# On the Numerical Solution of the Near Field Refractor Problem

## TL;DR

This paper introduces a numerical scheme for solving the near field refractor problem with arbitrary precision, proving finite termination and convergence based on Lipschitz estimates, with a broadly applicable algorithm.

## Contribution

It presents a novel numerical algorithm for the near field refractor problem, with proven finite termination and convergence, applicable in general settings.

## Key findings

- Algorithm terminates in finite steps
- Convergence relies on Lipschitz estimates
- Applicable to arbitrary precision solutions

## Abstract

A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving appropriate Lipschitz estimates for the refractor measure. The algorithm is presented in general terms and has independent interest.