The transmutation trajectory analysis (TTA) method is a traditional analytic depletion calculation algorithm. It’s capable of providing very accurate solutions with cutoff value being sufficiently small, but the main drawback is expensive time consumption. In this paper, the depletion problem was rephrased as a directed-graph module with additional properties attributed to vertices and edges. Based on this model a new approach for TTA implementation was conducted, to which dynamic programming technique could be introduced easily. Besides it, a new analytic algorithm is proposed based on the above model, which gives each nuclide a time dependent concentration function instead of a scalar value that other algorithms could only offer. One of the advantages brought by this algorithm is making time integration value calculations straightforward. Both of these two approaches are programmed. The resulting TTA code was proved to be very efficient, the running time for a typical ORIGEN2 problem with cutoff equals to 10−15 could be of the same magnitude with time spent on library reading process. The codes are analyzed in terms of time and space complexities, which could offer a theoretical point of view on their behaves.

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