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At least 1,081 records · Page 60

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗

Hierarchical calibration and validation for modeling bench-scale solvent-based carbon capture. Part 1: Non-reactive physical mass transfer across the wetted wall column

A hierarchical model calibration and validation are proposed here for quantifying the confidence level of mass transfer prediction using a computational fluid dynamics (CFD) model, where the solvent-based carbon dioxide (CO 2 ) capture is simulated and the predicted results are compared to the corresponding bench-scale experimental data. Two unit problems with an increasing level of complexity are proposed to break down the complex physical/chemical processes of solvent-based CO 2 capture into relatively simpler problems to separate the effects of physical transport and chemical reaction. This paper focuses on the calibration and validation of the first unit problem, i.e., the CO 2 mass transfer across a falling ethanolamine (MEA) film in the absence of chemical reaction. This problem is investigated both experimentally and numerically using non-reactive nitrous oxide (N 2 O) as a surrogate for CO 2 . To capture motion of the gas-liquid interface, a volume of fluid method is employed with a one-fluid formulation to compute the mass transfer between the two phases. Parallel bench-scale experiments are designed and conducted to validate and calibrate the CFD models using a general Bayesian calibration approach. Two important transport parameters, Henry's constant and gas diffusivity, are calibrated to produce the posterior distributions, which will be used as input for the second unit problem to address the chemical absorption of CO 2 across the MEA falling film, where both mass transfer and chemical reaction are involved. Finally, mass transfer coefficients predicted by CFD are also compared with those predicted by the traditional/empirical correlations under both steady and wavy falling film conditions.

54 ENVIRONMENTAL SCIENCES↗

Parallel accelerated vector similarity calculations for genomics applications

The surge in availability of genomic data holds promise for enabling determination of genetic causes of observed individual traits, with applications to problems such as discovery of the genetic roots of phenotypes, be they molecular phenotypes such as gene expression or metabolite concentrations, or complex phenotypes such as diseases. However, the growing sizes of these datasets and the quadratic, cubic or higher scaling characteristics of the relevant algorithms pose a serious computational challenge necessitating use of leadership scale computing. In this study we describe a new approach to performing vector similarity metrics calculations, suitable for parallel systems equipped with graphics processing units (GPUs) or Intel Xeon Phi processors. Our primary focus is the Proportional Similarity metric applied to Genome Wide Association Studies (GWAS) and Phenome Wide Association Studies (PheWAS). We describe the implementation of the algorithms on accelerated processors, methods used for eliminating redundant calculations due to symmetries, and techniques for efficient mapping of the calculations to many-node parallel systems. Finally, results are presented demonstrating high per-node performance and parallel scalability with rates of more than five quadrillion (5 × 10 15 ) elementwise comparisons achieved per second on the ORNL Titan system. In a companion paper we describe corresponding techniques applied to calculations of the Custom Correlation Coefficient for comparative genomics applications.

59 BASIC BIOLOGICAL SCIENCES↗

An O(N logN) multi-layer boundary element method for direct computation of sound propagation in shallow water environments

Direct three-dimensional (3D) numerical simulations of acoustic fields in range-dependent shallow water environments remains a challenge due to environmental complexities and large computational cost.We develop an efficient 3D boundary element method (BEM) for shallow water acoustic propagation which utilizes a Pre-corrected Fast Fourier Transform (PFFT) approach to reduce the computational effort from O ( N 2~3 ) to O ( N log N ) where N is the total number of boundary unknowns. To account for inhomogeneous media, the method allows for arbitrary number of coupled multi-layer BEM sub-domains. With O ( N log N ) efficiency and the use of massively parallel high-performance computing platforms, we are able to conduct multi-layer 3D direct simulations of low-mid frequency acoustics over kilometer ranges. Furthermore we perform extensive validations of the method and provide two shallow water waveguide examples benchmarked against theoretical solutions. To illustrate the efficacy and usefulness of the PFFT-BEM method, we perform 3D large-scale direct simulations to assess the performance of two established canonical models: axisymmetric coupled mode model for 3D seamount; and Kirchhoff approximation and perturbation theory for 3D rough surface scattering.

