Point source identification in non-linear advection-diffusion-reaction systems

TL;DR

This paper develops an iterative algorithm for identifying point sources in non-linear advection-diffusion-reaction systems, improving accuracy through adaptive measurement strategies based on previous solutions.

Contribution

It extends existing linear source identification methods to non-linear systems by creating an iterative algorithm that accounts for non-linearity and enhances accuracy with adaptive measurements.

Findings

The proposed algorithm effectively identifies point sources in non-linear systems.

Adaptive measurement strategies improve source localization accuracy.

The method demonstrates robustness to non-linear reaction terms.

Abstract

We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of non-linear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the non-linearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements.