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.

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A relaxation algorithm for chemical substructure search is simulated for implementation on general-purpose multiprocessors. An improved relaxation algorithm is described and the inherent parallelism detailed. The general-purpose simulation package PASSIM is described, and the methods used to simulate the algorithm are given. A variably sized pool of processors was assumed. The simulation was run on 71 structure/query pairs, and an average maximum speedup of 5.5 over a single processor was found, for approximately 20 processors. A great variation is found for individual structure/query pairs. The overall factor limiting the performance is the serial bottlenecks in the algorithm.An isomerism between polycyclic aromatic hydrocarbons and ring assembly compounds formed by replacing selected rings with acetylenic linkages was noted, but not developed, by Dias. A far more complete isomerism, which is the logical extension of the referenced isomerism, is

libCEED is a new lightweight, open-source library for highperformance matrix-free Finite Element computations. libCEED offers a portable interface to high-performance implementations, selectable at runtime, tuned for a variety of current and emerging computational architectures, including CPUs and GPUs. libCEED's interface is purely algebraic, facilitating co-design with vendors and enabling unintrusive integration in new and legacy software. In this work, we present libCEED's newly-available Python interface, which opens up new strategies for parallelism and scaling in high-performance Python, without compromising ease of use.