FDTD: Solving 1+1D delay PDE in parallel

The delay term is spatially non-local, rendering conventional approaches such as the method of lines inapplicable. We show that by properly designing the grid and by supplying the (partial) exact solution as the boundary condition, the delay PDE can be numerically solved.

In addition, we demonstrate that while the delay imposes strong data dependency, multi-thread parallelization can nevertheless be applied to such a problem. Our code provides a numerically exact solution to the time-dependent multi-photon scattering problem in waveguide QED.