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The programming tools and parallel algorithms created for the Massively Parallel Processor (MPP) located at the NASA Goddard Space Center are discussed. A user-friendly environment for high level language parallel algorithm development was developed. The issues involved in implementing certain algorithms on the MPP were researched. The expected results were compared with the actual results.
The present volume on parallel CFD discusses implementations on parallel machines, numerical algorithms for parallel CFD, and performance evaluation and computer science issues. Attention is given to a parallel algorithm for compressible flows through rotor-stator combinations, a massively parallel Euler solver for unstructured grids, a fast scheme to analyze 3D disk airflow on a parallel computer, and a block implicit multigrid solution of the Euler equations. Topics addressed include a 3D ADI algorithm on distributed memory multiprocessors, clustered element-by-element computations for fluid flow, hypercube FFT and the Fourier pseudospectral method, and an investigation of parallel iterative algorithms for CFD. Also discussed are fluid dynamics using interface methods on parallel processors, sorting for particle flow simulation on the connection machine, a large grain mapping method, and efforts toward a Teraflops capability for CFD.
We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.
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.
We survey recent work on approximation algorithms for computing degree-constrained subgraphs in graphs and their applications in combinatorial scientific computing. The problems we consider include maximization versions of cardinality matching, edge-weighted matching, vertex-weighted matching and edge-weighted $b$ -matching, and minimization versions of weighted edge cover and $b$ -edge cover. Exact algorithms for these problems are impractical for massive graphs with several millions of edges. For each problem we discuss theoretical foundations, the design of several linear or near-linear time approximation algorithms, their implementations on serial and parallel computers, and applications. Our focus is on practical algorithms that yield good performance on modern computer architectures with multiple threads and interconnected processors. We also include information about the software available for these problems.
In recent years k-means++ has become a popular initialization technique for improved k-means clustering. To date, most of the work done to improve its performance has involved parallelizing algorithms that are only approximations of k-means++. In this paper we present a parallelization of the exact k-means++ algorithm, with a proof of its correctness. We develop implementations for three distinct shared-memory architectures: multicore CPU, high performance GPU, and the massively multithreaded Cray XMT platform. We demonstrate the scalability of the algorithm on each platform. In addition we present a visual approach for showing which platform performed k-means++ the fastest for varying data sizes.
The feasibility of using the Massively Parallel Processor (MPP) and possible future machines with parallel architecture for weather prediction and climate simulation was studied. A shallow water model and a two-level primitive equations model were implemented.
A new massively parallel algorithm is presented for simulating large asymmetric circuit-switched networks, controlled by a randomized-routing policy that includes trunk-reservation. A single instruction multiple data (SIMD) implementation is described, and corresponding experiments on a 16384 processor MasPar parallel computer are reported. A multiple instruction multiple data (MIMD) implementation is also described, and corresponding experiments on an Intel IPSC/860 parallel computer, using 16 processors, are reported. By exploiting parallelism, our algorithm increases the possible execution rate of such complex simulations by as much as an order of magnitude.
MOOSE is an open-source computational platform for constructing multi-physics models and executing them in a massively parallel fashion. It has a stochastic tools module (STM) for forward/inverse uncertainty quantification (UQ) and surrogate modeling. This presentation details some recent developments to the STM with respect to the implementation of adaptive, active learning, and multifidelity Monte Carlo methods for forward UQ of computational models. Specifically, the adaptive Monte Carlo methods include Markov Chain Monte Carlo (MCMC)-driven algorithms like adaptive importance sampling and parallelized subset simulation for statistical QoI estimation, rare events analysis, and stochastic gradient-free optimization. The active learning methods include Gaussian Process (GP) surrogates and their training via Adam optimization, design of acquisition functions, and integration with samplers like Monte Carlo, adaptive importance, and parallelized subset simulation. These active learning methods are also designed to work in a batch mode, wherein, the required calls to the full computational model are executed in parallel whenever a user-specified batch size is met. The multifidelity methods in STM are broadly divided into two categories: hierarchical, where a defined hierarchy exists among the low-fidelity models, and peer, where all the low-fidelity models are treated equally. A GP surrogate is used to learn the differences between the low- and high-fidelity models in both multifidelity categories, and acquisition functions from the active learning classes are used to decide whether to rely on a low-fidelity model or call the expensive high-fidelity model. Alongside the software description and usage, applications are also presented to nuclear engineering computational models including a TRISO nuclear fuel particle, a reactor pressure vessel, and a heat-pipe microreactor.
