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At least 1,657 records · Page 92

FY25 Mid-Year Report: FNCL Enhancements Implementation

During the first half of FY25 the FNCL team has made consistent progress toward the completion of our project goals. The FNCL prototype panel design has been successfully applied to a fully instrumented 3-panel system which is actively under construction. The FNCL Demonstrator System contains solid scintillators instrumented with SiPMs, which operate on an updated CAEN digitizer, requires no high-voltage, and has a smaller overall footprint. The onboard software will include the LLNL-developed GMM-PSD signal processing. Later this year the system will be experimentally tested alongside the baseline FNCL instrument at LLNLs ISSA facility. In addition to a full systems test, the performance of a DD generator for active interrogation measurements compared to the standard AmLi source will be established for both systems. The data collected at the ISSA facility will be used to experimentally validate the FNCL-Fast Isotopic Fuel Assay’s (FIFA) capability to measure U-235 loading and to predict gadolinium poison content with passive interrogation. The FNCL-FIFA modal was benchmarked with simulation-based data and a user-friendly GUI was added earlier this year. Three separate codes have been submitted to the LLNL ESW system for review prior to their transfers. These include the Predictive Modeling Response toolkit, GMM-PSD firmware beta version, and the FNCL-FIFA analysis package with GUI and user documentation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

In this work, we present DFT-FE 1.0, building on DFT-FE 0.6 [Comput. Phys. Commun. 246, 106853 (2020)], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ~ 100,000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation—via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency—as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our implementation, which yields ~ 20× CPU-GPU speed-up by using GPU acceleration on hybrid CPU-GPU nodes. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80–140 seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing ~ 6, 000 – 15,000 electrons.

pseudopotential↗

Implementation of metal-friendly EAM/FS-type semi-empirical potentials in HOOMD-blue: A GPU-accelerated molecular dynamics software

We present an implementation of EAM and FS interatomic potentials, which are widely used in simulating metallic systems, in HOOMD-blue, a software designed to perform classical molecular dynamics simulations using GPU accelerations. We first discuss the details of our implementation and then report extensive benchmark tests. We demonstrate that single-precision floating point operations efficiently implemented on GPUs can produce sufficient accuracy when compared against double-precision codes, as demonstrated in test simulations of calculations of the glass-transition temperature of Cu 64.5 Zr 35.5 , and pair correlation function of liquid Ni 3 Al. Our code scales well with the size of the simulating system on NVIDIA Tesla M40 and P100 GPUs. Compared with another popular software LAMMPS running on 32 cores of AMD Opteron 6220 processors, the GPU/CPU performance ratio can reach as high as 4.6. In conclusion, the source code can be accessed through the HOOMD-blue web page for free by any interested user.

36 MATERIALS SCIENCE↗

Initial Development of Fusion Magnet Simulation Capabilities for Performance and Safety Evaluation Using the MOOSE Framework

