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DOE OSTI2025

Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy

This report describes how to produce reference solutions for the equilibrium core search of pebble bed reactors using the pyrates Python library. The pyrates library uses the kugelpy methodology to perform running-in calculations to reach an equilibrium core. This approach relies on full-core Monte Carlo neutron transport calculations and the shifting of fuel pebble inventory through the reactor to simulate pebble movement in the core from one step to the next of a running-in scenario. In addition to the use of Serpent for the Monte Carlo neutron transport calculations, as part of this work, updates for the use of the Shift Monte Carlo code were integrated into the official pyrates GitHub repository. Comparisons of running-in simulations for a generic pebble bed reactor produced by using pyrates with Serpent and Shift are shown. Although consistent trends are shown between the use of the two Monte Carlo codes, the limiting factor in either calculation is the computation time due to the need to perform several hundred full-core neutron transport calculations before an equilibrium core is reached.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Enhanced Component Performance Study: Emergency Diesel Generators 1998-2024

This report presents an enhanced performance evaluation of the emergency power system (EPS) and high-pressure core spray (HPCS) emergency diesel generators (EDGs) at U.S. commercial nuclear power plants. This report evaluates component performance over time using (1) Institute of Nuclear Power Operations (INPO) Industry Reporting and Information System (IRIS) data from 1998 through 2024 and (2) maintenance unavailability performance data from Mitigating Systems Performance Index (MSPI) Basis Document data from 2002 through 2024. The objective is to show estimates of current failure probabilities and rates related to EDGs, trend these data on an annual basis, determine if the current data are consistent with the probability distributions currently recommended for use in Nuclear Regulatory Commission (NRC) probabilistic risk assessments, show how the reliability data differ for different EDG manufacturers and for EDGs with different ratings; and summarize the subcomponents, causes, detection methods, and recovery associated with each EDG failure mode. The EDG failure modes considered are fail to start (FTS), fail to load and run (FTLR), and fail to run after one hour of operation (FTR>1H). Engineering analyses were performed with respect to time-period and failure mode without regard to the actual number of EDGs at each plant. The factors analyzed include subcomponent, failure cause, detection method, recovery, manufacturer, and EDG rating. The following increasing trends were identified for EDGs for the most recent 10-year period: • EPS and HPCS EDG frequency of start demands (demands per reactor year) • EPS and HPCS EDG frequency of FTLR demands • EPS and HPCS EDG frequency of run>1H hours. The following decreasing trends were identified for EDGs for the most recent 10-year period: • EPS EDG FTR>1H failure rate • EPS EDG unreliability • EPS and HPCS EDG frequency of FTR>1H events (failures per reactor year).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

NMF-Based Anomaly Detection in CMS 2D Tracking Occupancy Histograms

The CMS experiment relies on Data Quality Monitoring (DQM) to ensure that recorded collision data are suitable for physics analysis. During LHC Run 3, each run contains many lumisections and tracking monitoring elements, making offline inspection challenging, especially for localized detector effects that may appear only for short periods of time. This poster presents an unsupervised machine-learning approach to identify anomalous lumisections in CMS tracking occupancy histograms using Non-Negative Matrix Factorization (NMF). The workflow uses offline CMS DQMIO tracking histograms retrieved with the CMS DIALS API and organized as two-dimensional occupancy maps for each lumisection. After selecting stable lumisections, the occupancy maps are normalized and arranged into a non-negative data matrix. The NMF model learns a compact set of basis patterns describing normal tracking occupancy. Each lumisection is then reconstructed from these learned components, and the reconstruction error is used as an anomaly score. Large residuals indicate occupancy patterns that deviate from normal detector behavior and are flagged for further inspection. This NMF-based approach provides a fast and interpretable way to flag lumisections whose tracking occupancy patterns differ from normal detector behavior. Preliminary studies show sensitivity to known tracking anomalies, and ongoing work is focused on validating the method across additional Run 3 Pixel and Strip detector issues.

