Compact 3-D Envelope ADI-FDTD Algorithm for Simulations of Coherent Radiation Sources

A modified complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain solver for electromagnetic (EM) fields is presented. Like the conventional ADI scheme, the modified scheme is based on splitting the time step into two halves. In each substep, Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The new scheme is a combination of the conventional CE-ADI scheme and the leapfrog ADI scheme that was recently reported. The main features are a more compact form of the tridiagonal equations and greater flexibility in the application of boundary conditions. The boundary conditions on the six faces of the solution box are general and can be specified either as perfect conductor, symmetry boundary conditions, cavity modes, or arbitrary external specification. The new compact CE-ADI scheme is unconditionally stable; thus, the time step can be larger than the one imposed by the Courant-Friedrichs-Lewy (CFL) condition. Fast stable EM simulations of a planar slow-wave structure are demonstrated, with time steps exceeding the CFL limit by two orders of magnitude.