Fusion energy holds the promise of being a transformative technology as a carbon-neutral, sustainable source of energy. Whole device modeling and the development of fusion digital twins will be increasingly important for emerging fusion device concepts at both national laboratories and within the commercial fusion industry. However, meeting the challenge of whole device modeling of fusion energy devices requires robust, multiphysics, multiscale modeling and simulation technologies capable of running on large-scale supercomputers. Detailed analysis of individual systems at-scale is also required to ensure safe and efficient operation as well as provide the safety basis for future device designs and licensing activities. In a tokamak, toroidal and poloidal magnets confine and shape the fusion plasma to promote the fusion reaction. High plasma temperatures and high magnetic field requirements in modern design concepts (leading to high amounts of energy stored within each magnet) impose electrical, thermal, and mechanical loads on the magnet components, which in turn impacts the safety considerations of the magnet and their supporting systems. Idaho National Laboratory (INL) has a history of working in this space, including development and benchmarking of the Magnetic System Circuitry Analysis Program (MSCAP) and Magnet Arcing (MAGARC) codes to study magnet quench events; notably, MAGARC was used to study quenching during the ITER Engineering Design Activity. However, these legacy codes and capabilities are not parallel and scalable, and new tools are required for future advances in this area, which leads to the INL-developed Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Developed originally for fission reactor systems under United States Department of Energy, Office of Nuclear Energy modeling and simulation programs, the MOOSE framework has been well-suited to multiscale, multiphysics modeling and simulation needs for nuclear systems. The framework is open-source, well-tested, under continuous development and deployment, and developed to a Nuclear Quality Assurance, Level 1 software quality standard. MOOSE has also been used in the fusion space previously in several projects: INL’s Tritium Migration Analysis Program, Version 8 (TMAP8) for tritium migration, UK Atomic Energy Authority’s A Unified Resource for OpenMC (fusion) Reactor Applications (AURORA) code for fusion thermo-mechanical and neutronics analysis, and Argonne National Laboratory’s Cardinal for high-fidelity computational fluid dynamics and neutronics. However, to model superconducting magnets, several MOOSE enhancements are required: additions to the current MOOSE electromagnetic capabilities, new material libraries for superconductors of interest (such as YBCO), as well as fusion-specific models for thermo-mechanics. This talk will discuss initial development activities to build these capabilities in MOOSE, focusing on initial validation and benchmarking activities. Proposed coupling workflows and future work to support the simulation of fusion magnets and magnet structural assemblies for performance and safety evaluation in MOOSE will also be discussed.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Review of the 10 th Non-LTE Code Comparison Workshop

This work reports on the results of the 10 th Non-LTE code comparison workshop, which was held at the University of San Diego campus November 28 through December 1, 2017. Non-equilibrium collisional-radiative models predict the electronic state populations and attendant emission and absorption characteristics of hot, dense matter and are used to help design and diagnose high-energy-density experiments. At this workshop, fifteen codes from eleven institutions contributed results for steady-state and time-dependent neon, aluminum, silicon, and chlorine cases relevant to a variety of high-density experimental and radiation-driven astrophysical systems. We focus on differences in the predictions from codes with different internal structure, completeness, density effects, and rate fidelity and the impact of those differences on hot, dense plasma diagnostics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theoretical framework for new magnetic materials for quantum computing and information storage. Final report for the Award No. DE-SC0018910

The focus of this grant was on molecular magnetic materials for information storage and quantum computing. We have been developing robust, first-principle methods for computing relevant electronic and magnetic properties of molecular building blocks (SMMs) of novel magnetic materials and quantum computers. These tools enable theoretical modeling of SMMs’ behavior, facilitating the interpretation of experimental studies and aiding the design of novel magnetic materials. Our strategy is based on the spin-flip (SF) approach, which extends the hierarchy of black-box single-reference methods to strongly correlated systems. Specifically, we developed general scalable algorithms and computer codes for calculating molecular properties, with an emphasis on spin-related properties, such as zero-field splittings, hyperfine couplings, and g-tensors. While our primary focus was on SF wave functions and SF-TDDFT, the underlying theory and computer codes were formulated using reduced density matrices, such that these tools are applicable to a broader class of methods. To extend the scope of applicability of wave-function-based SF methods to larger systems, we developed reduced-scaling approaches for the equation-of-motion coupled-cluster (EOM-CC) methods and continue developing libtensor (our open-source general tensor contraction library for many-body methods). We carried out extensive benchmarks and also carried out several applications.

