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At least 847 records · Page 47

Batched sparse direct solver design and evaluation in SuperLU_DIST

Over the course of interactions with various application teams, the need for batched sparse linear algebra functions has emerged in order to make more efficient use of the GPUs for many small and sparse linear algebra problems. In this paper, we present our recent work on a batched sparse direct solver for GPUs. The sparse LU factorization is computed by the levels of the elimination tree, leveraging the batched dense operations at each level and a new batched Scatter GPU kernel. The sparse triangular solve is computed by the level sets of the directed acyclic graph (DAG) of the triangular matrix. Batched operations overcome the large overhead associated with launching many small kernels. For medium sized matrix batches with not-so-small bandwidth, using an NVIDIA A100 GPU, our new batched sparse direct solver is orders of magnitude faster than a batched banded solver and uses less than one-tenth of the memory.

Boukaram, Wajih↗

Skyrmion soliton motion on periodic substrates by atomistic and particle-based simulations

Abstract We compare the dynamical behavior of magnetic skyrmions interacting with square and triangular defect arrays just above commensuration using both atomistic and particle-based models. Under applied drives, the initial motion is a kink traveling through the pinned skyrmion lattice. For the square defect array, both models agree well and show a regime in which the soliton motion is locked along 45°. The atomistic model also produces locking of a soliton along 30°, which is absent in the particle-based model. For the triangular defect array, the atomistic model exhibits 30° soliton motion over a wide region of external current values. In contrast, the particle-based model gives 45° soliton motion over a small range of external driving force values. The difference arises because the nondeforming particle model facilitates meandering skyrmion orbits while the deformable atomistic model enables stronger skyrmion-skyrmion interactions that reduce the meandering. Our results indicate that soliton motion through pinned skyrmion lattices on a periodic substrate is a robust effect.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Overland flow numerical model prediction, Lower Triangle Region in East River Watershed, Colorado, 3 days

This data package contains numerical simulation results of surface flow variables such as flow velocity and water depth in Lower Triangle Region in East River Watershed, Colorado. The surface flow is a consequence of a high intensity rainfall event with a total duration of 3 days, available at a resolution of 10 minutes. The results are computed on triangular multiresolution meshes with resolutions ranging from 10 meter to 80 meter. The data package also contains a simulation on a uniform triangular mesh with a resolution of 10 meter. The simulations consider surface flow only and neglect subsurface flow, infiltration, and evapotranspiration. The purpose of the data is to assess the quality of a mesh refinement strategy.

54 ENVIRONMENTAL SCIENCES↗

A copula-based rank histogram ensemble filter

Serial ensemble filters implement triangular probability transport maps to reduce high-dimensional inference problems to sequences of state-by-state univariate inference problems. The univariate inference problems are solved by sampling posterior probability densities obtained by combining constructed prior densities with observational likelihoods according to Bayes' rule. Many serial filters in the literature focus on representing the marginal posterior densities of each state. However, rigorously capturing the conditional dependencies between the different univariate inferences is crucial to correctly sampling multidimensional posteriors. This work proposes a new serial ensemble filter, called the copula rank histogram filter (CoRHF), that seeks to capture the conditional dependency structure between variables via empirical copula estimates; these estimates are used to rigorously implement the triangular (state-by-state univariate) Bayesian inference. The success of the CoRHF is demonstrated on two-dimensional examples and the Lorenz'63 problem. A practical extension to the high-dimensional setting is developed by localizing the empirical copula estimation, and is demonstrated on the Lorenz'96 problem.

