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At least 1,315 records · Page 73

Hybrid memory module bridge network and buffers

Systems, apparatuses, and methods for implementing a hybrid memory module bridge network and buffers are disclosed. A system includes one or more host processors and multiple memory modules. Each memory module includes a relatively low pin count, high-bandwidth serial link to one or more other memory modules to perform inter-memory data transfers without consuming host-memory bandwidth. In one embodiment, a first memory module acts as a cache and a second memory module acts as the main memory for the system. The traffic between the host and the first memory module utilizes a first interface, and the cache traffic between the first and second memory modules utilizes a second interface. Cache line fill and writeback transfers between the first and second memory modules occur in parallel with timing-critical cache demand accesses from the host, in a latency-tolerant and buffered manner, without interfering with the cache demand accesses.

97 MATHEMATICS AND COMPUTING↗

Dayflow: CONUS Daily Streamflow Reanalysis, Version 2 (DayflowV2)

The DayflowV2 dataset provides multiple meteorologic forcings driven hourly streamflow information for approximately 2.7 million NHDPlusV2 stream reaches in the conterminous US (CONUS). DaymetV4, Stage-IV, and Analysis of Period of Record for Calibration (AORC) forcings and their corresponding hybrids drive a nationally scalable modeling framework integrating the simulated runoff from the Variable Infiltration Capacity (VIC) model with the Routing Application for Parallel computatIon of Discharge (RAPID) routing model. Streamflow with (Assimilated) and without (Naturalized) streamflow assimilation at US Geological Survey (USGS) streamflow monitoring sites are included in DayflowV2. A comprehensive evaluation of streamflow at 7,526 USGS gauges is performed for both streamflow types. The resulting key evaluation metrics are also included in the Dayflow dataset. The reanalysis data are available for variable periods; 36 years (1980-2015) for DaymetV4 (DayflowV1), 18 years (2002-2019) for Stage-IV and its hybrids, and 40 years (1980-2019) for AORC and its hybrids.

13 HYDRO ENERGY↗

Comparing High Performance Computing Accelerator Programming Models

Accelerator devices are becoming a norm in High Performance Computing (HPC). With more systems opting for heterogeneous architectures, portable programming models like OpenMP and OpenACC are becoming increasingly important. The SPEC ACCEL 1.2 benchmark suite consists of comparable benchmarks in OpenCL, OpenMP 4.5, and OpenACC 2.5 that can be used to evaluate the performance and support for programming models and frameworks on heterogeneous platforms. In this paper we go beneath the normative metric of performance times and look at the individual kernels to study the usage, strengths, and weaknesses of the two prevalent portable heterogeneous programming models, OpenMP and OpenACC. From our analysis we identify that benchmarks like MRI-Q, SP and BT have better performance using OpenACC, while benchmarks like MiniGhost, LBM and LBDC do consistently better with the OpenMP programming model across supercomputers like Titan, and Summit.We deep dive into the kernels of select four benchmarks to answer questions like: Where does the benchmark spend most of its cycles? What is the parallelization strategy used? Why is one programming model more performant than the other? By identifying the similarities and dierences we want to contrast between the benchmark implementation strategies in the SPEC ACCEL 1.2 benchmarks and provide more insights into the OpenMP and OpenACC programming models.