36 MATERIALS SCIENCE↗

Parallel computation safety analysis irradiation targets fission product molybdenum in neutronic aspect using the successive over-relaxation algorithm

One of the research activities in support of commercial radioisotope production program is a safety research on target FPM (Fission Product Molybdenum) irradiation. FPM targets form a tube made of stainless steel which contains nuclear-grade high-enrichment uranium. The FPM irradiation tube is intended to obtain fission products. Fission materials such as Mo{sup 99} used widely the form of kits in the medical world. The neutronics problem is solved using first-order perturbation theory derived from the diffusion equation for four groups. In contrast, Mo isotopes have longer half-lives, about 3 days (66 hours), so the delivery of radioisotopes to consumer centers and storage is possible though still limited. The production of this isotope potentially gives significant economic value. The criticality and flux in multigroup diffusion model was calculated for various irradiation positions and uranium contents. This model involves complex computation, with large and sparse matrix system. Several parallel algorithms have been developed for the sparse and large matrix solution. In this paper, a successive over-relaxation (SOR) algorithm was implemented for the calculation of reactivity coefficients which can be done in parallel. Previous works performed reactivity calculations serially with Gauss-Seidel iteratives. The parallel method can be used to solve multigroup diffusion equation system and calculate the criticality and reactivity coefficients. In this research a computer code was developed to exploit parallel processing to perform reactivity calculations which were to be used in safety analysis. The parallel processing in the multicore computer system allows the calculation to be performed more quickly. This code was applied for the safety limits calculation of irradiated FPM targets containing highly enriched uranium. The results of calculations neutron show that for uranium contents of 1.7676 g and 6.1866 g (× 10{sup 6} cm{sup −1}) in a tube, their delta reactivities are the still within safety limits; however, for 7.9542 g and 8.838 g (× 10{sup 6} cm{sup −1}) the limits were exceeded.

07 ISOTOPE AND RADIATION SOURCES↗

Sensitivity Analysis of OECD ATLAS A5.1 Test using MARS-KS code

The ATLAS was designed to model a reduced-height primary system of a typical APR1400 which was developed by the Korean Nuclear Industry. The ATLAS has the 1/2-height, 1/144-area and 1/288-volume scales for the APR 1400 and it is scaled for full pressure and temperature conditions. A benchmark test, test A5.1, was performed to analyze and quantify the extent of scaling distortion in the ATLAS, as a part of a OECD-ATLAS project. The SB-CL-32 test which was conducted using the Large Scale Test Facility (LSTF) of the Rig-of-Safety Assessment-V (ROSA-V) Program was selected as the counterpart test to address the scaling issue. The detailed description of the LSTF test facility and the SB-CL-32 test can be found in the literature. The objective of the A5.1 test is to investigate the thermal hydraulic phenomena during cold leg small break LOCA with steam generator secondary side depressurization as the Accident Management action. In addition to that, the scaling effect analysis of ATLAS was performed in the several viewpoints. In this study, sensitivity analysis of A5.1 test was performed using MARS-KS code. Several experimental conditions of A5.1 test were varied to study effects on the reactor coolant system during the SBLOCA transient. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Transport model predictions of 225 Ac production cross sections via energetic p, d and α irradiation of 232 Th targets

Monte Carlo transport codes PHITS and MCNP6 were used to calculate the production cross sections of 225,227 Ac, 227,229 Th, 223,225 Ra, and 229,230,231 Pa via the bombardment of a 232 Th target with energetic protons, deuterons, and α-particles. The incident projectile energies ranged between 10 and 800 MeV/nucleon. When possible, the predicted production cross sections were compared with the available experimental data and other predictions. Here, the degree of the codes’ abilities to match the measured data provides a qualitative assessment of the codes’ abilities to predict data from similar, but unmeasured, projectile/target systems. In addition, a comparison between calculated cross sections and data may provide insight into possible improvements in the physics models employed by those transport codes.

