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DOE OSTI2023

Sierra/SD – User’s Manual (V.5.16)

Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high-fidelity, validated models used in modal, vibration, static and shock analysis of weapons systems. This document provides a user’s guide to the input for Sierra/SD. Details of input specifications for the different solution types, output options, element types and parameters are included. The appendices contain detailed examples, and instructions for running the software on parallel platforms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Sierra/SD – User's Manual – 5.22

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Sierra/SD – User's Manual (V.5.24)

42 ENGINEERING↗

DOE OSTI2022

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

The goal of influence maximization is to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. The problem has a number of important applications such as viral marketing, information spread, and epidemic control. Although computing optimal seed set is NP-Hard, due to the submodular nature of the problem efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM algorithm over large real-world social networks. We present an adaptive and memory-efficient optimization approach for a state-of-the-art multi-threaded parallel influence maximization algorithm. Our approach,HuffMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding, and queries directly on the compressed data to preserve the memory savings obtained through compression. We also propose an efficient sampling strategy based on the distribution of RR sets, which can further reduce the computation time for typical social networks with long-tail distributions. Considering a NUMA architecture, we scale up our solution on 128-core CPUs and reduce the memory footprint by up to 45.7% with negligible time overhead (or even faster) and without perceivable loss of accuracy.

Chen, Xinyu↗

NASA NTRS1994

Parallel DSMC Solution of Three-Dimensional Flow Over a Finite Flat Plate

This paper describes a parallel implementation of the direct simulation Monte Carlo (DSMC) method. Runtime library support is used for scheduling and execution of communication between nodes, and domain decomposition is performed dynamically to maintain a good load balance. Performance tests are conducted using the code to evaluate various remapping and remapping-interval policies, and it is shown that a one-dimensional chain-partitioning method works best for the problems considered. The parallel code is then used to simulate the Mach 20 nitrogen flow over a finite-thickness flat plate. It is shown that the parallel algorithm produces results which compare well with experimental data. Moreover, it yields significantly faster execution times than the scalar code, as well as very good load-balance characteristics.

Nance, Robert P.↗

NASA NTRS2013

Improving NASA's Multiscale Modeling Framework for Tropical Cyclone Climate Study

One of the current challenges in tropical cyclone (TC) research is how to improve our understanding of TC interannual variability and the impact of climate change on TCs. Recent advances in global modeling, visualization, and supercomputing technologies at NASA show potential for such studies. In this article, the authors discuss recent scalability improvement to the multiscale modeling framework (MMF) that makes it feasible to perform long-term TC-resolving simulations. The MMF consists of the finite-volume general circulation model (fvGCM), supplemented by a copy of the Goddard cumulus ensemble model (GCE) at each of the fvGCM grid points, giving 13,104 GCE copies. The original fvGCM implementation has a 1D data decomposition; the revised MMF implementation retains the 1D decomposition for most of the code, but uses a 2D decomposition for the massive copies of GCEs. Because the vast majority of computation time in the MMF is spent computing the GCEs, this approach can achieve excellent speedup without incurring the cost of modifying the entire code. Intelligent process mapping allows differing numbers of processes to be assigned to each domain for load balancing. The revised parallel implementation shows highly promising scalability, obtaining a nearly 80-fold speedup by increasing the number of cores from 30 to 3,335.

tropical cyclone interannual variability↗

DOE OSTI2018

Computing with Spikes: The Advantage of Fine-Grained Timing

Neural-inspired spike-based computing machines often claim to achieve considerable advantages in terms of energy and time efficiency by using spikes for computation and communication. However, fundamental questions about spike-based computation remain unanswered. For instance, how much advantage do spike-based approaches have over conventional methods, and under what circumstances does spike-based computing provide a comparative advantage? Simply implementing existing algorithms using spikes as the medium of computation and communication is not guaranteed to yield an advantage. Here, we demonstrate that spike-based communication and computation within algorithms can increase throughput, and they can decrease energy cost in some cases. We present several spiking algorithms, including sorting a set of numbers in ascending/descending order, as well as finding the maximum or minimum or median of a set of numbers. We also provide an example application: a spiking median-filtering approach for image processing providing a low-energy, parallel implementation. Furthermore, the algorithms and analyses presented here demonstrate that spiking algorithms can provide performance advantages and offer efficient computation of fundamental operations useful in more complex algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

An Adaptive Particle Tracking Algorithm for Lagrangian-Eulerian Simulations of Dispersed Multiphase Flows

The Lagrangian-Eulerian method is broadly used for simulations of dispersed multiphase flows by solving the continuous phase in the Eulerian framework while treating the dispersed phase as point particles in a Lagrangian framework. The accuracy of the Lagrangian-Eulerian method largely depends on the number of computational particles tracked for the Lagrangian phase. In this study, an adaptive Lagrangian particle tracking algorithm is proposed to balance the statistical error and the computational cost by dividing and merging the particles according to the local particle statistics in the computational domain. The computational particles are considered as weighted sampling points of the particle probability density functions (PDF) which represents a statistical equivalence of the Lagrangian phase. The algorithm is implemented as a part of a C++ library for Lagrangian particles, Grit, with performance portability to multi-core or many-core CPUs and Graphic Processing Unit (GPU) architectures. The accuracy of the proposed algorithm with two different schemes are studied through a test problem with analytical solutions for both the particle number density and momentum source term. The results are used to evaluate the proposed algorithm as well as to validate the parallel implementation.

