Diffusion synthetic acceleration for arbitrary-order discontinuous finite elements on polygons

In this work, a diffusion synthetic acceleration (DSA) technique applied to the S_N transport equation is analyzed using discontinuous finite elements with arbitrary-order reduced-space Bernstein-Bezier basis functions on polygonal grids. The modified interior penalty (MIP) discretization is used yielding a symmetric positive definite (SPD) system which is efficiently solved using PCG and appropriate multigrid methods. Numerical results demonstrate a robust and stable scheme on unstructured polygonal grids. Comparative analysis is made against the modified four-step (M4S) method and MIP demonstrates stability when M4S diverges. (author)