Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Efficient exascale discretizations: High-order finite element methods

Journal Article · · International Journal of High Performance Computing Applications
 [1];  [2];  [3];  [4];  [5];  [1];  [6];  [4];  [7];  [4];  [5];  [4];  [1];  [8];  [1];  [9];  [1];  [3];  [3];  [10] more »;  [11];  [3];  [1];  [12];  [4];  [12];  [13];  [5];  [14];  [1] « less
  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA
  2. Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
  3. Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA
  4. Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, USA
  5. Department of Computer Science, University of Colorado, Boulder, CO, USA
  6. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
  7. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, USA
  8. AMD Research, Austin, TX, USA
  9. Mechanical Engineering Department, Middle East Technical University, Ankara, Turkey
  10. Occalytics LLC, Weehawken, NJ, USA
  11. Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA, Department of Nuclear Engineering, Penn State, PA, USA
  12. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA
  13. Pacific Northwest National Laboratory, WA, USA
  14. Mathematics and Computer Science, Argonne National Laboratory, Lemont, IL, USA, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Greece
+ Show Author Affiliations

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

Sponsoring Organization:
USDOE
OSTI ID:
1787877
Alternate ID(s):
OSTI ID: 1864159
Journal Information:
International Journal of High Performance Computing Applications, Journal Name: International Journal of High Performance Computing Applications Journal Issue: 6 Vol. 35; ISSN 1094-3420
Publisher:
SAGE PublicationsCopyright Statement
Country of Publication:
United States
Language:
English

References (53)

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
Comparison of multigrid algorithms for high‐order continuous finite element discretizations journal April 2015
Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations
  • Dobrev, Veselin A.; Lazarov, Raytcho D.; Vassilevski, Panayot S.
  • Numerical Linear Algebra with Applications, Vol. 13, Issue 9 https://doi.org/10.1002/nla.504
journal January 2006
Performance, Design, and Autotuning of Batched GEMM for GPUs book June 2016
Spectral Methods book January 2006
Automatic p-version mesh generation for curved domains journal July 2004
Parallel mesh adaptation for high-order finite element methods with curved element geometry journal September 2013
LES of the Gas-Exchange Process Inside an Internal Combustion Engine Using a High-Order Method journal September 2019
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method journal July 2005
A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems journal August 2016
A Characteristic-Based Spectral Element Method for Moving-Domain Problems journal December 2018
Spectral methods for problems in complex geometries journal August 1980
A spectral element method for fluid dynamics: Laminar flow in a channel expansion journal June 1984
Stabilization of spectral methods by finite element bubble functions journal January 1994
MFEM: A modular finite element methods library journal January 2021
Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations journal February 2020
Nonconforming Schwarz-spectral element methods for incompressible flow journal September 2019
Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting journal March 2020
Simulation-driven optimization of high-order meshes in ALE hydrodynamics journal August 2020
A novel numerical treatment of the near-wall regions in the k − ω class of RANS models journal August 2018
On the use of LES-based turbulent thermal-stress models for rod bundle simulations journal October 2019
Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal January 2004
High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation journal April 2017
Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods journal February 2018
Discontinuous Galerkin discretizations of the Boltzmann–BGK equations for nearly incompressible flows: Semi-analytic time stepping and absorbing boundary layers journal August 2019
A GPU accelerated discontinuous Galerkin incompressible flow solver journal August 2019
High-performance Tensor Contractions for GPUs journal January 2016
High-Order Methods for Incompressible Fluid Flow book January 2009
RF wave simulation for cold edge plasmas using the MFEM library journal January 2017
Design, Optimization, and Benchmarking of Dense Linear Algebra Algorithms on AMD GPUs conference September 2020
RAJA: Portable Performance for Large-Scale Scientific Applications conference November 2019
BDDC Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity in Three Dimensions journal January 2010
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal January 2012
PCBDDC: A Class of Robust Dual-Primal Methods in PETSc journal January 2016
High-Order Multi-Material ALE Hydrodynamics journal January 2018
Low-Order Preconditioning of High-Order Triangular Finite Elements journal January 2018
The Target-Matrix Optimization Paradigm for High-Order Meshes journal January 2019
Local Fourier Analysis of Balancing Domain Decomposition By Constraints Algorithms journal January 2019
Nonconforming Mesh Refinement for High-Order Finite Elements journal January 2019
Scalable Low-Order Finite Element Preconditioners for High-Order Spectral Element Poisson Solvers journal January 2019
Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods journal January 2020
A Preconditioner for Substructuring Based on Constrained Energy Minimization journal January 2003
PUMI: Parallel Unstructured Mesh Infrastructure journal May 2016
Why is MPI so slow?: analyzing the fundamental limits in implementing MPI-3.1
  • Raffenetti, Ken; Blocksome, Michael; Si, Min
  • Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '17 https://doi.org/10.1145/3126908.3126963
conference January 2017
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
Scalability of high-performance PDE solvers journal June 2020
High-performance operator evaluations with ease of use: libCEED's Python interface conference January 2020
Scaling Limits for PDE-Based Simulation (Invited) conference June 2015
Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation conference June 2018
Parallel Auxiliary Space AMG for H(Curl) Problems journal June 2009

Similar Records

GPU algorithms for Efficient Exascale Discretizations
Journal Article · Sat Sep 25 00:00:00 EDT 2021 · Parallel Computing · OSTI ID:1845216
Center for Efficient Exascale Discretizations Software Suite
Software · Tue Aug 29 20:00:00 EDT 2017 · OSTI ID:code-45457

Related Subjects