Diffusion Synthetic Acceleration of Discontinuous Finite Element Transport Iterations

The authors present a discretization of the diffusion equation that can be used to accelerate transport iterations when the transport equation is spatially differenced by a discontinuous finite element (DFE) method. That is, they present a prescription for diffusion synthetic acceleration of DFE transport iterations. (The well-known linear discontinuous and bilinear discontinuous schemes are examples of DFE transport differencings.) They demonstrate that the diffusion discretization can be obtained in any coordinate system on any grid. They show that the diffusion discretization is not strictly consistent with the transport discretization in the usual sense. Nevertheless, they find that it yields a scheme with unconditional stability and rapid convergence. Further, they find that as the optical thickness of spatial cells becomes large, the spectral radius of the iteration scheme approaches zero (i.e., instant convergence). They give analysis results for one- and two-dimensional Cartesian geometries and numerical results for one-dimensional Cartesian and spherical geometries.