A low-rank method for time-dependent transport calculations

Abstract

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing, compression, and regression. In this work, a dynamical low-rank approximation method is developed for the time-dependent radiation transport equation in slab geometry. Using a finite volume discretization in space and Legendre polynomials in angle we construct a system that evolves on a low-rank manifold via an operator splitting approach. We demonstrate that the lowrank solution gives better accuracy than solving the full rank equations given the same amount of memory.