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

Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University Centre, 106 91 Stockholm, Sweden
e-mail: johan.bjorgen@astro.su.se

Received: 13 December 2016
Accepted: 4 January 2017

Abstract

Context. 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 the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as O(n²), with n the number of grid points. When the grid becomes finer, the computational cost increases quadratically.

Aims. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI.

Methods. 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 magnetohydrodynamics (MHD) simulations as input atmospheres.

Results. With multigrid, we obtain a factor 3.3–4.5 speed-up compared to MALI. With full-multigrid, the speed-up increases to a factor 6. The speed-up is expected to increase for input atmospheres with more grid points and finer grid spacing.

Conclusions. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial increase in speed.