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DOE OSTI2024

FuseIM: Fusing Probabilistic Traversals for Influence Maximization on Exascale Systems

Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as influence maximization. These applications heavily rely on BPTs to implement a Monte-Carlo sampling step for their approximations. Given the large sampling complexity, stochasticity of the diffusion process, and the inherent irregularity in real-world graph topologies, efficiently parallelizing these BPTs remains significantly challenging. In this paper, we present a new algorithm to fuse massive number of concurrently executing BPTs with random starts on the input graph. Our algorithm is designed to fuse BPTs by combining separate traversals into a unified frontier on distributed multi-GPU systems. To show the general applicability of the fused BPT technique, we have incorporated it into two state-of-the-art influence maximization parallel implementations (gIM and Ripples). Our experiments on up to 4K nodes of the OLCF Frontier supercomputer (32,768 GPUs and 196K CPU cores) show strong scaling behavior, and that fused BPTs can improve the performance of these implementations up to 34x (for gIM) and ~360x (for Ripples).

Neff, Reece W.↗

DOE OSTI2019

Multi-rate time integration on overset meshes

Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly smaller than on the remaining meshes, standard explicit time integrators impose inefficiencies for time-accurate calculations by requiring that all meshes advance with the smallest timestep. With the targeted use of multi-rate time integrators, separate meshes can be time-marched at independent rates to avoid wasteful computation while maintaining accuracy and stability. This work applies time-explicit multi-rate integrators to the simulation of the compressible Navier-Stokes equations discretized on overset meshes using summation-by-parts (SBP) operators and simultaneous approximation term (SAT) boundary conditions. We introduce a class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods. We present numerical results that confirm the efficacy of MRAB integrators, outline a number of implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB. We also look at the use of our method in the setting of a large-scale distributed-memory parallel implementation where we discuss concerns involving load balancing and communication efficiency.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Speedup of UEDGE Parameter Scans Using Machine-Learning Optimized OpenMP Parallelization and a Continuation Solver

This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Space-time discretizations using constrained first-order system least squares (CFOSLS)

This work studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting, subject to a space-time conservation constraint (coming from the original PDE). Available piecewise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 2, 3 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multigrid preconditioners are presented for the discrete CFOSLS system. The results are obtained from a parallel implementation of the methods for which we report reasonable scalability.

4D de Rham sequence↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Leveraging FPGA Advantages for Quicker Data Processing for LBNF

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, Jacob↗

DOE OSTI2025

Real-Time FPGA Implementation For Frequency Sweep Interferometry In The LBNF Complex

Rossel, A. Jacob [Fermilab; Unlisted]↗

DOE OSTI2021

Critical percolation on the kagome hypergraph

In this report we study the percolation critical surface of the kagome lattice in which each triangle is allowed an arbitrary connectivity. Using the method of critical polynomials, we find points along this critical surface to high precision. This kagome hypergraph contains many unsolved problems as special cases, including bond percolation on the kagome and (3, 12 2 ) lattices, and site percolation on the hexagonal, or honeycomb, lattice, as well as a single point for which there is an exact solution. We are able to compute enough points along the critical surface to find a very accurate fit, essentially a Taylor series about the exact point, that allows estimations of the critical point of any system that lies on the surface to precision rivaling Monte Carlo and traditional techniques of similar accuracy. We find also that this system sheds light on some of the surprising aspects of the method of critical polynomials, such as why it is so accurate for certain problems, like the kagome and (3, 12 2 ) lattices. The bond percolation critical points of these lattices can be found to 17 and 18 digits, respectively, because they are in close proximity, in a sense that can be made quantitative, to the exact point on the critical surface. We also discuss in detail a parallel implementation of the method which we use here for a few calculations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Addressing Load Imbalance in Bioinformatics and Biomedical Applications: Efficient Scheduling across Multiple GPUs

