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...While our focus is on high-order finite elements, the approach is mostly algebraic and thus applicable to other discretizations in factored form, as explained in the user manual and API implementation portion of the documentation. 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.