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

TL;DR

This paper introduces a stable and efficient computational algorithm for non-homogeneous waveguide equations using modified Dirichlet-to-Neumann maps, reducing memory and computational demands.

Contribution

The paper develops a novel recursive method based on modified DtN maps for piecewise uniform waveguides, enhancing stability and efficiency over traditional algorithms.

Findings

Algorithm is stable and efficient in numerical tests.

Reduces memory and computational requirements.

Applicable to waveguides with piecewise uniform structures.

Abstract

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.