Pophale, Swaroop S.↗

Scalable Pattern Matching in Metadata Graphs via Constraint Checking

Pattern matching is a fundamental tool for answering complex graph queries. Unfortunately, existing solutions have limited capabilities: They do not scale to process large graphs and/or support only a restricted set of search templates or usage scenarios. Moreover, the algorithms at the core of the existing techniques are not suitable for today’s graph processing infrastructures relying on horizontal scalability and shared-nothing clusters, as most of these algorithms are inherently sequential and difficult to parallelize. In this article we present an algorithmic pipeline that bases pattern matching on constraint checking. The key intuition is that each vertex and edge participating in a match has to meet a set of constraints implicitly specified by the search template. These constraints can be verified independently and typically are less expensive to compute than searching the full template. The pipeline we propose generates these constraints and iterates over them to eliminate all the vertices and edges that do not participate in any match, thus reducing the background graph to a subgraph that is the union of all template matches—the complete set of all vertices and edges that participate in at least one match. Additional analysis can be performed on this annotated, reduced graph, such as full match enumeration, match counting, or computing vertex/edge centrality. Furthermore, a vertex-centric formulation for constraint checking algorithms exists, and this makes it possible to harness existing high-performance, vertex-centric graph processing frameworks. This technique (i) enables highly scalable pattern matching in metadata (labeled) graphs; (ii) supports arbitrary patterns with 100% precision; (iii) enables tradeoffs between precision and time-to-solution, while always selects all vertices and edges that participate in matches, thus offering 100% recall; and (iv) supports a set of popular data analytics scenarios. We implement our approach on top of HavoqGT, an open-source asynchronous graph processing framework, and demonstrate its advantages through strong and weak scaling experiments on massive scale real-world (up to 257 billion edges) and synthetic (up to 4.4 trillion edges) labeled graphs, respectively, and at scales (1,024 nodes / 36,864 cores), orders of magnitude larger than used in the past for similar problems. This article serves two purposes: First, it synthesises the knowledge accumulated during a long-term project. Second, it presents new system features, usage scenarios, optimizations, and comparisons with related work that strengthen the confidence that pattern matching based on iterative pruning via constraint checking is an effective and scalable approach in practice. The new contributions include the following: (i) We demonstrate the ability of the constraint checking approach to efficiently support two additional search scenarios that often emerge in practice, interactive incremental search and exploratory search. (ii) We empirically compare our solution with two additional state-of-the-art systems, Arabsque and TriAD. (iii) We show the ability of our solution to accommodate a more diverse range of datasets with varying properties, e.g., scale, skewness, label distribution, and match frequency. (iv) We introduce or extend a number of system features (e.g., work aggregation, load balancing, and the ability to cap the generated traffic) and design optimizations and demonstrate their advantages with respect to improving performance and scalability. (v) We present bottleneck analysis and insights into artifacts that influence performance. (vi) We present a theoretical complexity argument that motivates the performance gains we observe.

97 MATHEMATICS AND COMPUTING↗

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

03 NATURAL GAS↗

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

In this work, we present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [1]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗

Single-Bubble Flow Boiling Phenomena - Interface Tracking Simulation

Boiling, as one of the most efficient heat transfer mechanisms, is widely used in various engineering systems. Better understanding and modeling of this process remains a major challenge in multiphase flow research. The distribution of vapor in boiling system affects the heat transfer rate and may cause unfavorable conditions, such as heater burn-out. A number of flow regimes have been observed experimentally. In general, there are three regimes under boiling conditions: nucleate boiling, transition boiling, and film boiling. The nucleate boiling regime is categorized into partial boiling regime and fully developed nucleate boiling, according to behavior of bubble dynamics and heat transfer characteristics. In the first region, as the wall temperature increases, the fraction of the wall surface subject to nucleate boiling increases until bubble formation occupies the entire heated surface. Heat transfer in this region is a complex mixture of single-phase forced convection and nucleate boiling. As bubble density increases, bubbles turn to coalesce and form insulating vapor patches, which impedes liquid flow back to the surface. The heat transfer rate under this condition reduces dramatically. This point is called Critical Heat Flux (CHF), which leads to boiling crisis. The behavior of boiling crisis is dependent on local fluid conditions due to bubble growth and departure. Experiments are the ultimate tool for boiling model development and verification, but they still lack some capabilities needed for better understanding of the local mechanism of this phenomena. It's difficult to capture many important details at the pressure/temperature conditions of interest using experimental techniques, such as full three dimensional measurements of velocity and temperature distribution and estimates of heat flux partitioning during the boiling process. The interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. The advances of high performance computing (HPC) in recent years made it possible to apply DNS to a wide variety of adiabatic flows. Some work has been done to implement evaporation / condensation models as well. Lee and Nydahl performed a numerical simulation of bubble growth and departure assuming that the bubble has the shape of a truncated sphere and a micro-layer exists during bubble growth. A 2-D cylindrical bubbles simulation has been done by Son with a simplified model to predict the heat flux in a thin liquid micro-layer. A direct simulation of 2D film boiling is conducted by Juric and Tryggvason. The film boiling, below critical pressure with a modified Level Set Method, is studied by Son and Dhir. Ose and Kunugi have developed a boiling and condensation model on subcooled boiling phenomena. Fuchs performed numerical simulations of bubble growth and departure considering wall conduction effects. Fully transient heat and fluid flow is modeled with a free surface of a rising bubble and a periodic calculation of the whole cycling of a growing, detaching, and rising bubble. Mukherjee and Kandikar have done a numerical simulation of an evaporating meniscus on a moving heated surface with level set method. The heat transfer associated with the advancing and receding contact angle has been studied. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate single-bubble growth scenarios. For a single bubble simulation in infinite liquid, the analytical solution exists and can be compared with the numerical results for verification purposes. The presented capabilities will be utilized in the large scale DNS of boiling flows in the future. The finite-element based code, PHASTA is used for the simulation. It is a parallel, hierarchic, higher-order accurate, adaptive, stabilized, transient analysis flow solver, which has been shown to be an effective tool for a wide range of single and two-phase flow problems. It has been shown to be highly scalable on top supercomputers ({approx}85% scaling on up to 3 million mesh partitions using a 92 billion element mesh . PHASTA has been shown to reliably predict the details of adiabatic bubbly flows as well as single-phase flows with heat transfer. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate a single-bubble growth scenario. For a single bubble growth in superheated water, the analytical solution exists and can be compared with the numerical results for verification purposes. The second-order accurate spatial and time discretization is used for the flow solver in the presented work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Highly scalable distributed-memory sparse triangular solution algorithms.