Summary Important computational physics problems are often large‐scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to determine whether a computational framework is performing efficiently or is scalable. The aim of this paper is to present various strategies for better understanding the performance of any parallel computational frameworks for solving PDEs. Important performance issues that negatively impact time‐to‐solution are discussed, and we propose a performance spectrum analysis that can enhance one's understanding of critical aforementioned performance issues. As proof of concept, we examine commonly used finite element simulation packages and software and apply the performance spectrum to quickly analyze the performance and scalability across various hardware platforms, software implementations, and numerical discretizations. It is shown that the proposed performance spectrum is a versatile performance model that is not only extendable to more complex PDEs such as hydrostatic ice sheet flow equations but also useful for understanding hardware performance in a massively parallel computing environment. Potential applications and future extensions of this work are also discussed.
Designing and refactoring complex scientific code, such as the E3SM land model (ELM), for new computing architectures is challenging. This paper presents design strategies and technical approaches to develop a data-oriented, GPU-ready ELM model using compiler directives (OpenACC/OpenMP). We first analyze the datatypes and processes in the original ELM code. Then we present design considerations for ultrahigh-resolution ELM (uELM) development for massive GPU systems. These techniques include the global data-oriented simulation workflow, domain partition, code porting and data copy, memory reduction, parallel loop restructure and flattening, and race condition detection. We implemented the first version of uELM using OpenACC targeting the NVidia GPUs in the Summit supercomputer at Oak Ridge National Laboratory. During the implementation, we developed a software tool (named SPEL) to facilitate code generation, verification, and performance tuning using these techniques. The first uELM implementation for Nvidia GPUs on Summit delivered promising results: 1) over 98% of the ELM code was automatically generated and tuned by scripts. Most ELM modules had better computational performances than the original ELM code for CPUs. The GPU-ready uELM is more scalable than the CPU code on fully-loaded Summit nodes. Example profiling results from several modules are also presented to illustrate the performance improvements and race condition detection. The lessons learned and toolkit developed in the study are also suitable for further uELM deployment using OpenMP on the first US exascale computer, Frontier, equipped with AMD CPUs and GPUs.
CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension. TDK has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 716142). VRR has been supported by the Swiss National Science Foundation in the form of Ambizione grant No. PZ00P2 174227 and RZK by the Natural Sciences and Engineering Research Council of Canada (NSERC) through Discovery Grants (RGPIN-2016-0505). GKS and CJM are supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. UK based work was funded under the embedded CSE programme of the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk), grants eCSE03-011, eCSE06-6, eCSE08-9, eCSE13-17 and the EPSRC (EP/P022235/1) grant “Surface and Interface Toolkit for the Materials Chemistry Community". Computational resources were provided by the Swiss National Supercomputing Centre (CSCS) and Compute Canada. The generous allocation of computing time on the FPGA-based supercomputer “Noctua" at PC2 is kindly acknowledged.
In order to simulate the effects of the impingement of hot exhaust jets of High Performance Aircraft on landing surfaces a multi-disciplinary computation coupling flow dynamics to heat conduction in the runway needs to be carried out. Such simulations, which are essentially unsteady, require very large computational power in order to be completed within a reasonable time frame of the order of an hour. Such power can be furnished by the latest generation of massively parallel computers. These remove the bottleneck of ever more congested data paths to one or a few highly specialized central processing units (CPU's) by having many off-the-shelf CPU's work independently on their own data, and exchange information only when needed. During the past year the first phase of this project was completed, in which the optimal strategy for mapping an ADI-algorithm for the three dimensional unsteady heat equation to a MIMD parallel computer was identified. This was done by implementing and comparing three different domain decomposition techniques that define the tasks for the CPU's in the parallel machine. These implementations were done for a Cartesian grid and Dirichlet boundary conditions. The most promising technique was then used to implement the heat equation solver on a general curvilinear grid with a suite of nontrivial boundary conditions. Finally, this technique was also used to implement the Scalar Penta-diagonal (SP) benchmark, which was taken from the NAS Parallel Benchmarks report. All implementations were done in the programming language C on the Intel iPSC/860 computer.
