Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations

Abstract

In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain, which means that, for a given accuracy, we can often use a smaller overall rank compared to classic dynamical low-rank methods. In particular, we can solve problems with point sources efficiently, that for classic algorithms require almost full rank. Our algorithm only transfers boundary data between subdomains and is thus very attractive for distributed memory parallelization, where classic dynamical low-rank algorithms suffer from global data dependency. We demonstrate the efficiency of our algorithm by a number of challenging test examples that have both very optical thin and thick regions.