97 MATHEMATICS AND COMPUTING↗

Atomically Precise Membranes for the Separation of Hydrocarbons

Separations often account for a majority of process costs. This is because all traditional separation processes have inherent weaknesses that prevent the system from achieving perfect (or even near perfect in many instances) selectivity. These weaknesses result in large recycle streams and require multiple separation units in concert in order to produce a product clean enough for use or sale. An atomically precise membrane capable of allowing passage to only certain molecules would greatly improve process economics. We have synthesized atomically precise, triangular and rectangular-shaped, pore-containing macromolecules (channel molecules) using a unique, stiff, programmable molecular scaffold developed in Prof. Christian Schafmeister’s lab at Temple University. We synthesized porous triangular and rectangular macromolecules from our unique, poly-cyclic, shape-programmable, and functional group-programmable spiroligomer scaffolds. These macromolecules display functional groups pointing outward that will covalently cross-link with other functional groups on other copies of the molecule. The pores are of programmable size and shape to selectively allow some molecules and ions to pass through the pores while resisting others. These molecules were confirmed with H-NMR and HPLC/HRMS. Self-assembled layers of these molecules were fabricated with the use of a Langmuir trough where they were compressed to a mean area that is close to their corresponding macrocycle size (~0.5-1 nm 2 ). We have also demonstrated several strategies for supporting films of these selective membranes on polysulfone.

Amundsen, Ted↗

Data Locality Enhancement of Dynamic Simulations for Exascale Computing (Final Report)

The development of modern processors exhibits two trends that complicate the optimizations of modern software. The first is the increasing sensitivity of processors' throughput to irregularities in computation. With more processors produced through a massive integration of simple cores, future systems will increasingly favor regular data-level parallel computations, but deviate from the needs of applications with complex patterns. Some evidences are already shown on Graphic Processing Units (GPU): Irregular data accesses (e.g., indirect references A[D[i]]) and conditional branches are limiting many GPU applications' performance at a level an order of magnitude lower than the peak of GPU. The second hardware trend is the growing gap between memory bandwidth and the aggregate speed—that is, the sum of all cores' computing power—of a Chip Multiprocessor (CMP). Despite the capped growth of the peak CPU speed, the aggregate speed of a CMP keeps increasing as more cores get into a single chip. It is expected that by 2018, node concurrency in an exascale system will increase by hundreds of times, whereas, memory bandwidth will expand by only 10 to 20 times. Consequently, data movement and storage is expected to consume more than 70% of the total system power. Bridging this gap is difficult; the complexities of modern CMP memory hierarchy make it even harder: Data cache becomes shared among computing units, and the sharing is often non-uniform—whether two computing units share a cache depends on their proximity and the level of the cache. On the recent IBM Power7 architecture, for instance, four hardware contexts (or SMT threads) in a core share the entire memory hierarchy, all cores in one chip share an on-chip L3 cache, and cores across chips share L3 and main memory through off-chip connections. These two trends complicate the translation of computing power into performance, especially for a program with either intensive data accesses or complex patterns in data accesses or control flow paths. Unfortunately, both attributes present and will persist in a class of important applications. For instance, many scientific simulations deal with a large volume of data. And meanwhile, as most real-world processes are non-uniform and evolving (e.g., the evolution of a galaxy or the process of a drug injection), both the computations and data accesses of these programs tend to be irregular and dynamically changing. Currently, the lack of support to these applications on modern CMP severely limits their performance. On GPU, as our recent study shows and other studies echo, performance enhancement of a factor of integers is possible when memory accesses or control flows are streamlined for a set of GPU applications. On multicore CPU, our studies show that traditional locality enhancement, for being oblivious to the new features of multicore memory hierarchy, may even cause large slowdown to data-intensive dynamic applications. The severity of the issues is expected to worsen as the two hardware trends continue. Some recent studies try to match software with the trends, but in a limited scope or manner. For irregularities on GPU, most studies focus on irregularities analyzable through static analysis (e.g., data accesses in regular loops). Dynamic irregularities are harder to address because the needed analysis and transformations typically have to happen at run time. Some other research resorts to hardware extensions, an actual adoption of which is unclear for the entailed space cost and complexity. For data locality, recent years have seen some exploitations of the new memory hierarchy on multicore for performance, but most of them are on process or thread scheduling, rather than program transformations. Our recent study reveals that program-level transformations may magnify the scheduling benefits by a factor of seven, concluding that program-level transformation should play a central role for data locality enhancement on modern CMP. But research in this direction has been sparse, and most have focused on data layout or cache performance modeling, rather than program transformations to match with the new memory hierarchy features. Overall, it is still an open question how to bridge the gap between dynamic computations and the two prominent properties of modern processors. The goal of this project is to develop a set of techniques and software tools to enhance the matching between memory accesses in dynamic simulations and the prominent features of modern and future CMP, alleviating the memory performance issues for petascale and exascale computing. This report summarizes the discoveries and products produced throughout this project. It includes free launch, a new software approach to overcoming the shortcomings of both methods; coherence-free multiview, an approach that allows multiple views of a single data object to co-exist on GPU memory during a GPU kernel execution; algorithmic optimizations to data analytics problems, especially those that involve lots of distance calculations. Supporting dynamic parallelism is important for GPU to benefit a broad range of applications. There are currently two fundamental ways for programs to exploit dynamic parallelism on GPU: a software-based approach with software-managed worklists, and a hardware-based approach through dynamic subkernel launches. Neither is satisfactory. The former is complicated to program and is often subject to some load imbalance; the latter suffers large runtime overhead. In this work, we propose free launch, a new software approach to overcoming the shortcomings of both methods. It allows programmers to use subkernel launches to express dynamic parallelism. It employs a novel compiler-based code transformation named subkernel launch removal to replace the subkernel launches with the reuse of parent threads. Coupled with an adaptive task assignment mechanism, the transformation reassigns the tasks in the subkernels to the parent threads with a good load balance. The technique requires no hardware extensions, immediately deployable on existing GPUs. It keeps the programming convenience of the subkernel launch-based approach while avoiding its large runtime overhead. Meanwhile, its superior load balancing makes it outperform manual worklist-based techniques by 3X on average. The work was published at the 48th Annual IEEE/ACM International Symposium on Microarchitecture (Micro'2015). A Graphic Processing Unit (GPU) system is typically equipped with many types of memory (e.g., global, constant, texture, shared, cache). Data placement determines what data are placed on which type of memory, essential for GPU memory performance. Prior optimizations of data placement always require a single view of a data object on memory, which limits the optimization effectiveness. In this work, we propose coherence-free multiview, an approach that allows multiple views of a single data object to co-exist on GPU memory during a GPU kernel execution. We demonstrate that under certain conditions, the multiple views can remain incoherent while facilitating enhanced data placement. We present a theorem and some compiler support to ensure the soundness of the usage of coherence-free multiview. We further develop reference-discerning data placement, a new way to enhance data placements on GPU. It enables more flexible data placements by using coherence-free multiview to leverage the slack in coherence requirement of some GPU programs. Experiments on three types of GPU systems show that, with less than 200KB space cost, the new data placement technique can provide a 1.6X average (up to 4.27X) speedup. In addition, we have examined algorithmic optimizations to data analytics problems, especially those that involve lots of distance calculations. Computing distances among data points is an essential part of many important algorithms in data analytics, graph analysis, and other domains. In each of these domains, developers have spent significant manual effort optimizing algorithms, often through novel applications of the triangle equality, in order to minimize the number of distance computations in the algorithms. In this work, we observe that many algorithms across these domains can be generalized as an instance of a generic distance-related abstraction. Based on this abstraction, we derive seven principles for correctly applying the triangular inequality to optimize distance-related algorithms. Guided by the findings, we develop Triangular OPtimizer (TOP), the first software framework that is able to automatically produce optimized algorithms that either matches or outperforms manually designed algorithms for solving distance-related problems. TOP achieves up to 237x speedups and 2.5X on average. The work has been published at the 32nd International Conference on Machine Learning (ICML'15) and the 41st International Conference on Very Large Data Bases (VLDB'15).

42 ENGINEERING↗

Revolutionizing Turbine Cooling with Micro-Architectures Enabled by Direct Metal Laser Sintering

The objective of this research effort was to explore innovative cooling architectures enabled by additive manufacturing techniques for improved turbine cooling performance. The ability to create complex internal geometries was leveraged to better distribute coolant as well as to integrate inherently unstable flow devices to enhance internal and external heat transfer. This was accomplished with a multi-faceted approach including analytical, experimental, and computational components. This final report documents progress during the total 4.25 year effort that was extended (at no additional cost) from the original 3-year cooperative agreement. Prior to starting the project, significant effort was invested in investigating innovative cooling designs from the open literature. When the project started, we quickly down-selected to 4 configurations: impingement jet fluidic oscillators (for internal leading edge cooling), reverse film cooling (for pressure surface), sweeping film cooling jets (for suction surface), and trailing edge slot cooling with microchannels. During the 2nd year, the reverse film cooling design was shown to be sub-optimal and work on that topic was halted. The three remaining technologies were integrated into a large scale nozzle guide vane and installed into a low-speed linear cascade facility for further interrogation. Initial results showed the sweeping film cooling jets (on the suction surface) to be the most promising technology compared to a baseline diffusion shaped film hole (777 design). The benefit was particularly evident at high blowing ratios (>1.5) when the 777 coolant film separated from the downstream surface. Benefits were also evident at elevated freestream turbulence levels. The leading edge cooling with unsteady jets was less effective in terms of peak or average cooling – however it was superior to round hole impingement cooling in terms of spatial uniformity. Finally, the trailing edge cooling design with micro-channels was scrapped in favor of a pinned arrangement with centerbody. During the 3rd year, the same three technologies were integrated into a transonic linear cascade for an assessment of compressibility effects. Again, the sweeping film cooling jets proved superior at high blowing ratios while the unsteady leading edge impingement and trailing edge pin-fins with centerbody designs yielded mixed results. Finally, during the 4th and final year, these 3 technologies were integrated into a direct metal laser sintered (DMLS) nozzle guide vane for testing in a high temperature, transonic annular vane cascade. The facility matches the flow temperature, Mach number, and coolant pressure ratios of an actual gas turbine. Before doing this, an additional series of tests were completed to validate a redesigned trailing edge cooling architecture. This final design included a centerbody with triangular pins between the centerbody and the vane external skin. The majority of these triangular pins are fabricated with a 30% gap to the centerbody – reducing their pressure drop considerably while still providing excellent heat transfer augmentation. This additional test campaign required an additional 3-month extension request to complete testing in the high temperature NGV test facility (Turbine Reacting Flow Rig – TuRFR). Testing of the DMLS vane in TuRFR pitted the 3 innovative cooling technologies against more traditional technologies (shaped 777 film hole, round impingement jet, and full pin arrangement in the trailing edge. The sweeping film cooling jets (on the suction surface) showed approximately 15% improvement in overall effectiveness compared to the 777 film hole while the trailing edge showed up to 20% improvement. The leading edge impingement was disappointing with a substantially lower effectiveness than traditional direct impingement. In summary, the study was successful in demonstrating that DMLS-enabled cooling technologies can yield significant gains in cooling performance.

03 NATURAL GAS↗

Seven Percent Critical Experiment Core Analysis Approach on Fuel Rods – Core Configurations T155-NoMo, and T155-397Mo.

A series of experiments will be performed to test the integral effects of molybdenum on the reactivity of a critical system. These experiments will use the 7uPCX assembly with the 1.55 cm triangular pitch grid plates. Molybdenum sleeves, consisting of 19.6 inch long 0.5-inch nominal outside diameter molybdenum tubes with 0.031-inch nominal wall thickness and centering hardware, will be placed on some of the fuel rods in the array. The purpose of this analysis is to examine two configurations of the 7uPCX using the 1.55 cm triangular pitch grid plates in fully-reflected approach-to-critical experiments with the number of fuel rods in the array as the approach parameter. This document presents the results of the analysis that was done to allow completion of the 7uPCX Configuration Checklist from Appendix A of SPRF-AP-005 [SNL 2020] for the cores noted above. The checklists for these cores are shown in Appendix A.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Exploring the Great Pyramid: Detector Technical Design Report with Stand-Alone Monte Carlo Simulations

