Inverse point source location with the Helmholtz equation on a bounded domain

An inverse random source problem for the Helmholtz equation

This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation, which is to reconstruct the statistical properties of the random source function from boundary measurements of the radiating random electric field. Although the emphasis of the paper is on the inverse problem, we adapt a computationally more efficient approach to study the soluti...

Numerical solution of the inverse source problem for the Helmholtz Equation with multiple frequency data

The inverse source problem of the Helmholtz Equation with multiple frequency data is investigated. Three cases are considered: (1) both the magnitude and phase of measurements on the whole boundary (full aperture data) are available; (2) only limited aperture measurements of the field are available; (3) only the magnitude information of the fields on the boundary is available. A continuation me...

The Helmholtz Equation Ii: Source on a General Smooth Manifold

A multigrid solver to the Helmholtz equation with a point source based on travel time and amplitude

The Helmholtz equation arises when modeling wave propagation in the frequency domain. The equation is discretized as an indefinite linear system, which is difficult to solve at high wave numbers. In many applications, the solution of the Helmholtz equation is required for a point source. In this case, it is possible to reformulate the equation as two separate equations: one for the travel time ...

An inverse problem for Helmholtz equation

This article is concerned with subsurface material identification for the 2-D Helmholtz equation. The algorithm is iterative in nature. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. It linearizes the otherwise nonlinear problem around the background field. The background field is the field variable generated using the guessed value of the unk...