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.

中文翻译：

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高效的百亿亿次离散化：高阶有限元方法

有效利用百亿亿级架构需要重新思考许多大规模应用中使用的数值算法。这些架构偏向于公开超细粒度并行性并最大化浮点运算与能源密集型数据移动比率的算法。在非结构化网格的 PDE 离散化领域实现高效率的少数可行方法之一是使用无矩阵/部分组装的高阶有限元方法，因为这些方法可以提高准确性和/或减少计算时间由于减少了数据移动。在本文中，我们概述了高效 Exascale 离散化中心 (CEED) 的研究和开发活动，Exascale 计算项目中的一个联合设计中心，专注于下一代离散化软件和算法的开发，使广泛的有限元应用程序能够在未来的硬件上高效运行。CEED 是一个研究伙伴关系，涉及来自两个美国国家实验室和五所大学的 30 多名计算科学家，其中包括 Nek5000、MFEM、MAGMA 和 PETSc 项目的成员。我们讨论了基于目标基准、微型应用程序和离散化库的 CEED 协同设计活动，以及我们在大规模 GPU 架构的性能优化方面的工作。我们还对非结构化自适应网格细化算法、无矩阵线性求解器、高阶数据可视化、