This paper presents a highly efficient distributed-memory parallel sparse triangular solver. The triangular solution phase is often performed following factorization phase in the sparse linear solvers and has become increasingly computa­tionally expensive for direct solvers with many right hand sides (RHSs) or preconditioned iterative solvers. However, the low arithmetic intensity and sequential nature of the triangular solve algorithm pose performance challenges for its large-scale distributed-memory parallelization. In this work, we propose several strategies to enhance scalability of an algorithm with 2D block cyclic process layout. First, an asynchronous binary-tree-based communication scheme implemented via non-blocking MPI functions is leveraged to broadcast partial solutions and reduce partial updates among a subset of processes for each block column and row of the triangular matrix, respectively. This scheme reduces message latency, improves communication load balance and significantly accelerates asynchronous execution of the triangular solve. In addition, efficient BLAS operations and threading implementations are exploited to accelerate local computations and further reduce process idle time. The proposed strategies are implemented in SuperLU_DIST and numerical experiments show up to 4.4x improvement with one right-hand side and up to 6.1x improvement with 50 right- hand sides on 4096 processes, compared to the current release. This is the first time that sparse triangular solution is demonstrated strong scaling on more than 4000 cores.

Liu, Yang↗

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗

Analyzing and modeling the kinetics of amyloid beta pores associated with Alzheimer’s disease pathology

Amyloid beta (Aβ) oligomers associated with Alzheimer’s disease (AD) form Ca 2+ -permeable plasma membrane pores, leading to a disruption of the otherwise well-controlled intracellular calcium (Ca 2+ ) homeostasis. The resultant up-regulation of intracellular Ca 2+ concentration has detrimental implications for memory formation and cell survival. The gating kinetics and Ca 2+ permeability of Aβ pores are not well understood. We have used computational modeling in conjunction with the ability of optical patch-clamping for massively parallel imaging of Ca 2+ flux through thousands of pores in the cell membrane of Xenopus oocytes to elucidate the kinetic properties of Aβ pores. The fluorescence time-series data from individual pores were idealized and used to develop data-driven Markov chain models for the kinetics of the Aβ pore at different stages of its evolution. Our study provides the first demonstration of developing Markov chain models for ion channel gating that are driven by optical-patch clamp data with the advantage of experiments being performed under close to physiological conditions. As a result, we demonstrate the up-regulation of gating of various Ca 2+ release channels due to Aβ pores and show that the extent and spatial range of such up-regulation increases as Aβ pores with low open probability and Ca 2+ permeability transition into those with high open probability and Ca 2+ permeability.

