# Numerical non-LTE 3D radiative transfer using a multigrid method

## TL;DR

This paper introduces a multigrid method to significantly accelerate 3D non-LTE radiative transfer calculations, outperforming the traditional MALI approach in computational efficiency.

## Contribution

The authors develop and implement a non-linear multigrid scheme within the existing radiative transfer code, achieving faster solutions for complex 3D non-LTE problems.

## Key findings

- Multigrid method achieves 3.3-4.5 times speedup over MALI.
- Full-multigrid increases speed-up to a factor of 6.
- Method is effective on realistic 3D radiative-MHD simulation atmospheres.

## Abstract

3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as $\mathcal{O}(n^2)$, with $n$ the number of grid points. When the grid gets finer, the computational cost increases quadratically. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative-MHD simulations as input atmospheres. With multigrid, we obtain a factor 3.3-4.5 speedup compared to MALI. With full-multigrid the speed-up increases to a factor 6. The speedup is expected to increase for input atmospheres with more grid points and finer grid spacing. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial speed-up.