@Article{Kirby:2014:HPE,
  author =       "Robert C. Kirby",
  title =        "High-Performance Evaluation of Finite Element Variational
                  Forms via Commuting Diagrams and Duality",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       40,
  number =       4,
  year    =      2014,
  month   =      jun,
  pages =        "25:1--25:24",
  url =          "http://doi.acm.org/10.1145/2559983",
  accepted =     "12 December 2013",
  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.",
}