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At least 559 records · Page 31

Enabling Parallel Performance and Portability of Solid Mechanics Simulations Across CPU and GPU Architectures

Efficiently simulating solid mechanics is vital across various engineering applications. As constitutive models grow more complex and simulations scale up in size, harnessing the capabilities of modern computer architectures has become essential for achieving timely results. This paper presents advancements in running parallel simulations of solid mechanics on multi-core CPUs and GPUs using a single-code implementation. This portability is made possible by the C++ matrix and array (MATAR) library, which interfaces with the C++ Kokkos library, enabling the selection of fine-grained parallelism backends (e.g., CUDA, HIP, OpenMP, pthreads, etc.) at compile time. MATAR simplifies the transition from Fortran to C++ and Kokkos, making it easier to modernize legacy solid mechanics codes. We applied this approach to modernize a suite of constitutive models and to demonstrate substantial performance improvements across different computer architectures. This paper includes comparative performance studies using multi-core CPUs along with AMD and NVIDIA GPUs. Results are presented using a hypoelastic–plastic model, a crystal plasticity model, and the viscoplastic self-consistent generalized material model (VPSC-GMM). The results underscore the potential of using the MATAR library and modern computer architectures to accelerate solid mechanics simulations.

Morgan, Nathaniel (ORCID:0000000276118449)↗

Near-continuum, hypersonic oxygen flow over a double cone simulated by direct simulation Monte Carlo informed from quantum chemistry

A large-scale, fully resolved direct simulation Monte Carlo (DSMC) computation of a non-equilibrium, reactive flow of pure oxygen over a double cone is presented. Under the simulated near-continuum conditions, the computational demands are shown to be significant because of the wide range of length scales that must be resolved. Therefore, robust grid adaption capabilities and efficient parallelization of the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code that is utilized in this work are essential. The thermochemical and transport collision models were selected for efficiency and simplicity. First-principles data, obtained from the highly accurate direct molecular simulation method, were used to inform the collision models’ parameters. Importantly, because SPARTA implements molecular collision models using collision-specific energies, the resulting macroscopic relaxation rates were evaluated a posteriori via zero-dimensional heat bath simulations. The comparisons of surface properties, namely heat flux and pressure, show very close agreement with previous computational fluid dynamics (CFD) results. Differences with the measurements were found to be similar to the CFD simulations. The unresolved discrepancy with the measurements could be due to inconsistent free stream conditions with the actual experimental data or missing physical phenomena altogether, for example atomic and molecular oxygen electronically excited states, three-dimensional effects, or more complex gas–surface interactions. As shown in this work, the advantages of obtaining a DSMC particle solution for these flows reside in the method's ability to be directly informed from first principles and to seamlessly describe internal energy non-equilibrium for all modes. With the advent of exascale computing and beyond, particle methods will be an increasingly important tool to verify the validity of physical assumptions in reduced-order models via fully resolved, experimental-scale simulations, down to the level of molecular-level distributions.

Mechanics↗

SLoG: Large-Scale Logging Middleware for HPC and Big Data Convergence

Cloud developers traditionally rely on purpose-specific services to provide the storage model they need for an application. In contrast, HPC developers have a much more limited choice, typically restricted to a centralized parallel file system for persistent storage. Unfortunately, these systems often offer low performance when subject to highly concurrent, conflicting I/O patterns. This makes difficult the implementation of inherently concurrent data structures such as distributed shared logs. Yet, this data structure is key to applications such as computational steering, data collection from physical sensor grids, or discrete event generators. In this paper we tackle this issue. We present SLoG, shared log middleware providing a shared log abstraction over a parallel file system, designed to circumvent the aforementioned limitations. We evaluate SLoG’s design on up to 100,000 cores of the Theta supercomputer: the results show high append velocity at scale while also providing substantial benefits for other persistent backend storage systems.

big data↗

Testing predictions of electron scale turbulent pedestal transport in two DIII-D ELMy H-modes

