Krylov Subspace Methods with Energy Block Gauss-Seidel Preconditioners for Accelerating Multigroup Coupled Discrete Ordinates Transport Calculation on Tetrahedral Meshes

Abstract

The block Gauss-Seidel preconditioners in energy groups have been suggested in this work to accelerate multigroup coupled transport calculations with linear discontinuous expansion method with subcell balance (LDEM-SCB) on tetrahedral meshes. As the block preconditioner, two types of preconditioner were proposed: lower triangle block (Ltri) and Diagonal within-group block (Diag) having no upscattering blocks. Two Krylov subspace methods (i.e., BiCGSTAB and restarted GMRES) were newly implemented in the STRAUM (SN Transport for Radiation Analysis with Unstructured Meshes) code, and its convergence performance with the proposed multigroup preconditioners have been analyzed based on the diffusion synthetic acceleration (DSA) and transport synthetic acceleration (TSA) methods. In this study, a MATXS-formatted cross section processing code (MATXS-based XS Processor for SN Transport, MATXST) was also developed for generating neutron-gamma coupled multigroup cross sections for STRAUM. The MATXST code reads MATXS-formatted cross section files and generates multigroup cross sections for the STRAUM code using the transport corrections and the Bondarenko iteration for self-shielding effect. The coupled calculation of STRAUM and MATXST was applied to a simplified reactor shielding problem and the results were compared with the MCNP6 calculation results for numerical validation, which showed good agreements between the fluxes estimated with STRAUM and MCNP6. To analyze the performances of the Krylov subspace methods with and without the proposed preconditioners, the numerical tests were performed on three problems from a simple 3D shielding problem to one realistic 3D reactor shielding problem containing the pressure vessel and concrete shield. From the numerical tests, it was shown that the BiCGSTAB and GMRES(m) methods were very effective for most groups, and the DSA preconditioning for the Richardson, BiCGSTAB, and GMRES(m) methods improves significantly the convergences and reduces computing time in comparison with the conventional Richardson method for the within-group source iteration. In particular, BiCGSTAB showed better speedups than GMRES(m) irrespective of the preconditioners, and the TSA preconditioner was much less effective than the DSA one for all the cases. It was noted that the TSA preconditioner does not give any computing time saving for the within-group source iteration for the cases taking a large computing time portion in TSA calculation. For the energy group chunk having upscattering, the GMRES(30) and BiCGSTAB methods with the suggested block preconditioners were very effective in reducing the number of iterations and computing time compared with the Richardson iteration. For example, the BiCGSTAB and GMRES(30) methods with LtriDSA preconditioner for the last group chunk having upscattering reduced the computing time by the factors of 21.3 and 16.4, respectively in comparison with the Richardson iteration for the realistic 3D reactor shielding problem.