A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient

Abstract

Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an accelerated Schwarz method for radiative transfer equations that makes use of approximate local solution maps constructed offline via a random sampling strategy. Numerical examples demonstrate the accuracy, robustness, and efficiency of the proposed approach.

Schwarz iteration method for elliptic equation with rough media based on random sampling

“…(Our approach in [6] approximates the range of the solution space instead.) This procedure was discussed in [7] for the case of the radiative transfer equation, where there are two scales both needing to be resolved. In this article, we target an elliptic homogenization problem.…”