223Ra↗

A gimbal platform stabilization for topographic applications

The aim of this work is the stabilization of a Gimbal platform for optical sensors acquisitions in topographic applications using mobile vehicles. The stabilization of the line of sight (LOS) consists in tracking the command velocity in presence of nonlinear noise due to the external environment. The hardware architecture is characterized by an Ardupilot platform that allows the control of both the mobile device and the Gimbal. Here we developed a new approach to stabilize the Gimbal platform, which is based on neural network. For the control system, we considered a plant that represents the transfer function of the servo system control model for an inertial stabilized Gimbal platform. The transductor used in the feed-back line control is characterized by the Rate Gyro transfer function installed onboard of Ardupilot. For the simulation and investigation of the system performance, we used the Simulink tool of Matlab. Results show that the hardware/software approach is efficient, reliable and cheap for direct photogrammetry, as well as for general purpose applications using mobile vehicles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-phase model development to assess RCIC system capabilities under severe accident conditions

The Reactor Core Isolation Cooling (RCIC) System is a safety-related system that provides makeup water for core cooling of some Boiling Water Reactors (BWRs) with a Mark I containment. The RCIC System consists of a steam-driven Terry turbine that powers a centrifugal, multi-stage pump for providing water to the reactor pressure vessel. The Fukushima Dai-ichi accidents demonstrated that the RCIC System can play an important role under accident conditions in removing core decay heat. The unexpectedly sustained, good performance of the RCIC System in the Fukushima reactor demonstrates, firstly, that its capabilities are not well understood, and secondly, that the system has high potential for extended core cooling in accident scenarios. Better understanding and analysis tools would allow for more options to cope with a severe accident situation and to reduce the consequences. The objectives of this project were to develop physics-based models of the RCIC System, incorporate them into a multi-phase code and validate the models. This Final Technical Report details the progress throughout the project duration and the accomplishments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SU-D-16A-01: A Novel Method to Estimate Normal Tissue Dose for Radiotherapy Patients to Support Epidemiologic Studies of Second Cancer Risk

Purpose: Patient cohort of second cancer study often involves radiotherapy patients with no radiological images available: We developed methods to construct a realistic surrogate anatomy by using computational human phantoms. We tested this phantom images both in a commercial treatment planning system (Eclipse) and a custom Monte Carlo (MC) transport code. Methods: We used a reference adult male phantom defined by International Commission on Radiological Protection (ICRP). The hybrid phantom which was originally developed in Non-Uniform Rational B-Spline (NURBS) and polygon mesh format was converted into more common medical imaging format. Electron density was calculated from the material composition of the organs and tissues and then converted into DICOM format. The DICOM images were imported into the Eclipse system for treatment planning, and then the resulting DICOM-RT files were imported into the MC code for MC-based dose calculation. Normal tissue doses were calculation in Eclipse and MC code for an illustrative prostate treatment case and compared to each other. Results: DICOM images were generated from the adult male reference phantom. Densities and volumes of selected organs between the original phantom and ones represented within Eclipse showed good agreements, less than 0.6%. Mean dose from Eclipse and MC code match less than 7%, whereas maximum and minimum doses were different up to 45%. Conclusion: The methods established in this study will be useful for the reconstruction of organ dose to support epidemiological studies of second cancer in cancer survivors treated by radiotherapy. We also work on implementing body size-dependent computational phantoms to better represent patient's anatomy when the height and weight of patients are available.

60 APPLIED LIFE SCIENCES↗

Regional heritability advanced complex trait analysis for GPU and traditional parallel architectures

Motivation: Quantification of the contribution of genetic variation to phenotypic variation for complex traits becomes increasingly computationally demanding with increasing numbers of single-nucleotide polymorphisms and individuals. To meet the challenges in making feasible large-scale studies, we present the REgional heritability advanced complex trait analysis software. Adapted from advanced complex trait analysis (and, in turn, genome-wide complex trait analysis), it is tailored to exploit the parallelism present in modern traditional and graphics processing unit (GPU)-accelerated machines, from workstations to supercomputers. Results: We adapt the genetic relationship matrix estimation algorithm to remove limitations on memory, allowing the analysis of large datasets. Further, we build on this to develop a version of the code able to efficiently exploit GPU-accelerated systems for both the genetic relationship matrix and REstricted maximum likelihood (REML) parts of the analysis, offering substantial speedup over the traditional central processing unit version. We develop the ability to analyze multiple small regions of the genome across multiple compute nodes in parallel, following the ‘regional heritability’ approach. We demonstrate the new software using 1024 GPUs in parallel on one of the world’s fastest supercomputers. Availability: The code is freely available at http://www.epcc.ed.ac.uk/software-products

