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High-performance finite elements with MFEM

Julian Andrej, Nabil Atallah, Jan-Phillip Bäcker, John Camier, Dylan Copeland, Veselin Dobrev, Yohann Dudouit, Tobias Duswald, Brendan Keith, Dohyun Kim, Tzanio Kolev, Boyan Lazarov, Ketan Mittal, Will Pazner, Socratis Petrides, Syun'ichi Shiraiwa, Mark Stowell, Vladimir Tomov

TL;DR

Some of the recent research and development in MFEM is described, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications.

Abstract

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy's Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

High-performance finite elements with MFEM

TL;DR

Some of the recent research and development in MFEM is described, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications.

Abstract

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy's Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).
Paper Structure (28 sections, 8 equations, 19 figures)

This paper contains 28 sections, 8 equations, 19 figures.

Table of Contents

  1. Introduction
  2. GPU Acceleration and High-Performance Computing
  3. Matrix-free solvers for high-order finite elements
  4. State-of-the-art performance on exascale platforms and AMD GPUs
  5. Kernel fusion
  6. Mixed meshes, nonconforming meshes, and p-adaptivity
  7. Matrix-free discontinuous Galerkin methods on non-conforming meshes.
  8. Mixed meshes and p-adaptivity.
  9. Discretizations
  10. Discontinuous Petrov-Galerkin (DPG) methods
  11. Proximal Galerkin
  12. Immersed discretizations
  13. Integration over cut elements.
  14. Shifted boundary method.
  15. Distance and extrapolation solvers.
  16. ...and 13 more sections

Figures (19)

  • Figure 1: Comparison of the performance on the mass and diffusion benchmark problems (CEED BP1 and BP3) on NVIDIA V100 and AMD MI250X using the libCEED and default MFEM backends.
  • Figure 2: Throughput for fused kernel mass matrix benchmark
  • Figure 3: Performance comparison of matrix-free discontinuous Galerkin mass operators and advection operators (NVIDIA V100).
  • Figure 4: Performance of a matrix-free mass operator (BP1 benchmark problem) for different type of meshes using an AMD MI250X GPU.
  • Figure 5: Ultraweak DPG formulations for time-harmonic Maxwell equations for Tokamak simulations(left), 2D scattering of an acoustics beam (center), and for the time-harmonic Maxwell equations with AMR for the simulation of the microwave oven problem (right).
  • ...and 14 more figures