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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.

This is an active area of research for our team and we are interested in feedback and collaboration.

For more information, visit https://github.com/CEED/libCEED.