59 BASIC BIOLOGICAL SCIENCES↗

Experimental and Theoretical Evaluation of Feed Flow Collar Design for Shell Fed Hollow Fiber Membrane Modules

An experimental and theoretical study of module collar design is presented here. Hollow fiber membranes are prepared by dip coating a poly(vinylidene) (PVDF) support with a polydimethylsiloxane (PDMS) gutter layer and a Pebax 2533 selective layer. Fiber bundles with a well-defined fiber packing are prepared using a 3D printed module. A parallel fiber bundle consisting of 4-9 uniformly spaced fibers is created with printed tabs that align the fibers and create a tubesheet. The tabs are sealed within a printed case that possesses a series of external ports for gas introduction and removal. Uniquely, both port location and the use of a collar to assist fluid distribution in the shell can be varied for the same fiber bundle. Experimental measurements are compared to computational fluid dynamics (CFD) simulations. The experimental module design allows high-fidelity representation of the fiber bundle and module case in the simulations. Comparisons between experiment and simulation are in good agreement over a broad range of experimental conditions. The detrimental effect of having ports located too close, leading to stagnation regions, is captured as well as the beneficial effects of using a collar for shell-side fluid distribution around the fiber bundle. Such results help validate the use of CFD to develop high-performance module designs.

Tran, Thien↗

Theoretical foundation for measuring the groundwater age distribution.

In this study, we use PFLOTRAN, a highly scalable, parallel, flow and reactive transport code to simulate the concentrations of 3H, 3He, CFC-11, CFC-12, CFC-113, SF6, 39Ar, 81Kr, 4He and themean groundwater age in heterogeneous fields on grids with an excess of 10 million nodes. We utilize this computational platform to simulate the concentration of multiple tracers in high-resolution, heterogeneous 2-D and 3-D domains, and calculate tracer-derived ages. Tracer-derived ages show systematic biases toward younger ages when the groundwater age distribution contains water older than the maximum tracer age. The deviation of the tracer-derived age distribution from the true groundwater age distribution increases with increasing heterogeneity of the system. However, the effect of heterogeneity is diminished as the mean travel time gets closer the tracer age limit. Age distributions in 3-D domains differ significantly from 2-D domains. 3D simulations show decreased mean age, and less variance in age distribution for identical heterogeneity statistics. High-performance computing allows for investigation of tracer and groundwater age systematics in high-resolution domains, providing a platform for understanding and utilizing environmental tracer and groundwater age information in heterogeneous 3-D systems. Groundwater environmental tracers can provide important constraints for the calibration of groundwater flow models. Direct simulation of environmental tracer concentrations in models has the additional advantage of avoiding assumptions associated with using calculated groundwater age values. This study quantifies model uncertainty reduction resulting from the addition of environmental tracer concentration data. The analysis uses a synthetic heterogeneous aquifer and the calibration of a flow and transport model using the pilot point method. Results indicate a significant reduction in the uncertainty in permeability with the addition of environmental tracer data, relative to the use of hydraulic measurements alone. Anthropogenic tracers and their decay products, such as CFC11, 3H, and 3He, provide significant constraint oninput permeability values in the model. Tracer data for 39Ar provide even more complete information on the heterogeneity of permeability and variability in the flow system than the anthropogenic tracers, leading to greater parameter uncertainty reduction.

Gardner, William Payton↗

Nonlinear Dynamics and Phase Space Manipulations of High-Brightness Beams

The project consisted of two main tasks. Each task had several specific aims. The three main objectives of Task 1 were: 1. Investigation of the flat beam technique to produce high transverse emittance ratio longitudinally-compressed bunches, 2. Exploration of a new chicane-like transverse-to-longitudinal phase space exchanger for precise pulse shaping and emittance exchange, 3. Applications of flat-beam with shaped current profile(s) to dielectric wakefield acceleration in an asymmetric waveguide. The outcome of our research was to performed details simulations of flat-beam generation and compression. Some preliminary experiment on flat-beam generation and compression were conducted at the FAST-IOTA injector in parallel to commissioning activities. Likewise, the longitudinal phase-space transformation was not fully explored; we participated in experiments conducted at the Argonne Wakefield Accelerator and especially introduced a simple transverse-shaping technique.