Rodríguez Ramos, Iliomar [Puerto Rico U., Mayaguez↗
DOE OSTI2026

A New Era for Bubble Chamber Technology

Neutrino experiments like DUNE are limited by how well we understand the way neutrinos actually interact with atoms. The best way to fix that is to measure interactions on hydrogen, since a hydrogen nucleus is just a single free proton with largely none of the nuclear effects that heavier targets like argon have. The catch is that no one has built a hydrogen bubble chamber for a neutrino beam since the 1980s, mostly because the old chambers had too low of an active time. MAMBA is a project focused on bringing that technology back but built to cycle continuously at 1 Hz. I spent my summer internship on two of the subsystems that make that kind of speed possible. First, I helped install and test a new solid copper thermal link that replaced the old flexible braided cooling path, and it brought the coldhead down to 21.3 K, right at the target temperature. Second, I built and tested a Raspberry Pi based PLC control system, and across 20,000 trials it answered in a median of 0.64 ms, with only 0.66\% of trials running past 1 ms. Both results point the same direction: that inexpensive, off the shelf hardware can perform fast and reliable enough to eventually run a bubble chamber the way MAMBA needs it to run.

Williams, Nicholas [DuPage Coll.]↗
DOE OSTI2022

Status of the Mu2e experiment at Fermilab

The Mu2e experiment at Fermilab aims to measure the charged-lepton flavour violating (CLFV) neutrino-less conversion of a negative muon into an electron in the field of a nucleus with an unprecedented single event sensitivity of 3x10^{-17}. This document illustrates the physics motivation and design of the experiment.In the current schedule Mu2e is expected to start taking data in 2025 with a reduced average beam intensity for about two years (Run 1). After a shut down for the upgrade of Fermilab accelerator complex, data taking will restart at full beam intensity (Run 2). A detailed update of the expected experiment sensitivity for Mu2e Run 1 is presented, together with an estimate of the final Mu2e sensitivity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Measurement of the anomalous spin precession frequency $\omega_\alpha$ in the Muon g-2 experiment at Fermilab

The Muon $g-2$ Experiment at Fermilab aims to measure the muon magnetic moment anomaly, $a_{\mu} = (g-2)/2$, with a final accuracy of 0.14 parts per million (ppm). A $3.1$-GeV muon beam is injected into a storage ring of $14\,$m diameter, in the presence of a $1.45\,$T magnetic field. The anomaly $a_\mu$ can be extracted by accurately measuring the anomalous muon spin precession frequency $\omega_a$, based on the arrival time distribution of decay positrons observed by $24$ calorimeters, and the magnetic field. In 2023, the experiment published its second result based on the two datasets Run-2 and Run-3, reaching the unprecedented sensitivity of $0.21\,$ppm --- a factor $\sim2.2$ improvement since its first result published in 2021, based on the first dataset (Run-1). In this paper, we will focus on the measurement of the $\omega_a$ frequency, describing the techniques and major sources of systematic uncertainty in the 2023 publication, and outlining the improvements since the 2021 result. We will also cover the status of the ongoing $\omega_a$ analysis for the last three datasets, collected from 2020 to 2023, along with the projected uncertainties on the final Muon $g-2$ measurement at Fermilab.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Selecting Minimal Motion Primitive Libraries with Genetic Algorithms

Motion primitives allow for application of discrete search algorithms to rapidly produce trajectories in complex continuous space. The maneuver automaton (MA) provides an elegant formulation for creating a primitive library based on trims and maneuvers. However, performance is fundamentally limited by the contents of the primitive library. If the library is too sparse, performance can be poor in terms of path cost, whereas a library that is too large can increase run time. This work outlines new methods for using genetic algorithms to prune a primitive library. The proposed methods balance the path cost and planning time while maintaining the reachability of the MA. The genetic algorithm in this paper evaluates and mutates populations of motion primitive libraries to optimize both objectives. Here, we illustrate the performance of these methods with a simulated study using a nonlinear medium-fidelity F-16 model. We optimize a library with the presented algorithm for obstacle-free navigation and a nap-of-the-Earth navigation task. In the obstacle-free navigation task, we show a tradeoff of a 10.16% higher planning cost for a 96.63% improvement in run time. In the nap-of-the-Earth task, we show a tradeoff of a 9.712% higher planning cost for a 92.06% improvement in run time.