Ge, Wenjun↗

DOE OSTI2018

Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems

This work discusses techniques for computing a few selected eigenvalue–eigenvector pairs of large and sparse symmetric matrices. A recently developed class of techniques to solve this type of problems is based on integrating the matrix resolvent operator along a complex contour that encloses the interval containing the eigenvalues of interest. This paper considers such contour integration techniques from a domain decomposition viewpoint and proposes two schemes. The first scheme can be seen as an extension of domain decomposition linear system solvers in the framework of contour integration methods for eigenvalue problems, such as FEAST. The second scheme focuses on integrating the resolvent operator primarily along the interface region defined by adjacent subdomains. A parallel implementation of the proposed schemes is described, and results on distributed computing environments are reported. These results show that domain decomposition approaches can lead to reduced run times and improved scalability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr↗

NASA NTRS1998

Performance Analysis and Portability of the PLUM Load Balancing System

The ability to dynamically adapt an unstructured mesh is a powerful tool for solving computational problems with evolving physical features; however, an efficient parallel implementation is rather difficult. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive numerical computations in a message-passing environment. PLUM requires that all data be globally redistributed after each mesh adaption to achieve load balance. We present an algorithm for minimizing this remapping overhead by guaranteeing an optimal processor reassignment. We also show that the data redistribution cost can be significantly reduced by applying our heuristic processor reassignment algorithm to the default mapping of the parallel partitioner. Portability is examined by comparing performance on a SP2, an Origin2000, and a T3E. Results show that PLUM can be successfully ported to different platforms without any code modifications.

Oliker, Leonid↗

DOE OSTI2024

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗

NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗

DOE OSTI2017

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for $\mathscr{O}(N)$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $\mathscr{O}(N)$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Assessing the reliability of fast Fourier transform-based crystal plasticity simulations of a polycrystalline material near a crack tip

Crystal plasticity simulations enable a physically-based description of the micromechanical fields associated with microstructural attributes in polycrystalline materials. Fast Fourier transforms implementation of crystal plasticity (CP-FFT) in periodic unit cells offers increased computational efficiency compared to traditional finite element methods (CP-FEM). Albeit, questions may arise concerning the accuracy of the CP-FFT approach given its underlying spectral framework, specifically in regards to: potential artifacts due to violating the traction-free conditions at internal free surface within the unit cell, Gibbs phenomenon near regions with sharp changes in local mechanical properties, and representation of free surfaces under the constraints imposed by the requirement of periodicity of the unit cell. This paper presents a custom massively parallelized implementation of CP-FFT. A direct comparison of simulation results for polycrystalline deformation near a crack in a Ti55531 alloy is presented between CP-FEM and CP-FFT. The micromechanical fields and slip system level values are quantified and are similar between the two methods. Up to 10% difference in the stress fields is reported at the crack tip and this value dissipates moving away from the crack tip after 5 voxels (7 µm). In conclusion, the results point towards the reliable use of CP-FFT simulations to model polycrystalline deformation with caveats based on the treatment of the discussed artifacts.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Avoiding Communication in Primal and Dual Block Coordinate Descent Methods

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large machine learning datasets. However, existing implementations communicate at every iteration, which, on modern data center and supercomputing architectures, often dominates the cost of floating-point computation. Recent results on communication-avoiding Krylov subspace methods suggest that large speedups are possible by re-organizing iterative algorithms to avoid communication. We show how applying similar algorithmic transformations can lead to primal and dual block coordinate descent methods that only communicate every $s$ iterations---where $s$ is a tuning parameter---instead of every iteration for the regularized least-squares problem. We show that the communication-avoiding variants reduce the number of synchronizations by a factor of $s$ on distributed-memory parallel machines without altering the convergence rate and attain strong scaling speedups of up to $6.1\times$ over the “standard algorithm" on a Cray XC30 supercomputer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

PSelInv – A distributed memory parallel algorithm for selected inversion: The non-symmetric case

This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non-symmetric matrices. We assume a general sparse matrix A has been decomposed as $PAQ$ = $LU$ on a distributed memory parallel machine, where L, U are lower and upper triangular matrices, and P, Q are permutation matrices, respectively. The PSelInvmethod computes selected elements of $A$ -1 . The selection is confined by the sparsity pattern of the matrix A T . Here our algorithm does not assume any symmetry properties of A, and our parallel implementation is memory efficient, in the sense that the computed elements of $A$ -T overwrites the sparse matrix $L + U$ in situ . PSelInv involves a large number of collective data communication activities within different processor groups of various sizes. In order to minimize idle time and improve load balancing, tree-based asynchronous communication is used to coordinate all such collective communication. Numerical results demonstrate that PSelInv can scale efficiently to 6,400 cores for a variety of matrices.

97 MATHEMATICS AND COMPUTING↗