59 BASIC BIOLOGICAL SCIENCES↗

North American Board of Certified Energy Practitioners Final Report

The U.S. DOE’s Office of EERE National Solar Energy Technology Program (SETP) calls for a “National Accreditation and Certification Program for Installation and Acceptance of Photovoltaic Systems.” A near-term goal listed in the U.S. Photovoltaic Industry’s Roadmap, 2000 - 2020 is to work to establish standards, codes, and certifications which are essential for consumer protection and acceptance as part of the goal of building toward a viable future PV industry. This program paves the way for a voluntary national certification program for PV system practitioners and installers, initiation of the first steps toward certification of hardware, and reinforcement of all five of the technical objectives in the Systems category of SETPs Multi-Year technical Plan. Through this project, NABCEP will direct the continued initiation of and sustained implementation and administration of the NABCEP Solar PV Installer Certification Program (hereafter the “Program”). The NABCEP Program is a national, voluntary program designed to provide certification for those PV installers who demonstrate the requisite skills, abilities and knowledge typically required to install and maintain PV systems. The core document upon which the Program was developed and upon which the national exam is based, is referred to as the (Program) Task Analysis. It is a thorough descriptive document containing specific psychomotor and cognitive tasks for the purposes of identifying the types of training/assessment methods that apply. Psychomotor skills require measuring, assembling, fastening and related activities. Cognitive skills require knowledge processing, decision-making and computations. NABCEP effectively evaluates an applicant’s psychomotor skills through review of a candidate’s PV installations and hands-on training received. NABCEP evaluates the candidate’s cognitive skills through administration of its national Program exam. By first qualifying for and then obtaining the required passing score, NABCEP certificants receive an accreditation that upholds NABCEP’s standards of quality, compliance to applicable codes and safety in PV installation. The objectives of DOE’s National Solar Energy Technology Program (SETP) are intrinsic to NABCEP. As detailed in the PV Roadmap, the lifespan of a PV system is a function of reliability and value. PV system reliability is directly dependent upon the quality of components and, design, installation and maintenance of a system. The latter three are all core components of the NABCEP Task Analysis - accordingly NABCEP certified installers will be instrumental in improving reliability of systems through safe, code and manufacturer-compliant installation and necessary post-installation maintenance of PV systems. This will have the effect of ensuring and increasing the performance of installed systems and, as consumers realize the benefits of well-installed and maintained systems, increased demand will follow and manufacturers will respond - supporting further growth in the PV industry. Furthermore, as more NABCEP certified installers perform these installations and maintenance competently, additional installations (whole system re-installations) and unnecessary repairs can be avoided. This will drive down system costs. This combined with creation/enhancement of the DE-FG36-04GO14348/005 NABCEP Central Data Base of Installers – providing consumers with installation/maintenance service options will further reduce system costs and help meet the overall goal of reducing life cycle costs. As consumers receive more value from PV systems which are providing longer, trouble free, renewable energy, they will join the ranks of professionals and enthusiasts calling for reduced technological barriers to installation (particularly for grid-tied systems). States and utilities will react to pressure and begin easing onerous net-metering and other technological restrictions. The benefits of NABCEP’s Program will be evident to consumers, manufacturers, distributors, state energy officials and solar academic institutions. Consumers benefit through increased system performance and reduced costs. Manufacturers of PV and balance of system components as well as distributors support and benefit from NABCEP because of assurances that systems are installed in accordance to code (i.e., NEC) and their specifications, resulting in longer life. Collaborators including state energy officials (i.e., New York State Energy Research and Development Authority) benefit by knowing that rebate funds are spent on systems whose benefits will far exceed system costs. Program Objectives The improvements and advantages offered by a national voluntary certification program can only expand the horizons for photovoltaic applications.