42 ENGINEERING↗

Anisotropic Thermal Response of Packed Copper Wire

The apparent thermal conductivity of packed copper wire test specimens was measured parallel and perpendicular to the axis of the wire using laser flash, transient plane source, and transmittance test methods. Approximately 50% wire packing efficiency was produced in the specimens using either 670- or 925-μm-diameter copper wires that both had an insulation coating thickness of 37 μm. The interstices were filled with a conventional varnish material and also contained some remnant porosity. The apparent thermal conductivity perpendicular to the wire axis was about 0.5–1 W/mK, whereas it was over 200 W/mK in the parallel direction. The Kanzaki model and an finite element analysis (FEA) model were found to reasonably predict the apparent thermal conductivity perpendicular to the wires but thermal conductivity percolation from nonideal wire-packing may result in their underestimation of it.

30 DIRECT ENERGY CONVERSION↗

Growth and characterization of HgBa 2 CaCu 2 O 6+δ and HgBa 2 Ca 2 Cu 3 O 8+δ crystals

We report the successful growth of sizable crystals of the cuprate superconductors HgBa 2 CaCu 2 O 6+δ and HgBa 2 Ca 2 Cu 3 O 8+δ . These compounds are well known for their high optimal superconducting critical temperatures of T c = 128 K and 134 K at ambient pressure, respectively, and for their challenging synthesis. Using a conventional quartz-tube encapsulation method and a two-layer encapsulation method that utilizes custom-built high-pressure furnaces, we are able to grow single crystals with linear dimensions up to several millimeters parallel to the CuO 2 planes. Extended postgrowth annealing is shown to lead to sharp superconducting transitions, indicative of high macroscopic homogeneity. X-ray diffraction and polarized Raman spectroscopy are identified as viable nondestructive methods to help separate the two compounds from synthesis products, as the latter often contain intergrowths of the former. Furthermore, our work helps to remove obstacles toward the study of these model cuprate systems with experimental probes that require sizable high-quality crystals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-Wave Frequency Division Multiplexing in an Yttrium Iron Garnet Microstripe Magnetized by Inhomogeneous Field.

Spin waves are promising candidates for information processing and transmission in a broad frequency range. In the realization of magnonic devices, the frequency related division of the spin waves is a critical function for parallel information processing. In this work, we demonstrate a proof-of-concept spin-wave frequency division multiplexing method by magnetizing a homogeneous magnetic microstripe with an inhomogeneous field. The symmetry breaking additional field is introduced by a Permalloy stripe simply placed in lateral proximity to an yttrium iron garnet waveguide. Spin waves with different frequencies can propagate independently, simultaneously, and separately in space along the shared waveguide. This work demonstrates one potential way for parallel information transmission and processing in magnonics.

Zhang, Zhizhi↗

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗

Efficient smoothed particle radiation hydrodynamics I: Thermal radiative transfer

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Overlapping localized exponential time differencing methods for diffusion problems

The localized exponential time differencing (ETD) based on overlapping domain decomposition has been recently introduced for extreme-scale phase field simulations of coarsening dynamics, which displays excellent parallel scalability in supercomputers. This paper serves as the first step toward building a solid mathematical foundation for this approach. We study the overlapping localized ETD schemes for a model time-dependent diffusion equation discretized in space by the standard central difference. Two methods are proposed and analyzed for solving the fully discrete localized ETD systems: the first one is based on Schwarz iteration applied at each time step and involves solving stationary problems in the subdomains at each iteration, while the second one is based on the Schwarz waveform relaxation algorithm in which time-dependent subdomain problems are solved at each iteration. The convergences of the associated iterative solutions to the corresponding fully discrete localized ETD solution and to the exact semidiscrete solution are rigorously proved. Finally, numerical experiments are also carried out to confirm theoretical results and to compare the performance of the two methods.

58 GEOSCIENCES↗

Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning

Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive self-consistent ground-state electronic structure calculations that can often scale cubically with the number of atoms. Linearly scaling methods depend on computing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The second-order spectral projection (SP2) algorithm is an O(N) algorithm that computes P with a sequence of 40 - 50 matrix-matrix multiplications. In this paper, we present task-based implementations of a recently developed data-parallel graph-based approach to the SP2 algorithm, G-SP2. We represent the density matrix P as an undirected graph and use graph partitioning techniques to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPI-based implementations. This load-balancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using task-based programming models. We develop task-based implementations of the data-parallel G-SP2 algorithm using both Intel's Concurrent Collections (CnC) as well as the Charm++ programming model and evaluate these implementations for future use. Scaling and performance results of our implementations are investigated for representative segments of QMD simulations for solvated protein systems containing more than 10,000 atoms.

