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DOE OSTI2019

A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Coupled Electron-Photon Monte Carlo Radiation Transport for Next-Generation Computing Systems

Traditional Monte Carlo particle transport codes are expected to run inefficiently on next-generation architectures as they are memory-intensive and highly divergent. Since electrons and photons also behave differently, the future for coupled electron-photon radiation transport looks even worse. This project describes preliminary efforts to improve the performance of Monte Carlo particle transport codes when using accelerators like the graphics processing unit (GPU). Two key issues are addressed: how to handle memory-intensive tallies, and how to reduce divergence. Tallying on the GPU can be done efficiently by post-processing particle data, or by using a feature called warp shuffle for summing scores in parallel during the simulation. Reducing divergence is possible by using an event-based algorithm for particle tracking instead of the traditional history-based one. Although performance tests presented in this work show that the history-based algorithm generally outperformed the event-based one for simple problems, this outcome will likely change as the complexity of the code increases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Kmer-SSR: a fast and exhaustive SSR search algorithm

Motivation: One of the main challenges with bioinformatics software is that the size and complexity of datasets necessitate trading speed for accuracy, or completeness. To combat this problem of computational complexity, a plethora of heuristic algorithms have arisen that report a ‘good enough’ solution to biological questions. However, in instances such as Simple Sequence Repeats (SSRs), a ‘good enough’ solution may not accurately portray results in population genetics, phylogenetics and forensics, which require accurate SSRs to calculate intra- and inter-species interactions. Results: We present Kmer-SSR, which finds all SSRs faster than most heuristic SSR identification algorithms in a parallelized, easy-to-use manner. The exhaustive Kmer-SSR option has 100% precision and 100% recall and accurately identifies every SSR of any specified length. To identify more biologically pertinent SSRs, we also developed several filters that allow users to easily view a subset of SSRs based on user input. Kmer-SSR, coupled with the filter options, accurately and intuitively identifies SSRs quickly and in a more user-friendly manner than any other SSR identification algorithm. Availability and implementation: The source code is freely available on GitHub at https://github. com/ridgelab/Kmer-SSR.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Automatic Generation of Algorithms for High-Speed Reliable Lossy Data Compression (Final Report)

Fast reliable data compression is urgently needed for many leading-edge scientific instruments and for exascale high-performance computing applications because they produce vast amounts of data at extremely high rates. The goal of this project has been to develop a framework named LC that is able to automatically generate high-speed lossless and reliable lossy compression and decompression algorithms that can be customized for different kinds of data. The resulting LC framework is freely available on GitHub. To achieve high-speed operation, LC outputs optimized and parallelized CPU and GPU implementations of the generated algorithms. To ensure the quality of lossily compressed data, LC guarantees the user-provided error bound. To be able to customize the compression algorithm to various use cases, LC can synthesize millions of different algorithms and automatically search for the one that works best for the given data. We have already employed LC to create state-of-the-art lossless and lossy compressors for scientific data as well as leading lossless compressors for images. We hope that LC and the customized, fast, reliable, and CPU/GPU-compatible compression algorithms that it can generate will greatly benefit the many scientific applications that need not only high trustworthiness but also high performance.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Particle simulation in a multiprocessor environment

A parallel implementation of a particle simulation method that is portable between a wide class of multiprocessor computers is presented. A fine grain spatial decomposition is utilized where several subdomains having a regular structure are computed at each processing node. This leads directly to an efficient and straightforward load balancing scheme if the number of subdomains at each processor is permitted to vary in an appropriate manner. Three dimensional simulations incorporating full thermochemical nonequilibrium are possible using the resulting code. Vectorizable algorithms are retained from earlier work allowing efficient use of deeply pipelined node processors where available. Performance results are presented from three different machine architectures demonstrating the portability of the code. On a 128-node Intel iPSC/860, performance is twice that of a single Cray-Y/MP CPU running a highly vectorized simulation code. Speedup is linear over the full range of number of processors on all target machines, indicating scalability of the method to higher degrees of parallelism.

