# Real-time reconstruction of moving point/dipole wave sources from boundary measurements

## TL;DR

This paper presents a real-time method to reconstruct multiple moving wave sources' locations and strengths from boundary measurements, using algebraic relations and reciprocity gap functionals, with demonstrated numerical effectiveness.

## Contribution

It introduces a novel real-time reconstruction approach for unknown moving wave sources based on algebraic relations and reciprocity gap functionals.

## Key findings

- Successful numerical experiments validate the reconstruction method.
- Effective real-time reconstruction of source parameters from boundary data.
- Method handles multiple moving sources with unknown number and properties.

## Abstract

This paper is concerned with a reconstruction method for multiple moving point/dipole wave sources. We assume that the number, locations, and magnitudes/moments of wave sources are unknown, and consider the problem to reconstruct these parameters from the measurement of the wave field on the boundary. For this problem, we derive algebraic relations between the parameters of wave sources and the reciprocity gap functionals, and propose a real-time reconstruction procedure based on these relations. We perform some numerical experiments, and show the effectiveness of our reconstruction procedure.