Cosmic-ray muon imaging has been used to non-destructively examine the Pyramids of Khufu and Khafre on the Giza Plateau; the EGP project will continue this line of research by undertaking a full tomographic scan of the former and by doing so will increase the sensitivity of the technique by upwards of two orders of magnitude. For this purpose, a muon telescope using triangular (vernier) detector cells far outperforms one with rectangular cells, providing an angular and positional RMS improvement by a factor of 4 for the same cost per unit area. A refinement algorithm was developed to handle tracks that produce secondaries. The triangular detector yields a positional resolution for a back-projection to the center of the pyramid of less than 20 cm, ensuring that a feature large enough to be of significance will still be seen by the telescope. This method is shown to be able to accurately and precisely reconstruct tracks of muons that pass through the King s Chamber, Queen s Chamber, and Grand Gallery.

43 PARTICLE ACCELERATORS↗

Study of propellant dynamics in a shuttle type launch vehicle

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Jones, C. E.↗

Vee-notching device

A device is described for forming vee-notches in tensile test specimens comprising a vertically reciprocating, triangular, triple-edged cutting tool guided in a corresponding triangular slot. The specimen to be vee-notched is mounted on a carriage that is movable toward and away from the cutting tool. The specimen is precisely positioned on the carriage by tapered studs that extend into holes in the specimen and are used to expand spring collets against the wall of the holes.

Spier, R. A.↗

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Utku, S.↗

Theoretical and experimental longitudinal aerodynamic characteristics of an aspect ratio 0.25 sharp-edge delta wing at subsonic, supersonic, and hypersonic speeds

The suction analogy concept of Polhamus for predicting vortex lift in conjunction with an appropriate potential-flow solution is called the present method. This method is applied to an aspect ratio 0.25 sharp-edge delta wing from a Mach number of 0.143 to 10.4 in free air and at 0.074 in ground effect, and also to an aspect ratio 0.35 triangular crosssectional body at a Mach number of 6.9. The models had subsonic leading edges at the test Mach numbers. Vortex-flow effects could be neither confirmed nor denied to exist at high speeds because of the lack of flow visualization above a Mach number of 0.143. The data, however, could be better predicted by including a vortex-flow effect, although not always to the extent predicted from the present method because of the presence of actual and hypothesized unmodeled flow situations. The method of Nenni and Tung (NASA CR-1860) tended to confirm the existence of vortex flow at hypersonic speeds. The hypersonic-tangent-cone method predicted best the delta-wing results over the test angle-of-attack range and hypersonic Mach number range and did equally as well as the present method for the triangular body.

Fox, C. H., Jr.↗

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗

Inviscid to turbulent transition of trailing vortices

The plateau region in which trailing vortices initially exhibit slow decay of maximum tangential speed is demonstrated with the aid of constant and variable eddy viscosity models. The existence of the plateau is explained by the presence of the viscous core and by the necessity for transition of the initial, nearly inviscid profile to similarity far downstream. Span loading is shown to affect the initial maximum tangential speed as well as the duration of the plateau region. Triangular span loading is shown to present less hazard to trailing aircraft, at least in the near field, than elliptic loading because the inviscid profile for triangular loading exhibits a finite tangential speed at the vortex centerline and a large inviscid core.

Iversen, J. D.↗

Multivariate normal integration

Monte Carlo program evaluates integrals over rectangular regions for dimensions less than six and over elliptical regions in bivariate case. Program gives positive definite symmetric variance/covariance matrix factorization and calculates reciprocal of lower triangular matrix and product of diagonal elements of triangular matrix.

Falls, L. W.↗

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