An operator marching method for inverse problems in range-dependent waveguides

Abstract

For large-scale inverse problems in acoustics and electromagnetics, numerical schemes based on direct methods, e.g. FEM and meshless methods, often result in huge linear systems, and thus are not feasible in terms of computing speed and memory storage. This work proposes the “inverse fundamental operator marching method” based on the Dirichlet-to-Neumann map for solving large-scale inverse boundary-value problems in range-dependent waveguides. Truncated singular value decomposition is employed to solve ill-conditioned linear systems arising in marching process, and the number of propagating modes in the waveguide assumes the role of a regularization parameter. Numerical results show that the method is computationally efficient, highly accurate, stable with respect to data noise for retrieving the propagating part of the starting field. It particularly suits to long-range wave propagation in slowly varying stratified waveguide.