Mcdonald, Jeffrey D.↗

DOE OSTI2016

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics

n this paper, we introduce a multigrid block-based preconditioner for solving linear systems arising from a Discontinuous Galerkin discretization of the all-speed Navier-Stokes equations with phase change. The equations are discretized in conservative form with a reconstructed Discontinuous Galerkin (rDG) method and integrated with fully-implicit time discretization schemes. To robustly converge the numerically stiff systems, we use the Newton-Krylov framework with a primitive-variable formulation (pressure, velocity, and temperature), which is better conditioned than the conservative-variable form at low-Mach number. In the limit of large acoustic CFL number and viscous Fourier number, there is a strong coupling between the velocity-pressure system and the linear systems become non-diagonally dominant. To effectively solve these ill-conditioned systems, an approximate block factorization preconditioner is developed, which uses the Schur complement to reduce a 3 x 3 block system into a sequence of two 2 x 2 block systems: velocity-pressure,v P , and velocity-temperature, v T . We compare the performance of the v P -v T Schur complement preconditioner to classic preconditioning strategies: monolithic algebraic multigrid (AMG), element-block SOR, and primitive variable block Gauss-Seidel. The performance of the preconditioned solver is investigated in the limit of large CFL and Fourier numbers for low-Mach lid-driven cavity flow, Rayleigh-Bénard melt convection, compressible internally heated convection, and 3D laser-induced melt pool flow. Here, numerical results demonstrate that the v P -v T Schur complement preconditioned solver scales well both algorithmically and in parallel, and is robust for highly ill-conditioned systems, for all tested rDG discretization schemes (up to 4th-order).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Geometrical characterization of perlite-metal syntactic foam

This paper introduces an improved method for the detailed geometrical characterization of perlite-metal syntactic foam. This novel metallic foam is created by infiltrating a packed bed of expanded perlite particles with liquid aluminium alloy. The geometry of the solidified metal is thus defined by the perlite particle shape, size and morphology. The method is based on a segmented micro-computed tomography data and allows for automated determination of the distributions of pore size, sphericity, orientation and location. The pore (i.e. particle) size distribution and pore orientation is determined by a multi-criteria k-nearest neighbour algorithm for pore identification. The results indicate a weak density gradient parallel to the casting direction and a slight preference of particle orientation perpendicular to the casting direction. - Highlights: •A new method for identification of pores in porous materials was developed. •It was applied on perlite-metal syntactic foam samples. •A porosity decrease in the axial direction of the samples was determined. •Pore shape analysis showed a high percentage of spherical pores. •Orientation analysis showed that more pores are oriented in the radial direction.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods

Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration. It is a known issue that the beam quality can be artificially degraded by numerical Cherenkov radiation (NCR) resulting primarily from an incorrectly modeled dispersion relation. Pseudo-spectral solvers featuring infinite order stencils can strongly reduce NCR - or even suppress it - and are therefore well suited to correctly model the beam properties. For efficient parallelization of the PIC algorithm, however, localized solvers are inevitable. Arbitrary order pseudo-spectral methods provide this needed locality. Yet, these methods can again be prone to NCR. Here in this paper, we show that acceptably low solver orders are sufficient to correctly model the physics of interest, while allowing for parallel computation by domain decomposition.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

spammpack, Version 2013-06-18

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Source record↗

DOE OSTI2022

A massively parallel time-domain coupled electrodynamics–micromagnetics solver

We present a high-performance coupled electrodynamics–micromagnetics solver for full physical modeling of signals in microelectronic circuitry. The overall strategy couples a finite-difference time-domain approach for Maxwell’s equations to a magnetization model described by the Landau–Lifshitz–Gilbert equation. The algorithm is implemented in the Exascale Computing Project software framework, AMReX, which provides effective scalability on manycore and GPU-based supercomputing architectures. Furthermore, the code leverages ongoing developments of the Exascale Application Code, WarpX, which is primarily being developed for plasma wakefield accelerator modeling. Our temporal coupling scheme provides second-order accuracy in space and time by combining the integration steps for the magnetic field and magnetization into an iterative sub-step that includes a trapezoidal temporal discretization for the magnetization. The performance of the algorithm is demonstrated by the excellent scaling results on NERSC multicore and GPU systems, with a significant (59×) speedup on the GPU using a node-by-node comparison. We demonstrate the utility of our code by performing simulations of an electromagnetic waveguide and a magnetically tunable filter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Equilipy: a python package for calculating phase equilibria

The CALPHAD (CALculation of PHAse Diagram) approach (Nigel Saunders & Miodownik, 1998) provides predictions for thermodynamically stable phases in multicomponent-multiphase materials across a wide range of temperatures. Consequently, the CALPHAD calculations became an essential tool in materials and process design (Luo, 2015). Such design tasks frequently require navigating a high-dimensional space due to multiple components involved in the system. This increasing complexity demands high-throughput CALPHAD calculations, especially in the rapidly evolving field of alloy design. In response to the need, we developed Equilipy an open-source Python package designed for calculating phase equilibria of multicomponent-multiphase systems. Equilipy is specifically tailored for high-throughput CALPHAD calculations, offering parallel computations across multiple processors and nodes with the given NPT input conditions namely elemental compositions (N), pressure (P), and temperature (T). Equilipy utilizes the program structure and Gibbs energy functions from the Fortran-based program, Thermochimica (Piro et al., 2013), with incorporating a new Gibbs energy minimization algorithm. This algorithm, originally developed by Capitani and Brown in 1987 (Capitani & Brown, 1987), has been revised and implemented to enhance the stability and performance of calculations. The Fortran codes are precompiled and interfaced with Python via F2PY, ensuring high computation speed. Benchmark tests shown in Figure 1 demonstrate that Equilipy’s computation speed is comparable to those of established commercial software, TC-Python and PanPython. This result highlights its efficiency and potential applications in various scientific and industrial fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

