EIS)-based approaches either (i) hand-engineer a few Nyquist-plot features for shallow models—fast but does not generalize across geometries—or (ii) learn directly from Nyquist plots with deep networks, which removes manual feature extraction, yet still limited to a single plot type. As a result, cross-geometry robustness and deployability on constrained Internet of Things (IoT) devices remain open problems. We propose a compact Convolutional Neural Network (CNN) (∼ 10k parameters) that takes multi-representation EIS inputs—Nyquist (real/imaginary) and phase–magnitude (|Z|/ϕ) stacked as four channels, so the model can learn complementary degradation signatures while remaining small enough for fast inference. We build a dataset from cyclic aging of two geometries (LG INR18650MJ1 cylindrical cells and LIR2032 coin cells), acquire EIS every ten cycles from 10 kHz to 10 mHz (10 points/decade), and evaluate with leave-one-cell-out testing strategy. We further study fusion vs. single-representation inputs and assess feasibility for on-device deployment (e.g., NVIDIA Jetson device). The results show that training on multiple EIS representations improves SOH estimation accuracy and cross-geometry generalization compared to single-representation models, which uses only Nyquist or phase–magnitude plots. This design targets accurate, generalizable SOH prediction without manual feature engineering while enabling practical real-time use.

Bakr, Ahmed [The University of Alabama (UA)]↗
DOE OSTI2026

Enabling Grid-Forming Control with Fault Ride-Through in Unbalanced Distribution Networks

Distribution networks are often unbalanced, causing oscillatory responses in inverter control designed for balanced conditions. Here, to address this problem, this paper proposes a novel time-domain transformation appropriate for inverter control and enables the decomposition of three-phase unbalanced signals into constant positive and negative components. Relations useful for calculating unbalanced active and reactive power are derived from first principle, providing insight into vector products of unbalanced three-phase signals. Furthermore, a grid-forming control effective under unbalanced conditions is developed, which delivers superior performance while meeting UNIFI1 specifications for grid-forming control under unbalanced conditions. specifications applicable to category 4 inverter-based resource, like setting and regulating frequency/voltage, providing voltage support, sharing active power, injecting negative sequence current, and riding through faults. A current limiter is proposed for safe fault ride-through and integrates with the grid-forming control featuring frequency/voltage droop controllers and current and voltage control loops. The transformation of interconnected inverters is formulated and stability of the proposed control analyzed to support robust parameter selections. The effectiveness of the proposed transformation and grid-forming control is demonstrated through analytical results and real-time simulation of a IEEE 123 distribution network on the Real-Time Digital Simulator. Comparison with existing methods shows that the proposed strategy satisfies the UNIFI specifications with a much better performance.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Development of a Gibbs Energy Minimiser for the MOOSE-based Corrosion Modelling App Yellowjacket and Validation of MSTDB

Nuclear materials are highly complex multiscale, multiphysics systems,and an effective prediction of nuclear reactor performance and safety requires simulation capabilities that tightly couple different physical phenomena. The Idaho National Laboratory’s Multiphysics Object Oriented Simulation Environment (MOOSE) provides the computational foundation for performing such simulations. With the move towards advanced reactors, such as the Molten Salt Reactor (MSR), that employ high temperature fluids compared to conventional reactors, corrosion has become a problem of great interest. A new application called Yellowjacket is currently under development to directly couple thermodynamic equilibrium and kinetics with phase field models in order to model corrosion in MSRs. As part of Yellowjacket, a Gibbs energy minimiser is being developed to perform thermochemical equilibrium calculations for a range of different materials, which is currently in its infancy. This report describes the further progress towards the development of Yellowjacket Gibbs energy minimiser. Ontario Tech University is developing a new Gibbs energy minimiser for Yellowjacket which is the primary contribution of this work. The aim to develop a thermochemistry solver for the MOOSE framework following the same development philosophy and using the same tools and libraries. A special focus is on performance, documentation and SQA. Furthermore through a scope extension partway through the fiscal year a thorough assessment of the MSTDB-TC v1.3 was performed at Ontario Tech University in the context of continuous improvement and quality assurance. The objective of the work was to have an arm’s length review of the database to give confidence that the database is performing as it was intended while assessing its current state to give recommendations to future developments. This assessment involved two parts: A) a quantitative assessment, and B) a qualitative assessment. Part A involved developing an automated test-suite that would compute values from the database using Thermochimica with comparisons to experimental measurements for validation purposes, which gives confidence to the database’s stakeholders that its functioning properly. Part B involved reviewing all binary systems in the database and making a qualitative assessment with two performance indicators: comprehensiveness and overall confidence. It is important to note that the models in the database are empirical, which is to say that the quality of any model is highly dependent on the experimental data used to inform its development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