43 PARTICLE ACCELERATORS↗

Symmetric Indefinite Linear Solver Using OpenMP Task on Multicore Architectures

Recently, the Open Multi-Processing (OpenMP) standard has incorporated task-based programming, where a function call with input and output data is treated as a task. At run time, OpenMP's superscalar scheduler tracks the data dependencies among the tasks and executes the tasks as their dependencies are resolved. On a shared-memory architecture with multiple cores, the independent tasks are executed on different cores in parallel, thereby enabling parallel execution of a seemingly sequential code. With the emergence of many-core architectures, this type of programming paradigm is gaining attention-not only because of its simplicity, but also because it breaks the artificial synchronization points of the program and improves its thread-level parallelization. In this paper, we use these new OpenMP features to develop a portable high-performance implementation of a dense symmetric indefinite linear solver. Obtaining high performance from this kind of solver is a challenge because the symmetric pivoting, which is required to maintain numerical stability, leads to data dependencies that prevent us from using some common performance-improving techniques. To fully utilize a large number of cores through tasking, while conforming to the OpenMP standard, we describe several techniques. Our performance results on current many-core architectures-including Intel's Broadwell, Intel's Knights Landing, IBM's Power8, and Arm's ARMv8-demonstrate the portable and superior performance of our implementation compared with the Linear Algebra PACKage (LAPACK). The resulting solver is now available as a part of the PLASMA software package.

Computer Science↗

BCL: A Cross-Platform Distributed Data Structures Library

One-sided communication is a useful paradigm for irregular parallel applications, but most one-sided programming environments, including MPI's one-sided interface and PGAS programming languages, lack application-level libraries to support these applications. We present the Berkeley Container Library, a set of generic, cross-platform, high-performance data structures for irregular applications, including queues, hash tables, Bloom filters and more. BCL is written in C++ using an internal DSL called the BCL Core that provides one-sided communication primitives such as remote get and remote put operations. The BCL Core has backends for MPI, OpenSHMEM, GASNet-EX, and UPC++, allowing BCL data structures to be used natively in programs written using any of these programming environments. Along with our internal DSL, we present the BCL ObjectContainer abstraction, which allows BCL data structures to transparently serialize complex data types while maintaining efficiency for primitive types. We also introduce the set of BCL data structures and evaluate their performance across a number of high-performance computing systems, demonstrating that BCL programs are competitive with hand-optimized code, even while hiding many of the underlying details of message aggregation, serialization, and synchronization.

Brock, Benjamin↗

Multi-scale calculation based on dual domain material point method combined with molecular dynamics

This dissertation combines the dual domain material point method (DDMP) with molecular dynamics (MD) in an attempt to create a multi-scale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically non-equilibrium state, and conventional constitutive relations are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a MD simulation of a group of atoms surrounding the material point. Rather than restricting the multi-scale simulation in a small spatial region, such as phase interfaces, or crack tips, this multi-scale method can be used to consider non-equilibrium thermodynamic e ects in a macroscopic domain. This method takes advantage that the material points only communicate with mesh nodes, not among themselves; therefore MD simulations for material points can be performed independently in parallel. First, using a one-dimensional shock problem as an example, the numerical properties of the original material point method (MPM), the generalized interpolation material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the DDMP method are investigated. Among these methods, only the DDMP method converges as the number of particles increases, but the large number of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of particles. The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU using CUDA to accelerate the computation. The numerical properties of the multiscale method are investigated as well as the results from this multi-scale calculation are compared of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of particles. The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU using CUDA to accelerate the computation. The numerical properties of the multiscale method are investigated as well as the results from this multi-scale calculation are compared with direct MD simulation results to demonstrate the feasibility of the method. Also, the multi-scale method is applied for a two dimensional problem of jet formation around copper notch under a strong impact.

74 ATOMIC AND MOLECULAR PHYSICS↗

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Investigation of the fragmentation of an explosively driven cylinder

Explosively driven fragmentation is highly complex. To better understand the field detonation, different methodologies (Lagrangian (with a failure threshold in VisIt and element erosion), ALE and embedded grid) were simulated to provide a comparison to the experimental data through the utilization of fragment distributions and gross deformation metrics. Provided with the geometrical parameters and the results from the experimental data, the computer simulations were conducted after the successful writing of each input file. Mesh refinement – a scalar multiplier applied to the mesh to refine the results – was then studied. The objective was to find a value that parallels the experimental results as the mesh can be refine indefinitely, theoretically. Various mesh resolution scales were simulated and the results graphically compared, using the damage and failure variables from a statistical Johnson Cook failure model, the number of fragments over time as well as time required for each simulation to run and number of processors utilized. The desired result is a calculated method to quantify the comparison being performed.

36 MATERIALS SCIENCE↗