97 MATHEMATICS AND COMPUTING↗

A progressively reduced pretension method to fabricate Bradbury-Nielsen gates with uniform tension

A Bradbury-Nielsen gate (BNG) is often used to modulate ion beams. It consists of two interleaved and electrically isolated sets of wires with uniform tension, which ideally keep parallel, equidistant, and coplanar over a wide temperature range, making the BNG reliable and robust. We have previously analyzed the non-uniformity problem of wire tensions with sequentially winding method and developed a template-based transfer method to solve this problem. In this paper, we introduced a progressively reduced pretension method, which allows directly and sequentially fixing wires onto the substrate without using a template. Theoretical analysis shows that by applying proper pretension to each wire when fixing it, the final wire tensions of all wires can be uniform. The algorithm and flowchart to calculate the pretension sequence are given, and the fabrication process is introduced in detail. Pretensions are generated by weight combination with a weaving device. A BNG with stainless steel wire and a printed circuit board substrate is constructed with this method. The non-uniformity of the final wire tensions is less than 2.5% in theory. The BNG is successfully employed in our ion mobility spectrometer, and the measured resolution is 33.5 at a gate opening time of 350 μs. Compared to the template-based method, this method is simpler, faster, and more flexible with comparable production quality when manufacturing BNGs with different configurations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Parallel DTFE Surface Density Field Reconstruction

We improve the interpolation accuracy and efficiency of the Delaunay tessellation field estimator (DTFE) for surface density field reconstruction by proposing an algorithm that takes advantage of the adaptive triangular mesh for line-of-sight integration. The costly computation of an intermediate 3D grid is completely avoided by our method and only optimally chosen interpolation points are computed, thus, the overall computational cost is significantly reduced. The algorithm is implemented as a parallel shared-memory kernel for large-scale grid rendered field reconstructions in our distributed-memory framework designed for N-body gravitational lensing simulations in large volumes. We also introduce a load balancing scheme to optimize the efficiency of processing a large number of field reconstructions. Our results show our kernel outperforms existing software packages for volume weighted density field reconstruction, achieving ~ 10x speedup, and our load balancing algorithm gains an additional ~ 3.6x speedup at scales with ~ 16k processes.

97 MATHEMATICS AND COMPUTING↗

Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs

Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient smoother algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined block structured grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi/Kepler GPUs and AMD multicore systems are presented.

97 MATHEMATICS AND COMPUTING↗

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nanopatterned electron beams for temporal coherence and deterministic phase control of x-ray free-electron lasers

A method includes accelerating an electron bunch along a direction of propagation to a relativistic energy and partitioning the electron bunch by transmitting the electron bunch through a grating at the relativistic energy. The grating includes a plurality of alternating narrow portions and wide portions. The narrow portions have a first thickness in a direction substantially parallel to the direction of propagation of the electron bunch, and the wide portions have a second thickness in the direction substantially parallel to the direction of propagation of the electron bunch. The second thickness is greater than the first thickness. The method also includes generating a pulse of light using the partitioned electron bunch.

Graves, William↗

Parallel Lattice Subpaving Map (plsm)

Custom spatial subdivision of N-dimensional lattice region in GPU memory. An extension of the method of a hyper-octree is used to allow for arbitrary subdivision ratios in each dimension. In addition, the decision to refine (or select) a given sub-region is based on a user-provided callback, allowing for arbitrary refinement domains to be expressed either geometrically or programmatically.

Fackler, Philip↗

High voltage DC power conversion system and method of operating the same

A fraction rated conversion system for coupling a plurality of high voltage direct current (HVDC) power strings in parallel to an HVDC transmission system includes at least one fraction rated power converter coupled to the plurality of HVDC power strings and at least one capacitive device coupled to the at least one fraction rated power converter. The at least one fraction rated power converter and the at least one capacitive device regulate a differential voltage across each HVDC power string of the plurality of HVDC power strings to be substantially similar to each other.

17 WIND ENERGY↗