Nested Acceleration Algorithm for Self-Adjoint Angular FILU

The second-order, self-adjoint angular flux (SAAF) equation,l modified to include continuous slowing down (CSD), was recently used for coupled electron-photon transport .2 Results using the standard discrete ordinates approach with linear continuous (LC) spatial finite elements, diamond difference (DD) in energy and DSA source iteration acceleration, generally compared very favorably against the first-order form of the transport equation.2 However, DD in energy discretization of the CSD operator dld not always yield stable, positive solutions for energy spectra and charge deposition, particularly for monoenergetic incident electrons. Here we investigate the numerical solution of the SAAF equation using a higher order, linear discontinuous (LD) discretization in energy with particular emphasis on jointly accelerating the source iteration and within group upscatter introduced by the LD discretization. The angular flux in energy group g is expressed as V.(Z, ~) = ~&(z)+ *(E –~g)~;,g(~), where W,g (z) is the average and W& (z) the slope angular flux. Applying the Galerkin procedure in energy, the SAAF equation reduces to the following coupled equations