A strongly connected component-based block solver for accelerated multi-node flowing-fuel depletion calculations

Spatially resolved depletion calculations for circulating-fuel systems couple nuclide transmutation with inter-node transport and generate large sparse spatial–nuclide matrices. Repeated factorization of the complex shifted systems can therefore dominate the computational cost of the Chebyshev rational approximation method (CRAM). This study develops a direct block solver based on strongly connected component (SCC) decomposition and implements it in MACT. The off-diagonal graph of the global depletion matrix is decomposed into SCCs and topologically ordered, transforming each CRAM shifted system into block lower-triangular form. Because the pole-dependent shifts affect only the diagonal entries, the same graph structure can be reused for all CRAM poles. The resulting block-forward solution retains all transmutation and migration couplings and is algebraically equivalent to the monolithic solution in exact arithmetic. The method was assessed for powered-node fraction, spatial scale, flow rate, zero-power decay, and a source-term history derived from the Molten-Salt Reactor Experiment (MSRE) model. For burnup calculations, the solver speedup increased with spatial scale and reached 420.8 for the 30-node case, whereas zero-power decay showed more modest acceleration. In the 30-node MSRE-derived source-term history comprising nine burnup and 15 post-shutdown decay steps, the unmerged SCC solver (SCC-RAW) achieved a solver speedup of 318.7; the maximum relative error among the reported aggregate inventories was 2.41 × 10 −10 at decay step 14, and the maximum all-nuclide decay-heat error was 5.87 × 10 −7 at decay step 15. The remaining runtime was dominated by factorization of the largest SCC. The method therefore provides an efficient structure-preserving solver for coupled depletion and transport calculations, although further treatment of dominant SCCs is required for larger systems.