In this study, we present linear and nonlinear gyrokinetic analyses in the pedestal region of two DIII-D ELMy H-mode discharges using the CGYRO code. The otherwise matched discharges employ different divertor configurations to investigate the impact of varying recycling and particle source on pedestal profiles. Linear gyrokinetic simulations find electrostatic ion-scale instabilities (ion temperature gradient and trapped electron modes, ITG-TEM) are present just inside the top of the pedestal with growth rates that are enhanced significantly by parallel velocity shear. In the sharp gradient region, E x B shearing rates are comparable or larger than ion scale growth rates, suggesting the suppression of ITG-TEM modes in this region. Instead, the electron temperature profiles are found to be correlated with and just above the electron temperature gradient (ETG) instability thresholds. Using gradients varied within experimental uncertainties, nonlinear electron-scale gyrokinetic simulations predict electron heat fluxes from ETG turbulence, that when added to neoclassical ion thermal transport simulated by NEO, account for 30-60% of the total experimental heat flux. In addition, the neoclassical electron particle flux is found to contribute significantly to the experimental fluxes inferred from SOLPS-ITER analysis. Additional nonlinear gyrokinetic simulations are run varying input gradients to develop a threshold-based reduced model for ETG transport, finding a relatively simple dependence on η e = L ne /L Te . Predictive transport simulations are used to validate this pedestal-specific ETG model, in conjunction with a model for neoclassical particle transport. In both discharges, the predicted electron temperatures are always overpredicted, indicative of the insufficient stiffness in the ETG pedestal model to account for all of the experimental electron thermal transport. In the case of the closed divertor discharge with lower particle source, the predicted electron density is close to the experiment, consistent with the magnitude of neoclassical particle transport in that discharge. However, the density profiles are overpredicted in the open divertor discharge (larger particle source), due to insufficient model transport. In conclusion, the implications for other mechanisms accounting for the remainder of transport in the sharp gradient region in the two discharges are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multirate partitioned Runge–Kutta methods for coupled Navier–Stokes equations

Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in physics, temporal, and spatial scales. Further, this study explores multirate partitioned Runge-Kutta methods for the fluid-fluid interaction problem and demonstrates its parallel performance by using the PETSc library. We consider compressible Navier-Stokes equations with gravity coupled through a rigid-lid interface. Our large-scale numerical experiments reveal that multirate partitioned Runge-Kutta coupling schemes (1) can conserve total mass; (2) have second-order accuracy in time; and (3) provide favorable strong- and weak-scaling performance on modern computing architectures. We also show that the speedup factors of multirate partitioned Runge-Kutta methods match theoretical expectations over their base (single-rate) method.

54 ENVIRONMENTAL SCIENCES↗

Investigation into the formation of the scrape-off layer density shoulder in JET ITER-like wall L-mode and H-mode plasmas

The low temperature boundary layer plasma (scrape-off layer or SOL) between the hot core and the surrounding vessel determines the level of power loading, erosion and implantation of material surfaces, and thus the viability of tokamak-based fusion as an energy source. Here, this study explores mechanisms affecting the formation of flattened density profiles, so-called 'density shoulders', in the low-field side (LFS) SOL, which modify ion and neutral fluxes to surfaces—and subsequent erosion. There is evidence against local enhancement of ionization inducing shoulder formation. We find that increases in SOL parallel resistivity, Λ div (=[ L || ν ei Ω i ]/ c s Ω e ), postulated to lead to shoulder growth through changes in SOL turbulence characteristics, correlates with increases in SOL shoulder amplitude, A s , but only under a subset of conditions (D 2 -fuelled L-mode density scans with outer strike point on the horizontal target). Λ div fails to correlate with A s for cases of N 2 seeding or during sweeping of the strike point across the horizontal target. The limited correlation of Λ div and A s is also found for H-mode discharges. Thus, while it may be necessary for Λ div to be above a threshold of ~1 for shoulder formation and/or growth, another mechanism is required. More significantly, we find that in contrast to parallel resistivity, outer divertor recycling, as quantified by the total outer divertor Balmer D α emission, I – D α , does scale with A s where Λ div does and even where Λ div does not. Divertor recycling could lead to SOL density shoulder formation through: (a) reducing the parallel to the field flow (loss) of ions out of the SOL to the divertor; and (b) changes in radial electric fields which lead to E × B poloidal flows as well as potentially affecting SOL turbulence birth characteristics. Therefore, changes in divertor recycling may be the sole process involved in bringing about SOL density shoulders or it may be that it acts in tandem with parallel resistivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy occupation of waves and structures in 3D compressive MHD turbulence