GPU Acceleration of a Diagnostic Wind Solver

Reducing QUIC-Fire simulation runtimes is crucial in enabling simulation ensembles to guide science-driven prescribed fire planning in regions of complex terrain. Utilizing GPUs through OpenACC and Kokkos frameworks to accelerate generation of 3D windfields in QUIC-Fire would provide substantial speedup to the runtime of the code. Using GPUs for the Successive Over-Relaxation (SOR) algorithm utilized in QUIC-Fire will require deriving a ‘four colored’ version of the well explored ‘Red-Black’ SOR parallelization scheme. This effort could open the door for utilizing GPUs in other portions of the QUIC-Fire algorithm, increasing its viability in more complex and larger domains.

58 GEOSCIENCES↗

DOE OSTI2024

Scaling the SciDAC QuantOm Workflow

As part of the Scientific Discovery through Advanced Computing (SciDAC) program, the Quantum Chromodynamics Nuclear Tomography (QuantOM) project aims to analyze data from Deep Inelastic Scattering (DIS) experiments conducted at Jefferson Lab and the upcoming Electron Ion Collider. The DIS data analysis is performed on an event-level by combining the input from theoretical and experimental nuclear physics into a single, composable workflow. The optimization itself (I.e. fitting the experimental data with theoretical predictions) is carried out by a machine / deep learning algorithm. The size of the acquired DIS data as well as the complexity of the workflow itself require that the analysis is performed across multiple GPUs on high performance computing systems, such as Polaris at Argonne National Laboratory. This presentation discusses the novelties and challenges that came along with parallelizing this workflow. Recent results are compared to common distributed training techniques.

Lersch, Daniel↗

DOE OSTI2020

Machine Committee Framework for Power Grid Disturbances Analysis Using Synchrophasors Data

Events detection is a key challenge in power grid frequency disturbances analysis. Accurate detection of events is crucial for situational awareness of the power system. In this paper, we study the problem of events detection in power grid frequency disturbance analysis using synchrophasors data streams. Current events detection approaches for power grid rely on individual detection algorithm. This study integrates some of the existing detection algorithms using the concept of machine committee to develop improved detection approaches for grid disturbance analysis. Specifically, we propose two algorithms—an Event Detection Machine Committee (EDMC) algorithm and a Change-Point Detection Machine Committee (CPDMC) algorithm. Both algorithms use parallel architecture to fuse detection knowledge of its individual methods to arrive at an overall output. The EDMC algorithm combines five individual event detection methods, while the CPDMC algorithm combines two change-point detection methods. Each method performs the detection task separately. The overall output of each algorithm is then computed using a voting strategy. The proposed algorithms are evaluated using three case studies of actual power grid disturbances. Compared with the individual results of the various detection methods, we found that the EDMC algorithm is a better fit for analyzing synchrophasors data; it improves the detection accuracy; and it is suitable for practical scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1989

Systematic generation of multibody equations of motion suitable for recursive and parallel manipulation

The formulation of a method known as the joint coordinate method for automatic generation of the equations of motion for multibody systems is summarized. For systems containing open or closed kinematic loops, the equations of motion can be reduced systematically to a minimum number of second order differential equations. The application of recursive and nonrecursive algorithms to this formulation, computational considerations and the feasibility of implementing this formulation on multiprocessor computers are discussed.

Nikravesh, Parviz E.↗

NASA NTRS1989

A single-assignment language in a distributed memory multiprocessor

The implementation of the single-assignment programming language SISAL (McGraw et al., 1985) on a Symult 2010 parallel computer is described. The advantages of single-assignment languages over imperative languages in a multiprocessor environment are reviewed; the characteristics of SISAL are summarized; the program-graph generation and dynamic data partitioning procedures are explained; and the application of SISAL in constructing a concurrent iterative multigrid algorithm is discussed in detail and illustrated with diagrams.

Evripidou, P.↗