  Modeling the behavior of superconducting electronic circuits containing
Josephson junctions is crucial for the design of superconducting information
processors and devices. In this paper, we introduce DEC-QED, a computational
approach for modeling the electrodynamics of superconducting electronic
circuits containing Josephson junctions in arbitrary three-dimensional
electromagnetic environments. DEC-QED captures the non-linear response and
induced currents in BCS superconductors and accurately captures phenomena such
as the Meissner effect, flux quantization and Josephson effects. Using a
spatial coarse-graining formulation based on Discrete Exterior Calculus (DEC),
DEC-QED can accurately simulate transient and long-time dynamics in
superconductors. The expression of the entire electrodynamic problem in terms
of the gauge-invariant flux field and charges makes the resulting classical
field theory suitable for second quantization.