Abstract Structures and propagating waves are often observed in solar wind turbulence. Their origins and features remain to be uncovered. In this work, we use 3D driven, compressible MHD turbulence simulations to investigate the global signatures of the driven fluctuations in whole spatial and temporal domain. With four-dimensional spatial-temporal (x, y, z, t) Fourier transformations implemented, we have identified two distinct main populations: waves, which satisfy the $\omega -\boldsymbol {k}$ dispersion relations and are propagating; and structures, which satisfy the polarization relations but non-propagating (ω = 0). Whereas the overall turbulent energy spectrum is still consistent with k−5/3, the contributions from waves and structures show very different behaviour in $\boldsymbol {k}$ space, with structures dominating at small k but waves becomes comparable to structures at large k. Overall, the fluctuations in the directions perpendicular to the large-scale mean field $\boldsymbol {B_0}$ are a manifestation of structures, while along the parallel direction, the fluctuations are dominated by waves. Also, a significant portion of the incompressible structures are the Alfvénic nature, and with imbalanced increased, the waves predominantly propagate in one direction and nearly perpendicular to $\boldsymbol {B_0}$. Differentiating the relative contributions from waves and structures could have important implications for understanding the non-linear cascade processes in the inertial range as well as particle-fluctuation interactions at small scales.

Yang, L. P.↗

Collaborative Research: Advancing Arctic Climate Projection Capability at Seasonal to Decadal Scales (Final Technical Report)