42 ENGINEERING↗
DOE OSTI2025

The Journal of Open Source Software (JOSS): Bringing Open-Source Software Practices to the Scholarly Publishing Community for Authors, Reviewers, Editors, and Publishers

Open-source software (OSS) is a critical component of open science, but contributions to the OSS ecosystem are systematically undervalued in the current academic system. The Journal of Open Source Software (JOSS) contributes to addressing this by providing a venue (that is itself free, diamond open access, and all open-source, built in a layered structure using widely available elements/services of the scholarly publishing ecosystem) for publishing OSS, run in the style of OSS itself. A particularly distinctive element of JOSS is that it uses open peer review in a collaborative, iterative format, unlike most publishers. Additionally, all the components of the process—from the reviews to the papers to the software that is the subject of the papers to the software that the journal runs—are open. We describe JOSS’s history and its peer review process using an editorial bot, and we present statistics gathered from JOSS’s public review history on GitHub showing an increasing number of peer reviewed papers each year. We discuss the new JOSSCast and use it as a data source to understand reasons why interviewed authors decided to publish in JOSS. JOSS’s process differs significantly from traditional journals, which has impeded JOSS’s inclusion in indexing services such as Web of Science. In turn, this discourages researchers within certain academic systems, such as Italy’s, which emphasize the importance of Web of Science and/or Scopus indexing for grant applications and promotions. JOSS is a fully diamond open-access journal with a cost of around US$\$$5 per paper for the 401 papers published in 2023. The scalability of running JOSS with volunteers and financing JOSS with grants and donations is discussed.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

A seamless approach for evaluating climate models across spatial scales

In regions of the world where topography varies significantly with distance, most global climate models (GCMs) have spatial resolutions that are too coarse to accurately simulate key meteorological variables that are influenced by topography, such as clouds, precipitation, and surface temperatures. One approach to tackle this challenge is to run climate models of sufficiently high resolution in those topographically complex regions such as the North American Regionally Refined Model (NARRM) subset of the Department of Energy’s (DOE) Energy Exascale Earth System Model version 2 (E3SM v2). Although high-resolution simulations are expected to provide unprecedented details of atmospheric processes, running models at such high resolutions remains computationally expensive compared to lower-resolution models such as the E3SM Low Resolution (LR). Moreover, because regionally refined and high-resolution GCMs are relatively new, there are a limited number of observational datasets and frameworks available for evaluating climate models with regionally varying spatial resolutions. As such, we developed a new framework to quantify the added value of high spatial resolution in simulating precipitation over the contiguous United States (CONUS). To determine its viability, we applied the framework to two model simulations and an observational dataset. We first remapped all the data into Hierarchical Equal-Area Iso-Latitude Pixelization (HEALPix) pixels. HEALPix offers several mathematical properties that enable seamless evaluation of climate models across different spatial resolutions including its equal-area and partitioning properties. The remapped HEALPix-based data are used to show how the spatial variability of both observed and simulated precipitation changes with resolution increases. This study provides valuable insights into the requirements for achieving accurate simulations of precipitation patterns over the CONUS. It highlights the importance of allocating sufficient computational resources to run climate models at higher temporal and spatial resolutions to capture spatial patterns effectively. Furthermore, the study demonstrates the effectiveness of the HEALPix framework in evaluating precipitation simulations across different spatial resolutions. This framework offers a viable approach for comparing observed and simulated data when dealing with datasets of varying spatial resolutions. By employing this framework, researchers can extend its usage to other climate variables, datasets, and disciplines that require comparing datasets with different spatial resolutions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Accelerating discoveries at DIII-D with the Integrated Research Infrastructure

