Convexification for a CIP for the RTE]{Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation

TL;DR

This paper introduces a convexification numerical method for solving a 3D coefficient inverse problem in the radiative transport equation, providing convergence analysis and numerical validation in 2D.

Contribution

It develops the first convexification approach for a 3D CIP in the radiative transport equation with proven convergence and numerical demonstrations.

Findings

The method is globally convergent.

Convergence analysis is based on Carleman estimates.

Numerical studies confirm effectiveness in 2D.

Abstract

An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Extensive numerical studies in the 2-D case are presented.