Abstract
We revisit the question of optimizing the construction and application of finite element matrices. By using commuting properties of the reference mappings and duality, we reorganize stiffness matrix construction and matrix-free application so that the bulk of the work can be done by optimized matrix multiplication libraries. We provide examples, including numerical experiments, with the Laplace and curl-curl operators as well as develop a general framework. Our techniques are applicable in general geometry and are not restricted to constant coefficient operators.
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