Marching schemes for inverse scattering problems in waveguides with curved boundaries

A marching scheme is developed for inverse scattering problems of the Helmholtz equation in waveguides with curved boundaries. We implement a local orthogonal transform to transform the irregular waveguide in physical plane into a regular rectangle in computing plane. Then the modified Helmholtz system in computational domain is piecewise solved through a second order numerical marching scheme, and we propose a spectral projector based on the truncated local propagating eigenfunction expansion to regularize the marching scheme. In the end, the marching scheme is verified by extensive numerical experiments, and it is shown that the scheme is efficient, stable and accurate in rapidly varying waveguides with curved boundaries, even when the number of propagating modes in the main propagation direction is variable.