The Regional Arctic System Model (RASM) at process resolving configurations has been used to (i) advance understanding of physical processes and feedbacks involved in Arctic amplification and (ii) understand and potentially reduce uncertainty in prediction of arctic climate change at seasonal to decadal scales. RASM consists the atmosphere (Weather and Research Forecasting model, WRF), ocean (Parallel Ocean Program, POP), sea ice (CICE), land hydrology (Variable Infiltration Capacity model, VIC), river routing scheme (RVIC), marine biogeochemistry components and the coupling framework (CPL7). Its domain is pan-Arctic, with the atmosphere and land components configured on a 50-km or 25-km grid and four configurations of the ocean and sea ice components: 1/12°(~9.3km) or 1/48°(~2.4km) and 45 or 60 vertical layers. These RASM configurations have been motivated by the emerging exascale capability for high performance computing to improve model fidelity. The dynamical downscaling of reanalysis allows comparison of RASM results with observations in place and time to: (i) advance system level understanding of physical processes and coupling involved in an event, (ii) optimize model parameter space, (iii) diagnose and reduce model biases and (iv) produce realistic and consistent across all the components initial conditions for predictions and predictability studies, which are all unique capabilities not available in global Earth System Models (ESMs). An evaluation of RASM 1.0 (Cassano et al. 2017) revealed that it had a cold bias over the oceans and a warm bias over land areas due largely to cloud and radiation biases in the model, with too little cloud cover simulated over land and too much cloud cover simulated over sub-polar oceans. This study has motivated an upgrade to WRF version 3.7.1 in RASM and allowed for the inclusion of the radiative impact of convective clouds. A variety of atmospheric physics parameterizations were evaluated against observations (e.g. data from the Arctic Clouds in Summer Experiment (ACSE); Sedlar et al. 2020) to identify an optimal suite of WRF physics options in RASM. The RASM with the optimized WRF physics were used to study the impact of strong mesoscale winds over the ocean around the southern tip of Greenland (DuVivier and Cassano 2016) and their impact on oceanic convection (DuVivier et al. 2017a). Data from the PolarWinds field campaign were used to evaluate WRF boundary layer physics and resolution impacts on the simulation of a Greenland barrier wind event (DuVivier et al. 2017b). The RVIC streamflow routing model has been implemented in RASM to realistically represent high-resolution streamflow processes (Hamman et al. 2017) and to couple the land buoyancy fluxes to the ocean. The RASM-RVIC high-resolution data set of all coastal freshwater fluxes for the Arctic drainage basin and surrounding areas for 1979-2014 was published as a separate product (https://doi.org/10.5281/zenodo.293037). The fidelity of atmospheric momentum transfer to and the response of polar marine Ekman layer in RASM and Community Earth System Model (CESM) was investigated by Roberts et al. (2015). The increased frequency of oceanic flux exchange in CESM, following the RASM guidance, caused a considerable increase in the median inertial ice speed across the Southern Ocean and parts of the Arctic. A comprehensive evaluation of the RASM1.0 atmosphere-ocean-sea ice-land interface was completed by Brunke et al. (2018). RASM was also demonstrated for its capability to simulate extreme events in agreement with observations in space and time (Lee et al. submitted). In particular, the development of three open water events, known as polynyas, have been simulated north of Greenland in February of 2011, 2017 and 2018, in agreement with satellite observations for the past four decades. The optimized RASM sea ice results have been favorably evaluated against satellite observations and a subset of eleven CMIP6 models (Watts et al. submitted). In a complementary project, Jin et al. (2018) have shown that RASM with higher-resolution and new sea-ice processes contributed to lower model errors in sea-ice conditions, concentrations of nutrients and ice algae, in comparison to results from the coarse-resolution (1°) CESM. In two other complementary studies, RASM results were used (i) to explain areas of concentrated use by bowhead whales, the seasonal progression in the use, and the physical environment within those areas (Citta et al. 2015) and (ii) for a synthesis of fall bowhead whales distribution and migration in the Bering-Chukchi-Beaufort (BCB) Sea to investigate whale movements and feeding to the local ocean hydrography and currents (Citta et al. 2018). However, the multi-decadal output from the CESM Large Ensemble yielded unrealistic forcing. Instead, the shorter NCEP CFSv2 9-month forecasts were successfully tested and afforded an increased ensemble size (~30) to demonstrate gains of dynamical downscaling at sub-seasonal to intra-annual time scales. The improved model physics and coupling among RASM model components have yielded more realistic representation of the sea ice cover and consistent across all model components initial conditions. Consequently, RASM demonstrates significant gains compared to simulation of sea ice in the NCEP reanalysis. In addition, RASM 6-month ensemble forecasts yield very realistic sea ice distribution, which demonstrates both significant gains of dynamical downscaling and the continued impact of the initial conditions on forecasts out to 6 months (https://nps.edu/web/rasm/predictions). A follow up study using RASM for dynamical downscaling of the more realistic CESM initialized Decadal Prediction Large Ensemble output is currently ongoing as part of the DOE RGMA HiLAT-RASM project.

54 ENVIRONMENTAL SCIENCES↗

Editorial: Advanced water splitting technologies development: Best practices and protocols

As the level of deployment and utilization of renewable energy sources, including wind and solar, continues to rise, large-scale, long-term energy storage technologies that could accommodate weekly and seasonal energy fluctuations will play a significant role in the overall deployment of renewable energies in the future. Harnessing and storing renewable energy resources via electrochemical, photoelectrochemical, or thermochemical processes by converting renewable energy into sustainable (energy storage) fuels have the potential to meet the long-term, terawatt scale energy storage challenge. Renewable hydrogen production is the cornerstone for sustainable fuel production and deep decarbonization of multiple sectors in our society. Cost-competitive clean hydrogen provides value to applications, such as 1) in the transportation sector for fuel cell vehicles, 2) in the electric grid sector for system stability and load balancing, and 3) in the industrial sector with metal refineries, cement production, and biomass upgrading (carbon-free fertilizer production). In addition, coupling clean renewable hydrogen with the carbon and nitrogen cycles enables known and well-established thermal-chemical processes to generate renewable hydrocarbon fuels and ammonia. The Advanced Water Splitting Technologies (AWST): low temperature electrolysis (LTE), high temperature electrolysis (HTE), photoelectrochemical (PEC) and solar thermo-chemical hydrogen (STCH) provide four unique and parallel approaches to produce low cost, low greenhouse gas (GHG) emission hydrogen at scale (Figure 1). Cost competitive clean hydrogen production using these four technologies is a current high priority focus for governments and industry. In June of 2022, the U.S. Department of Energy (DOE) launched the first in a series of Earthshot Initiatives. The Hydrogen Shot, “1 1 1” aims to reduce the cost of clean hydrogen by more than 80% to one dollar per one kilogram in 1 decade ($\$$1/kg H 2 ). The European Green Deal and the International Energy Agency (IEA) have implemented a strong focus on green hydrogen production for a clean and secure energy future.

