  The Yee algorithm for electromagnetic simulations is widely known to have
many advantages, including the following crucial two: (i) Its calculations are
local and therefore efficiently parallelizable--enabling simulations that
capitalize on the speed and scalability of high-performance computing
architecture. (ii) Yee's method faithfully preserves the symplectic geometry of
Maxwell's equations, improving its accuracy in long-time numerical simulations.
Whereas previous geometric generalizations of Yee's method have sacrificed its
scalability, in this article the Yee algorithm is generalized to higher order
and unstructured meshes in a manner that fully preserves both its scalability
and geometric naturalness. This generalization is achieved by prioritizing the
locality of the algorithm, reflecting the physical locality of Maxwell's
equations. Specifically, we demonstrate that Yee's method is but a special case
of a larger family of symplectic, finite element exterior calculus (FEEC)
methods that use scalable, local approximations of mass matrices. We discuss
the numerical advantages of this family of methods, which we call scalable FEEC
(SFEEC) methods.