The Ab Initio Molecular Dynamics (AIMD) method allows scientists to treat the dynamics of molecular and condensed phase systems while retaining a first-principles-based description of their interactions. This extremely important method has tremendous computational requirements, because the electronic Schr¨odinger equation, approximated using Kohn-Sham Density Functional Theory (DFT), is solved at every time step. With the advent of manycore architectures, application developers have a significant amount of processing power within each compute node that can only be exploited through massive parallelism. A compute intensive application such as AIMD forms a good candidate to leverage this processing power. In this paper, we focus on adding thread level parallelism to the plane wave DFT methodology implemented in NWChem. Through a careful optimization of tall-skinny matrix products, which are at the heart of the Lagrange multiplier and nonlocal pseudopotential kernels, as well as 3D FFTs, our OpenMP implementation delivers excellent strong scaling on the latest Intel Knights Landing (KNL) processor. We assess the efficiency of our Lagrange multiplier kernels by building a Roofline model of the platform, and verify that our implementation is close to the roofline for various problem sizes. Finally, we present strong scaling results on the complete AIMD simulation for a 64 water molecules test case, that scales up to all 68 cores of the Knights Landing processor.
PsDNS is a Python package which makes it easy to solve partial differential equation using a pseudo-spectral method. The code uses Python classes and Numpy-like arrays to provide a simple interface with which users can construct equations, integrators, and diagnostics. It also includes implementation for common problems, in particular, the incompressible Navier-Stokes equation in a periodic domain, which is commonly used as a benchmark problem for turbulence research. PsDNS uses MPI to allow massively parallel computation for large problems.
Implementation of a flexible Grazing Incidence Small-Angle Scattering (GISAXS). Simulation code based on the Distorted Wave Born Approximation (DWBA) theory that effectively utilizes the parallel processing power provided by graphic processors and multicore processors. This constitutes a handy tool for experimentalists facing a massive flux of data, allowing them to accurately simulate the GISAXS process and analyze the produced data. The software computes the diffraction image for any given super position of custom shapes or morphologies in a user-defined region of the reciprocal space for all possible grazing incidence angles and in-plane sample rotations. This flexibility then allows to easily tackle a wide range of possible sample structures such as nanoparticles o top of or embedded in a substrate or a multilayered structure. In cases where the sample displays regions of significant refractive index contrast, an algorithm has been implemented to perform a slicing of the sample along the vertical direction and compute the averaging refractive index profile to be used as the reference geometry of the unpertubed system. Preliminary tests show good agreement with experimental data for a variety of commonly encountered nanostructures.
Calibr8 provides an application to rapidly prototype and perform material model calibration for complex plasticity models using advanced adjoint or forward sensitivity analyses for execution on massively parallel machines. These techniques can be orders of magnitude faster than traditional finite difference approaches for material model calibration. The underlying technology used in Calibr8 is automatic differentiation, which allows for the rapid implementation and testing of new plasticity models within its framework. Additionally, Calibr8 can perform adjoint-based error estimation to approximate discretization errors for user-implemented plasticity models. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-10630 O
A high level language for the Massively Parallel Processor (MPP) was designed. This language, called Parallel Pascal, is described in detail. A description of the language design, a description of the intermediate language, Parallel P-Code, and details for the MPP implementation are included. Formal descriptions of Parallel Pascal and Parallel P-Code are given. A compiler was developed which converts programs in Parallel Pascal into the intermediate Parallel P-Code language. The code generator to complete the compiler for the MPP is being developed independently. A Parallel Pascal to Pascal translator was also developed. The architecture design for a VLSI version of the MPP was completed with a description of fault tolerant interconnection networks. The memory arrangement aspects of the MPP are discussed and a survey of other high level languages is given.