A Parallel First-Order Spherical Harmonics (P₁) Matrix-Free Method for Radiative Transport

Abstract

Radiative transfer in participating media is modeled using a first-order spherical harmonics (P 1 ), or its degenerate form, diffusion. The equations are discretized on an unstructured grid. The method uses a matrix-free algorithm employing an iterative solver from the Preconditioned Conjugate Gradient (PCG) solver package developed by Joubert and Carey [1]. The algorithm couples radiation transport and conduction, by casting them into a Picard iteration. Compared are solutions for two participating media problems indicating the method to be first-order accurate in time. Parallel scaling of the matrix-free method with use of in-situ preconditioners, symmetric successive overrelaxation (SSOR) and block Jacobi, are reported.