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GPU algorithms for Efficient Exascale Discretizations

Journal Article · · Parallel Computing
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  1. Univ. of Tennessee, Knoxville, TN (United States). Innovative Computing Lab.
  2. Univ. of Colorado, Boulder, CO (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  5. Advanced Micro Devices Inc., Austin, TX (United States)
  6. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
  7. Middle East Technical Univ., Ankara (Turkey)
  8. Argonne National Lab. (ANL), Lemont, IL (United States)
  9. Argonne National Lab. (ANL), Lemont, IL (United States); Pennsylvania State Univ., University Park, PA (United States)
  10. Univ. of Illinois at Urbana-Champaign, IL (United States)
  11. Argonne National Lab. (ANL), Lemont, IL (United States); Aristotle Univ. of Thessaloniki (Greece)
  12. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
+ Show Author Affiliations

In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. Furthermore, we discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
Grant/Contract Number:
AC52-07NA27344; AC02-06CH11357; AC05-00OR22725
OSTI ID:
1845216
Report Number(s):
LLNL-JRNL-816034; 1025529
Journal Information:
Parallel Computing, Journal Name: Parallel Computing Journal Issue: N/A Vol. 108; ISSN 0167-8191
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (32)

Monotonicity in high-order curvilinear finite element arbitrary Lagrangian-Eulerian remap: MONOTONICITY IN HIGH-ORDER CURVILINEAR FINITE ELEMENT ALE REMAP journal October 2014
Multi-material closure model for high-order finite element Lagrangian hydrodynamics: CLOSURE MODEL FOR HIGH-ORDER FINITE ELEMENT HYDRODYNAMICS journal April 2016
A method of computing numerically integrated stiffness matrices journal September 1972
Efficient numerical integration of element stiffness matrices journal September 1983
Fast simplicial finite element algorithms using Bernstein polynomials journal August 2010
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method journal July 2005
Nekbone performance on GPUs with OpenACC and CUDA Fortran implementations journal July 2016
Spectral methods for problems in complex geometries journal August 1980
Projection techniques for iterative solution of with successive right-hand sides journal September 1998
Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations journal February 2020
A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics journal June 2020
Simulation-driven optimization of high-order meshes in ALE hydrodynamics journal August 2020
From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations journal July 2010
High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation journal April 2017
OpenACC acceleration for the P N – P N - 2 algorithm in Nek5000 journal October 2019
High-Order Finite Element Method using Standard and Device-Level Batch GEMM on GPUs conference November 2020
Finite-Element Preconditioning of G-NI Spectral Methods journal January 2010
The p and h - p Versions of the Finite Element Method, Basic Principles and Properties journal December 1994
Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures journal January 2011
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal January 2012
A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers journal January 2018
High-Order Multi-Material ALE Hydrodynamics journal January 2018
The Target-Matrix Optimization Paradigm for High-Order Meshes journal January 2019
Scalable Low-Order Finite Element Preconditioners for High-Order Spectral Element Poisson Solvers journal January 2019
Efficient Matrix-Free High-Order Finite Element Evaluation for Simplicial Elements journal January 2020
Multigrid for Matrix-Free High-Order Finite Element Computations on Graphics Processors journal May 2019
An MPI/OpenACC implementation of a high-order electromagnetics solver with GPUDirect communication journal July 2016
Acceleration of tensor-product operations for high-order finite element methods journal September 2018
A study of vectorization for matrix-free finite element methods journal July 2020
libCEED: Fast algebra for high-order element-based discretizations journal July 2021
Scaling Limits for PDE-Based Simulation (Invited) conference June 2015
Comparison of accurate methods for the integration of hyperbolic equations journal January 1972

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97 MATHEMATICS AND COMPUTING
GPU acceleration
exascale applications
finite element methods
high-order discretizations
high-performance computing