benchmarking, low temperature electrolysis↗

Part-scale microstructure prediction for laser powder bed fusion Ti-6Al-4V using a hybrid mechanistic and machine learning model

Laser powder bed fusion (LPBF) Ti-6Al-4V is widely studied for use in structural applications in aerospace and medical industries, but mechanical anisotropy and microstructural inhomogeneity prohibits its wider adoption. Although successful microstructure prediction models have been developed, a remaining challenge is their limited integration across length/time scales and validation by experimental studies. Here, this work proposes a physics-augmented machine learning surrogate model to unite predictions of LPBF temperature, β phase morphology and texture, and α/α’ formation into a single framework that is calibrated and validated with experiments. First, a phase field (PF) model of the martensitic β→α’ transformation is developed and calibrated using data from in-situ synchrotron cyclic heating/cooling studies quantifying the variation of α phase fraction with time. In parallel, an established finite difference-Monte Carlo (FDMC) model predicts the part-scale temperature profile and β grain formation during solidification. A dataset is developed using LPBF cyclic temperature descriptors from the FDMC model as inputs and corresponding α/α’ phase fraction and width from the PF model as outputs. Five machine learning (ML) regression models are tested and optimized, having mean absolute error in testing ≤ 4 %, and the k-nearest neighbors (KNN) model is selected as the best performing. The KNN model is called at the nodal level during post-processing of the FDMC model to replace and downscale the response of the PF model. The combined agility and accuracy of the hybrid FDMC-ML model enables part-scale microstructure predictions that can be further used for property predictions to accelerate AM process optimization.

36 MATERIALS SCIENCE↗

HiPACE++: A portable, 3D quasi-static particle-in-cell code

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static, three-dimensional particle-in-cell code HiPACE++. By decomposing all the computation of a 3D domain in successive 2D transverse operations and choosing appropriate memory management, HiPACE++ demonstrates orders-of-magnitude speedups on modern scientific GPUs over CPU-only implementations. The 2D transverse operations are performed on a single GPU, avoiding time-consuming communications. The longitudinal parallelization is done through temporal domain decomposition, enabling near-optimal strong scaling from 1 to 512 GPUs. HiPACE++ is a modular, open-source code enabling efficient modeling of plasma accelerators from laptops to state-of-the-art supercomputers.

97 MATHEMATICS AND COMPUTING↗

Vision and Development of a Design, Implementation, and Verification Automation (DIVA) Software Platform for DNA Construction

Abstract DNA construction, while a prerequisite to many biological endeavors, is often a time-consuming distraction from an individual’s primary research objectives. We envisioned that with the right software infrastructure and cultural mindset, a single person could execute in parallel the batched DNA construction tasks of an entire research institute, at scales realizing efficiency gains through process and laboratory automation. In pursuit of this vision, we developed the Design, Implementation, and Verification Automation (DIVA) software platform. DIVA’s web interface enables researchers to design DNA constructs (using visual biological computer-aided design tools and biological parts repositories), submit designs for construction to dedicated staff, and track DNA construction as it progresses. DIVA supports the dedicated staff through the DNA construction process and records both successful and unsuccessful attempts toward improving the overall process. The platform is publicly available at public-diva.jbei.org and its open-source code through github.com/JBEI/DIVA.

