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libCEED is a high-order API library, that provides a common algebraic low-level operator description, allowing a wide variety of applications to take advantage of the efficient operator evaluation algorithms in the different CEED packages (from a single source).

One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, high-order methods require a new "format" that still represents a linear (or more generally non-linear) operator, but not through a sparse matrix.

The goal of libCEED is to propose such a format, as well as supporting implementations and data structures, that enable efficient operator evaluation on a variety of computational device types (CPUs, GPUs, etc.). This new operator description is based on algebraically factored form, which is easy to incorporate in a wide variety of applications, without significant refactoring of their own discretization infrastructure.

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