A Fourth-Order Derivative-Free Operator Marching Method for Helmholtz Equation in Waveguides (Journal of Computational Mathematics, 2021)
A fourth-order operator marching method for the Helmholtz equation in a waveguide is developed in this paper. It is derived from a  new fourth-order exponential integrator for linear evolution equations.  The method improves the second-order accuracy associated with the widely used step-wise coupled mode method where the waveguide is  approximated by segments that are uniform in the propagation direction. The Helmholtz equation is solved using a one-way reformulation based on the  Dirichlet-to-Neumann map. An alternative version closely related to  the coupled mode method is also given. Numerical results clearly indicate that the method is more accurate than the coupled mode method while the required computing effort is nearly the same.
Keywords: Helmholtz equation; Waveguides; Dirichlet-to-Neumann map; Operator marching.