A stable algorithm for non-homogeneous waveguide equation based on DtN maps

A new stable computational method for non-homogeneous waveguide equation with a piecewise uniform structure along the main propagation direction is constructed, based on the modified Dirichlet-to-Neumann (DtN) map of each uniform segment. For segments with the same structure, only a DtN map needs to be calculated on such a segment, and then the solution of the equation can be derived recursively. Numerical examples demonstrate that it is a stable and efficient algorithm for the waveguide equations. This method can greatly reduces the requirement of internal memory and the amount of computation compared with the traditional algorithms.