TY - JOUR
T1 - A Fourth-Order Derivative-Free Operator Marching Method for Helmholtz Equation in Waveguides
AU - Ya Yan Lu
JO - Journal of Computational Mathematics
VL - 6
SP - 719
EP - 729
PY - 2007
DA - 2007/12
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8725.html
KW - Helmholtz equation, Waveguides, Dirichlet-to-Neumann map, Operator marching.
AB - <p style="text-align: justify;">A fourth-order operator marching method for the Helmholtz equation in a waveguide is developed in this paper. It is derived from a &nbsp;new fourth-order exponential integrator for linear evolution equations. &nbsp;The method improves the second-order accuracy associated with the widely used step-wise coupled mode method where the waveguide is &nbsp;approximated by segments that are uniform in the propagation direction. The Helmholtz equation is solved using a one-way reformulation based on the &nbsp;Dirichlet-to-Neumann map. An alternative version closely related to &nbsp;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.</p>