DIII-D research is being accelerated by leveraging high performance computing (HPC) and data resources available through the National Energy Research Scientific Computing Center (NERSC) Superfacility initiative. As part of this initiative, a high-resolution, fully automated, whole discharge kinetic equilibrium reconstruction workflow was developed that runs at the NERSC for most DIII-D shots in under 20 min. This has eliminated a long-standing research barrier and opened the door to more sophisticated analyses, including plasma transport and stability. These capabilities would benefit from being automated and executed within the larger Department of Energy Advanced Scientific Computing Research program’s Integrated Research Infrastructure (IRI) framework. The goal of IRI is to empower researchers to meld DOE’s world-class research tools, infrastructure, and user facilities seamlessly and securely in novel ways to radically accelerate discovery and innovation. For transport, we are looking at producing flux matched profiles and also using particle tracing to predict fast ion heat deposition from neutral beam injection before a shot takes place. Our starting point for evaluating plasma stability focuses on the pedestal limits that must be navigated to achieve better confinement. This information is meant to help operators run more effective experiments, so it needs to be available rapidly inside the DIII-D control room. So far this has been achieved by ensuring the data is available with existing tools, but as more novel results are produced new visualization tools must be developed. In addition, all of the high-quality data we have generated has been collected into databases that can unlock even deeper insights. This has already been leveraged for model and code validation studies as well as for developing AI/ML surrogates. The workflows developed for this project are intended to serve as prototypes that can be replicated on other experiments and can be run to provide timely and essential information for ITER, as well as next stage fusion power plants.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Machine Learning Emulation of Spatial Deposition from a Multi-Physics Ensemble of Weather and Atmospheric Transport Models

In the event of an accidental or intentional hazardous material release in the atmosphere, researchers often run physics-based atmospheric transport and dispersion models to predict the extent and variation of the contaminant spread. These predictions are imperfect due to propagated uncertainty from atmospheric model physics (or parameterizations) and weather data initial conditions. Ensembles of simulations can be used to estimate uncertainty, but running large ensembles is often very time consuming and resource intensive, even using large supercomputers. In this paper, we present a machine-learning-based method which can be used to quickly emulate spatial deposition patterns from a multi-physics ensemble of dispersion simulations. We use a hybrid linear and logistic regression method that can predict deposition in more than 100,000 grid cells with as few as fifty training examples. Logistic regression provides probabilistic predictions of the presence or absence of hazardous materials, while linear regression predicts the quantity of hazardous materials. The coefficients of the linear regressions also open avenues of exploration regarding interpretability—the presented model can be used to find which physics schemes are most important over different spatial areas. A single regression prediction is on the order of 10,000 times faster than running a weather and dispersion simulation. However, considering the number of weather and dispersion simulations needed to train the regressions, the speed-up achieved when considering the whole ensemble is about 24 times. Ultimately, this work will allow atmospheric researchers to produce potential contamination scenarios with uncertainty estimates faster than previously possible, aiding public servants and first responders.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Gridded Solar Irradiance Ensemble Prediction System Based on WRF-Solar EPS and the Analog Ensemble

The WRF-Solar Ensemble Prediction System (WRF-Solar EPS) and a calibration method, the analog ensemble (AnEn), are used to generate calibrated gridded ensemble forecasts of solar irradiance over the contiguous United States (CONUS). Global horizontal irradiance (GHI) and direct normal irradiance (DNI) retrievals, based on geostationary satellites from the National Solar Radiation Database (NSRDB) are used for both calibrating and verifying the day-ahead GHI and DNI predictions (GDIP). A 10-member ensemble of WRF-Solar EPS is run in a re-forecast mode to generate day-ahead GDIP for three years. The AnEn is used to calibrate GDIP at each grid point independently using the NSRDB as the “ground truth”. Performance evaluations of deterministic and probabilistic attributes are carried out over the whole CONUS. The results demonstrate that using the AnEn calibrated ensemble forecast from WRF-Solar EPS contributes to improving the overall quality of the GHI predictions with respect to an AnEn calibrated system based only on the deterministic run of WRF-Solar. In fact, the calibrated WRF-Solar EPS’s mean exhibits a lower bias and RMSE than the calibrated deterministic WRF-Solar. Moreover, using the ensemble mean and spread as predictors for the AnEn allows a more effective calibration than using variables only from the deterministic runs. Finally, it has been shown that the recently introduced algorithm of correction for rare events is of paramount importance to obtain the lowest values of GHI from the calibrated ensemble (WRF-Solar EPS AnEn), qualitatively consistent with those observed from the NSRDB.

