Analysis and improvements of the DPN acceleration technique for the method of characteristics in unstructured meshes

Algebraic preconditioners, renumbering techniques and a two-level algebraic multigrid method have been implemented to speed up the Krylov iterations of the DPN equations used for the acceleration of the method of characteristics in unstructured meshes. These algorithms were customized to take advantage of the cell-based structure of the DPN equations. Moreover, two techniques to speed up the solution of the multigroup eigenvalue MOC equations have been implemented. A solution of the multigroup eigenvalue DPN equation has been developed to provide a first guess for the external transport iterations. Next, a multigroup DPN acceleration method has been developed to accelerate the thermal iterations. This latter development has been particularly useful because our standard multigroup rebalancing acceleration was counterproductive in the presence of heavy absorbents. All these acceleration techniques have been incorporated in the spectral code APOLLO2. Numerical examples and comparisons are given for the 6-group eigenvalue Atrium benchmark problem. Our best calculation, an initialized ILU0-preconditioned DP1 scheme with thermal acceleration, was 7.7 times faster that the free iteration calculation, while the total number of transport iterations was divided by 17.