Volume 15, pp. 132-151, 2003.
A multigrid algorithm for solving the multi-group, anisotropic scattering Boltzmann equation using first-order system least-squares methodology
B. Chang and B. Lee
Abstract
This paper describes a multilevel algorithm for
solving the multi-group, anisotropic scattering Boltzmann equation
formulated with a first-order system least-squares methodology. A
finite element discretization is used. The resulting angle
discretization of this approach does not exhibit the
so-called “ray effects,” but this discretization leads to a
large coupled system of partial differential equations for the
spatial coefficients, and, on scaling the system to achieve better
approximation, the system coupling depends strongly on the
material parameters. Away from the thick, low absorptive regime, a
relatively robust multigrid algorithm for solving these spatial
systems will be described. For the thick, low absorptive regime,
where an incompressible elasticity-like equation appears, an
additive/multiplicative Schwarz smoother gives substantial
multigrid improvement over standard nodal smoothers. Rather than
using higher-order or Raviart-Thomas finite element spaces, which
lead to complicated implementation, only low-order, conforming
finite elements are used. Numerical examples illustrating almost
independent convergence rates and locking-free discretization
accuracy will be given.
Full Text (PDF) [201 KB],
BibTeX
Key words
Boltzmann transport equation, first-order system least-squares, multigrid method.
AMS subject classifications
65N30, 65N55, 65N15.
Links to the cited ETNA articles