14 SOLAR ENERGY↗
DOE OSTI2020

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

The fate of water and water-soluble toxic wastes in the subsurface is of high importance for many scientific and practical applications. Although solute transport is proportional to water flow rates, theoretical and experimental studies show that heavy-tailed (power-law) solute transport distribution can cause chemical transport retardation, prolonging clean-up time-scales greatly. However, no consensus exists as to the physical basis of such transport laws. In percolation theory, the scaling behavior of such transport rarely relates to specific medium characteristics, but strongly to the dimensionality of the connectivity of the flow paths (for example, two- or three-dimensional, as in fractured-porous media or heterogeneous sediments), as well as to the saturation characteristics (i.e., wetting, drying, and entrapped air). In accordance with the proposed relevance of percolation models of solute transport to environmental clean-up, these predictions also prove relevant to transport-limited chemical weathering and soil formation, where the heavy-tailed distributions slow chemical weathering over time. The predictions of percolation theory have been tested in laboratory and field experiments on reactive solute transport, chemical weathering, and soil formation and found accurate. Recently, this theoretical framework has also been applied to the water partitioning at the Earth’s surface between evapotranspiration, ET, and run-off, Q, known as the water balance. A well-known phenomenological model by Budyko addressed the relationship between the ratio of the actual evapotranspiration (ET) and precipitation, ET/P, versus the aridity index, ET 0 /P, with P being the precipitation and ET 0 being the potential evapotranspiration. Existing work was able to predict the global fractions of P represented by Q and ET through an optimization of plant productivity, in which downward water fluxes affect soil depth, and upward fluxes plant growth. In the present work, based likewise on the concepts of percolation theory, we extend Budyko’s model, and address the partitioning of run-off Q into its surface and subsurface components, as well as the contribution of interception to ET. Using various published data sources on the magnitudes of interception and information regarding the partitioning of Q, we address the variability in ET resulting from these processes. The global success of this prediction demonstrated here provides additional support for the universal applicability of percolation theory for solute transport as well as guidance in predicting the component of subsurface run-off, important for predicting natural flow rates through contaminated aquifers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Coal Feed-Dependent Variation in Fly Ash Chemistry in a Single Pulverized-Combustion Unit

Four suites of fly ash, all generated at the same power plant, were selected for the study of the distribution of rare earth elements (REE). The fly ashes represented two runs of single-seam/single-mine coals and two runs of run-of-mine coals representing several coal seams from several mines. Plots of the upper continental crust-normalized REE, other parameters derived from the normalization, and the principal components analysis of the derived REE parameters (including the sum of the lanthanides plus yttrium and the ratio of the light to heavy REE) all demonstrated that the relatively rare earth-rich Fire Clay coal-derived fly ashes have a different REE distribution, with a greater concentration of REE with a relative dominance of the heavy REE, than the other fly ashes. Particularly with the Fire Clay coal-derived fly ashes, there is a systematic partitioning of the overall amount and distribution of the REE in the passage from the mechanical fly ash collection through to the last row of the electrostatic precipitator hoppers.

