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

Generalizing Yee's method: Scalable geometric higher-order FEEC algorithms for Maxwell's equations on an unstructured mesh