Computational bioinformatics and biomedical applications frequently contain heterogeneously sized units of work or tasks, for instance due to variability in the sizes of biological sequences and molecules. Variable-sized workloads lead to load imbalances in parallel implementations which detract from efficiency and performance. Many modern computing resources now have multiple graphics processing units(GPUs) per computer for acceleration. These multiple GPU resources need to be used efficiently through balancing of workloads across the GPUs. OpenMP is a portable directive-based parallel programming API used ubiquitously in bioscience applications to program CPUs; recently, the use of OpenMP directives for GPU acceleration has become possible. Here, motivated by experiences with imbalanced loads in GPU-accelerated bioinformatics applications, we address the load balancing problem using OpenMP task-to-GPU scheduling combined with OpenMP GPU offloading for multiply heterogeneous workloads – loads with both variable input sizes, and simultaneously, variable convergence rates for algorithms with a stochastic component – scheduled across multiple GPUs. We aim to develop strategies which are both easy to use and have lower overheads, and may be incorporated incrementally in existing programs which already make use of OpenMP for CPU-based threading in order to make use of multi-GPU computers. We test different combinations of input size variability and convergence rate variability, and characterize the effects of these different scenarios on the performance of scheduling strategies across multiple GPUs with OpenMP. We present several dynamic scheduling solutions for different parallel patterns, explore optimizations, and provide publicly available example computational kernels to make these strategies easy to use in programs. This work will enable application developers to efficiently and easily use multiple GPUs for imbalanced workloads found in bioinformatics and biomedical applications.

Thavappiragasam, Mathialakan↗

DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗

DOE OSTI2019

Uncollided flux techniques for arbitrary finite element meshes

The uncollided angular flux can be difficult to compute accurately in discrete-ordinate radiation transport codes, especially in weakly-scattering configurations with localized sources. It has long been recognized that an analytical or semi-analytical treatment of the uncollided flux, coupled with a discrete-ordinate solution for the collided flux, can yield dramatic improvements in solution accuracy and computational efficiency. In this paper, we present such an algorithm for the semi-analytical calculation of the uncollided flux. This algorithm is unique in several aspects: (1) it applies to arbitrary polyhedral cells (and can be thus coupled with collided flux solvers that support arbitrary polyhedral meshes without the need for explicit tetrahedral re-meshing), (2) it provides accurate uncollided solutions near sources, (3) it is devised with parallel implementation in mind, and (4) it minimizes the total number of traced rays and maintains a reasonable ray density on each local subdomain. This paper provides a complete derivation of the algorithm and demonstrates its important features on a set of simple examples and a standard transport benchmark. Assessment of its parallel performance will be the subject of a subsequent paper.

42 ENGINEERING↗

DOE OSTI2021

Local time stepping for the shallow water equations in MPAS

In this work we assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different time-steps on different regions of the computational grid. The LTS schemes considered here were originally introduced by Hoang et al. (2019) [26], who laid out the mathematical foundation of the methods. Here, the authors take on the task of presenting a fast, efficient and scalable parallel implementation of these LTS methods on high performance computing machines, with the aim to provide a recipe for other climate modeling groups that may be interested in employing LTS algorithms in their codes. As a matter of fact, even if MPAS is our framework of choice, our approach is general enough and could be of interest to other groups beyond the MPAS community. Due to their nature, LTS methods possess an inherent load imbalance that needs to be carefully addressed in order to obtain efficient scalability. Even more important is the far from trivial task of computing the right-hand side terms only on specific LTS regions during the time-stepping procedure. An inefficient handling of this task causes a drastic decay of the CPU time performance, making the LTS algorithms practically of no use. The emphasis of the present work is therefore on the computational and parallel aspects of the LTS methods, whose proper treatment is crucial to make the methods run faster against existing strategies, such as for instance high-order explicit global time-stepping schemes. This is in fact the ultimate goal of using an LTS procedure and it is the one to which we direct all our optimization efforts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Optimizing the hit finding algorithm for liquid argon TPC neutrino detectors using parallel architectures

Neutrinos are particles that interact rarely, so identifying them requires large detectors which produce lots of data. Processing this data with the computing power available is becoming even more difficult as the detectors increase in size to reach their physics goals. Liquid argon time projection chamber (LArTPC) neutrino experiments are expected to grow in the next decade to have 100 times more wires than in currently operating experiments, and modernization of LArTPC reconstruction code, including parallelization both at data- and instruction-level, will help to mitigate this challenge. The LArTPC hit finding algorithm is used across multiple experiments through a common software framework. In this paper we discuss a parallel implementation of this algorithm. Using a standalone setup we find speedup factors of two times from vectorization and 30–100 times from multi-threading on Intel architectures. The new version has been incorporated back into the framework so that it can be used by experiments. On a serial execution, the integrated version is about 10 times faster than the previous one and, once parallelization is enabled, more speedups comparable to the standalone program are achieved.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Sierra/SD - User's Manual - 4.56

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 OSTI2021

Sierra/SD - User's Manual

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 OSTI2020

Sierra/SD--User's Manual - 4.58

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 OSTI2021

Sierra/SD - User's Manual - 5.4

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