An Angular Multigrid Preconditioner for the Radiation Transport Equation with Forward-Peaked Scatter

10/09/2020
by   Danny Lathouwers, et al.
0

In a previous paper (Lathouwers and Perkó, 2019) we have developed an efficient angular multigrid preconditioner for the Boltzmann transport equation with forward-peaked scatter modeled by the Fokker-Planck approximation. The discretization was based on a completely discontinuous Galerkin finite element scheme both for space and angle. The scheme was found to be highly effective on isotropically and anisotropically refined angular meshes. The purpose of this paper is to extend the method to non-Fokker-Planck models describing the forward scatter by general Legendre expansions. As smoother the standard source iteration is used whereas solution on the coarsest angular mesh is effected by a special sweep procedure that is able to solve this problem with highly anisotropic scatter using only a small number of iterations. An efficient scheme is obtained by lowering the scatter order in the multigrid preconditioner. A set of test problems is presented to illustrate the effectivity of the method, i.e. in less iterations than the single-mesh case and more importantly with reduced computational effort.

READ FULL TEXT
02/06/2020

Hybrid Solver for the Radiative Transport Equation Using Finite Volume and Discontinuous Galerkin

We propose a hybrid spatial discretization for the radiative transport e...
03/12/2021

A reduced basis method for radiative transfer equation

Linear kinetic transport equations play a critical role in optical tomog...
11/05/2019

Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects

Boltzmann transport problems often involve heavy streaming, where partic...
05/13/2020

Nonlinear Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry

This paper introduces a nonlinear acceleration technique that accelerate...
03/03/2021

Bound states of a quartic and sextic inverse-powerlaw potential for all angular momenta

We use the tridiagonal representation approach to solve the radial Schrö...
06/06/2019

Acceleration of Radiation Transport Solves Using Artificial Neural Networks

Discontinuous Finite Element Methods (DFEM) have been widely used for so...