Efficient Exascale Discretizations: High-Order Finite Element Methods

Abstract

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.

arXiv comment22 pages, 18 figures

References in corpus (8)

• MFEM: a modular finite element methods library
• OCCA: A unified approach to multi-threading languages
• Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods
• Nonconforming Schwarz-Spectral Element Methods For Incompressible Flow
• Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods
• Simulation-Driven Optimization of High-Order Meshes in ALE Hydrodynamics
• Local Fourier analysis of Balancing Domain Decomposition by Constraints algorithms
• Discontinuous Galerkin Discretizations of the Boltzmann Equations in 2D: semi-analytic time stepping and absorbing boundary layers

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