58 GEOSCIENCES↗
DOE OSTI2022

Cosmic Reionization on Computers: Physical Origin of Long Dark Gaps in Quasar Absorption Spectra

I explore the properties of “dark gaps” - regions in quasar absorption spectra without significant transmission - with several simulations from the Cosmic Reionization On Computers (CROC) project. The CROC simulations in the largest available boxes (120 cMpc) come close to matching both the distribution of mean opacities and the frequency of dark gaps, but alas not in the same model: the run that matches the mean opacities fails to contain enough dark gaps and vice versa. Nevertheless, the run that matches the dark gap distributions serves as a counterexample to claims in the literature that the dark gap statistics requires a late end to reionization - in that run reionization ends at z = 6.7 (likely too early). While multiple factors contribute to the frequency of large dark gaps in the simulations, the primary factor that controls the overall shape of the dark gap distribution is the ionization level in voids—the lowest-density regions produce the highest transmission spikes that terminate long gaps. As the result, the dark gap distribution correlates strongly with the fraction of the spectrum above the gap detection threshold and the observed distribution is matched by the simulation in which this fraction is 2%. Hence, the gap distribution by itself does not constrain the timing of reionization, although it may do so in combination with the distribution of mean opacities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Jetted and Turbulent Stellar Deaths: New LVK-detectable Gravitational-wave Sources

Upcoming LIGO–Virgo–KAGRA (LVK) observing runs are expected to detect a variety of inspiralling gravitational-wave (GW) events that come from black hole and neutron star binary mergers. Detection of noninspiral GW sources is also anticipated. We report the discovery of a new class of noninspiral GW sources—the end states of massive stars—that can produce the brightest simulated stochastic GW burst signal in the LVK bands known to date, and could be detectable in LVK run A+. Some dying massive stars launch bipolar relativistic jets, which inflate a turbulent energetic bubble—cocoon—inside of the star. We simulate such a system using state-of-the-art 3D general relativistic magnetohydrodynamic simulations and show that these cocoons emit quasi-isotropic GW emission in the LVK band, ~10–100 Hz, over a characteristic jet activity timescale ~10–100 s. Our first-principles simulations show that jets exhibit a wobbling behavior, in which case cocoon-powered GWs might be detected already in LVK run A+, but it is more likely that these GWs will be detected by the third-generation GW detectors with an estimated rate of ~10 events yr –1 . The detection rate drops to ~1% of that value if all jets were to feature a traditional axisymmetric structure instead of a wobble. Accompanied by electromagnetic emission from the energetic core-collapse supernova and the cocoon, we predict that collapsars are powerful multimessenger events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Using neural network ensembles to separate ocean biogeochemical and physical drivers of phytoplankton biogeography in Earth system models

Abstract. Earth system models (ESMs) are useful tools for predicting and understanding past and future aspects of the climate system. However, the biological and physical parameters used in ESMs can have wide variations in their estimates. Even small changes in these parameters can yield unexpected results without a clear explanation of how a particular outcome was reached. The standard method for estimating ESM sensitivity is to compare spatiotemporal distributions of variables from different runs of a single ESM. However, a potential pitfall of this method is that ESM output could match observational patterns because of compensating errors. For example, if a model predicts overly weak upwelling and low nutrient concentrations, it might compensate for this by allowing phytoplankton to have a high sensitivity to nutrients. Recently, we demonstrated that neural network ensembles (NNEs) are capable of extracting relationships between predictor and target variables within ocean biogeochemical models. Being able to view the relationships between variables, along with spatiotemporal distributions, allows for a more mechanistically based examination of ESM outputs. Here, we investigated whether we could apply NNEs to help us determine why different ESMs produce different spatiotemporal distributions of phytoplankton biomass. We tested this using three cases. The first and second case used different runs of the same ESM, except that the physical circulations differed between them in the first case, while the biological equations differed between them in the second. Our results indicated that the NNEs were capable of extracting the relationships between variables for different runs of a single ESM, allowing us to distinguish between differences due to changes in circulation (which do not change relationships) from changes in biogeochemical formulation (which do change relationships). In the third case, we applied NNEs to two different ESMs. The results of the third case highlighted the capability of NNEs to contrast the apparent relationships of different ESMs and some of the challenges it presents. Although applied specifically to the ocean components of an ESM, our study demonstrates that Earth system modelers can use NNEs to separate the contributions of different components of ESMs. Specifically, this allows modelers to compare the apparent relationships across different ESMs and observational datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