A globally convergent numerical method for a 3D coefficient inverse problem for a wave-like equation

TL;DR

This paper introduces a globally convergent numerical method for solving a 3D coefficient inverse problem in wave equations, leveraging Carleman weights to ensure convexity and demonstrating effectiveness through numerical experiments.

Contribution

The paper develops a new convexification-based numerical method with global convergence guarantees for 3D wave coefficient inverse problems.

Findings

Method successfully reconstructs coefficients in 3D wave problems.

Numerical results confirm the method's effectiveness and efficiency.

Convexification ensures global convergence of the solution.

Abstract

A version of the convexification globally convergent numerical method is constructed for a coefficient inverse problem for a wave-like partial differential equation. The presence of the Carleman Weight Function in the corresponding Tikhonov-like cost functional ensures the global strict convexity of this functional. Numerical results are presented to illustrate the effectiveness and efficiency of the proposed method.