Fully consistent, linear discontinuous diffusion synthetic acceleration on 3D unstructured meshes

We extend a multi-level preconditioned solution method for a linear discontinuous discretization of the P{sub 1} equations in two-dimensional Cartesian geometry to three-dimensional, unstructured tetrahedral meshes. A diffusion synthetic acceleration (DSA) method based on these P{sub 1} equations is applied to linear discontinuous S{sub N} transport source iterations on tetrahedral meshes. It is a fully consistent method because the P{sub 1} equations and the transport equation are both discretized with a linear discontinuous finite element basis. Fourier analyses and computational results show the DSA scheme is stable and very effective. We compare the fully consistent scheme to other 'partially consistent' DSA methods.