A numerical method for inverse Helmholtz problem based on approximate inverse of a matrix

This note is concerned with a computational method for an inverse problem for Helmholtz equation. It seeks to recover a subsurface material property based on data collected at the boundary. The major improvement in this method is that it does not require the linearization of the working equations. The method is quite simple and requires only one set of data to obtain a good approximation of the unknown material property. Additional set of data can improve the quality of the recovered function. A number of numerical examples, both one-D and 2-D, are used to study the applicability of the method in the presence of noise

Automated summary

This article presents a computational method for the inverse problem of the Helmholtz equation, aiming to recover subsurface material properties based on boundary data. The major improvement of this method is that it eliminates the need for linearizing the working equations, making it simple and efficient. Using just one set of data is sufficient to obtain a good approximation of the unknown material property, while additional data sets can further improve the quality of the recovered function.