14 SOLAR ENERGY↗

MARVEL Project Code of Record, COR-0011

MARVEL Project Code of Record identifies the codes, standards, and procedures necessary to design, develop, construct, and startup the Microreactor Applications Research Validation and Evaluation (MARVEL) Project. No code exceptions to construction of the MARVEL reactor in the traditional sense were identified, meaning there are no technical aspects that fail to meet a code requirement. However, due to the novel design of the MARVEL reactor, not every aspect or system can be precisely covered by the existing ASME Boiler and Pressure Vessel Code. In those cases, the document identifies (with concurrences received) how the ASME Boiler and Pressure Vessel Code is applied in an equivalent or analogous manner.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Model Structural Inference Using Local Dynamic Operators

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Here, we (1) define a discrete, local representation of the structure of a partial differential equation, which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.

97 MATHEMATICS AND COMPUTING↗

Updating a PWR Simulator in Python

A nuclear reactor is a complicated system that is comprised of many systems and components. In order to fully model a reactor, several approximations and correlations must be used for a real-time simulation. In 1984 as part of a doctoral dissertation at Massachusetts Institute of Technology (MIT), a FORTRAN 77 program was developed to simulate a four-loop, Westinghouse pressurized water reactor (PWR). The program was later called PRISM and extended to include a comprehensive set of features accessible in a DOS-based user interface. This present work seeks to update the original PRISM program for cross platform deployment using the Python language. The goal of this present work is to update and improve a teaching tool for both students and reactor operators. Originally, PRISM was created as part of a PhD project in FORTRAN 77, but the code no longer works readily on modern operating systems. Python was chosen to rewrite the program because of the ease of use of the Python modules including Kivy as well as the portability of the program to various operating systems. This project aims to develop desktop and mobile versions of the software, allowing the user flexibility in choice of platform. This simulator is scheduled to be deployed in time for a live demonstration at the 2016 Annual ANS meeting. The project aims to produce a reactor simulator that will showcase the dynamics of a PWR system in real-time under various conditions. Some potential scenarios include startup conditions, scram operations, or failure conditions such as a break in a coolant leg. The user will be able to induce various failure scenarios and the program will simulate how the reactor will behave. The simulation will include a suite of monitoring functions that will allow automatic systems to attempt to adapt to the changing conditions, e.g., control rod movement. This program will provide an educational resource for anyone learning about nuclear reactor kinetics or dynamics of a reactor system. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Addressing Global Data Dependencies in Heterogeneous Asynchronous Runtime Systems on GPUs

Large-scale parallel applications with complex global data dependencies beyond those of reductions pose significant scalability challenges in an asynchronous runtime system. Internodal challenges include identifying the all-to-all communication of data dependencies among the nodes. Intranodal challenges include gathering together these data dependencies into usable data objects while avoiding data duplication. This paper addresses these challenges within the context of a large-scale, industrial coal boiler simulation using the Uintah asynchronous many-task runtime system on GPU architectures. We show significant reduction in time spent analyzing data dependencies through refinements in our dependency search algorithm. Multiple task graphs are used to eliminate subsequent analysis when task graphs change in predictable and repeatable ways. Using a combined data store and task scheduler redesign reduces data dependency duplication ensuring that problems fit within host and GPU memory. Furthermore, these modifications did not require any changes to application code or sweeping changes to the Uintah runtime system. We report results running on the DOE Titan system on 119K CPU cores and 7.5K GPUs simultaneously. Our solutions can be generalized to other task dependency problems with global dependencies among thousands of nodes which must be processed efficiently at large scale.

97 MATHEMATICS AND COMPUTING↗