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.

Abstract-The internal structures of type I spherules (melted micrometeorites rich in iron) have been investigated using synchrotron-based computed microtomography. Variations from sphericity are small-the average ratio of the largest to the smallest semimajor axis is 1.07 ± 0.06. The X-ray tomographs reveal interior cavities, four spherules with metal cores with diameters ranging from 57 to 143 µm and, in two spherules, high attenuation features thought to be nuggets rich in platinumgroup elements. Bulk densities range from 4.2 to 5.9 g/cm 3 and average grain densities from 4.5 to 6.5 (g/cm 3 ) with uncertainties of 10-15%. The average grain densities are those expected for materials containing mostly oxides of iron and nickel. The tomographic density measurements indicate an average void space ofThe void spaces may be contraction features or the skeletons of bubbles that formed in the molten precursors during atmospheric passage.

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