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A Convergent Numerical Method for a Multi-frequency Inverse Source Problem in Inhomogenous Media by Nguyen, Loc H.; Li, Qitong; Klibanov, Michael V. is a scholarly article available to read on EtoBox.

What is A Convergent Numerical Method for a Multi-frequency Inverse Source Problem in Inhomogenous Media about?

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in which the unknown source function is not involved. The Dirichlet boundary condition is given on the entire boundary of the domain of interest and the Neumann boundary condition is given on a part of this boundary. To solve this problem, the quasi-reversibility method is applied. Uniqueness and existence of the minimizer are proven. A new Carleman estimate is established. Next, the convergence of those minimizers to the exact solution is proven using that Carleman estimate. Results of numerical tests are presented.

Author

Nguyen, Loc H.; Li, Qitong; Klibanov, Michael V.

Published

2019

Language

EN