Two-Level Transport Methods with Independent Discretization

Abstract

In this paper, we present two-level nonlinear iteration methods for the transport equation in 1D slab geometry approximated by means of the linear discontinuous finite element method (LDFEM). We develop transport schemes based on the quasidiffusion (QD) method in which the low-order QD (LOQD) equations are discretized by the linear continuous finite element method (LCFEM). This requires a mapping of the LCFEM low-order solution to the LDFEM high-order solution to define the scattering term. Several mappings are proposed and analyzed. Another proposed transport discretization scheme is based on the step characteristics for the transport equation and LCFEM for the LOQD equations. We also develop new nonlinear synthetic acceleration (NSA) methods based on the LCFEM discretization of the QD equation. To gain iterative stability, the NSA algorithms are combined with the nonlinear Krylov acceleration method. We present numerical results that demonstrate performance and basic properties of the proposed discretization schemes and iterative solution methods.

Keywords:

• Particle transport equation
• radiative transfer equation
• iteration methods
• finite element methods
• quasidiffusion method
• variable Eddington factor