Plahar, Hector [DOE Agile BioFoundry , , ,; DOE Jo↗

Effects of wave damping and finite perpendicular scale on three-dimensional Alfvén wave parametric decay in low-beta plasmas

Shear Alfvén wave parametric decay instability (PDI) provides a potential path toward significant wave dissipation and plasma heating. However, fundamental questions regarding how PDI is excited in a realistic three-dimensional (3D) open system and how the finite perpendicular wave scale—as found in both laboratory and space plasmas—affects the excitation remain poorly understood. Here, we present the first 3D, open-boundary, hybrid kinetic-fluid simulations of kinetic Alfvén wave PDI in low-beta plasmas. Key findings are that the PDI excitation is strongly limited by the wave damping present, including electron–ion collisional damping (represented by a constant resistivity) and geometrical attenuation associated with the finite-scale Alfvén wave, and ion Landau damping of the child acoustic wave. The perpendicular wave scale alone, however, plays no discernible role: waves of different perpendicular scales exhibit similar instability excitation as long as the magnitude of the parallel ponderomotive force remains unchanged. These findings are corroborated by theoretical analysis and estimates. This new understanding of 3D kinetic Alfvén wave PDI physics is essential for laboratory study of the basic plasma process and may also aid future evaluation of the relevance/role of PDI in low-beta space plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low power on-chip data transmission for wafer-scale monolithic active pixel sensors

Here, this paper details the implementation of the digital pulse shaping subsystem within the Backbone Transmission Line Encoding (BTLE) driver, a low-power, long-distance on-chip data transmission solution designed in a 65 nm CMOS process. Digital pulse shaping is critical for minimizing inter-symbol interference (ISI) caused by bandwidth limitations of on-chip interconnects, especially in wafer-scale monolithic active pixel sensors (MAPS). A duobinary encoder coupled with a parallelized polyphase finite impulse response (FIR) filter is used for efficient shaping of the transmitted signal spectrum. This reconfigurable architecture achieves reliable 160 Mb/s data transfer over a 10 cm on-chip link, as validated by simulations demonstrating low power consumption (FoM 37.3 fJ/bit/mm of transmission line length) and effective ISI mitigation.

47 OTHER INSTRUMENTATION↗

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such `sparse' frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E , 80 , 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources.

Chemistry↗

Future of plasma etching for microelectronics: Challenges and opportunities

Plasma etching is an essential semiconductor manufacturing technology required to enable the current microelectronics industry. Along with lithographic patterning, thin-film formation methods, and others, plasma etching has dynamically evolved to meet the exponentially growing demands of the microelectronics industry that enables modern society. At this time, plasma etching faces a period of unprecedented changes owing to numerous factors, including aggressive transition to three-dimensional (3D) device architectures, process precision approaching atomic-scale critical dimensions, introduction of new materials, fundamental silicon device limits, and parallel evolution of post-CMOS approaches. The vast growth of the microelectronics industry has emphasized its role in addressing major societal challenges, including questions on the sustainability of the associated energy use, semiconductor manufacturing related emissions of greenhouse gases, and others. The goal of this article is to help both define the challenges for plasma etching and point out effective plasma etching technology options that may play essential roles in defining microelectronics manufacturing in the future. The challenges are accompanied by significant new opportunities, including integrating experiments with various computational approaches such as machine learning/artificial intelligence and progress in computational approaches, including the realization of digital twins of physical etch chambers through hybrid/coupled models. These prospects can enable innovative solutions to problems that were not available during the past 50 years of plasma etch development in the microelectronics industry. To elaborate on these perspectives, the present article brings together the views of various experts on the different topics that will shape plasma etching for microelectronics manufacturing of the future.

Engineering↗

TA_solver -- Traffic Assignment solver package

TA_solver is a modular software framework for solving user equilibrium traffic assignment problems, both static and dynamic, utilizing the OTM (Open Traffic Models) API to encode traffic scenarios. The design is based on the formulation of the problem as a variational inequality. Unlike most existing traffic assignment software which focus on specific traffic models, TA_solver accommodates various traffic models, but also enables using parallel computation in high performance computing environments to speed up large-scale equilibrium calculations.

Ugirumurera, Juliette↗