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PreprintCC BY 4.0arXiv

Monte Carlo Power Iteration Algorithms: Convergence, Analysis and Application to Reactor Criticality Calculations

  • Alexander M. G. Cox
  • Tom Davis
  • Julian Hofstadler
  • Andreas E. Kyprianou
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Abstract

We study Monte Carlo power iteration algorithms in the context of reactor criticality simulations. Under mild conditions on the underlying physical system and the algorithmic structure, we derive explicit error bounds, which are to the best of our knowledge the first rigorous results for such methods which are ubiquitous in nuclear engineering. This is done by exploiting connections to Sequential Monte Carlo algorithms, and extending recent developments about stochastic neutron transport. We demonstrate the applicability of our results by considering a concrete version of the Monte Carlo power iteration algorithm as well as variance reduction schemes.

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Cite

BibTeXRIS
BibTeX
@misc{cox2026monte,
  title = {{Monte Carlo Power Iteration Algorithms: Convergence, Analysis and Application to Reactor Criticality Calculations}},
  author = {Alexander M. G. Cox and Tom Davis and Julian Hofstadler and Andreas E. Kyprianou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36266},
  eprint = {2610.36266},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36266},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Monte Carlo Power Iteration Algorithms: Convergence, Analysis and Application to Reactor Criticality Calculations
AU  - Alexander M. G. Cox
AU  - Tom Davis
AU  - Julian Hofstadler
AU  - Andreas E. Kyprianou
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.36266
UR  - https://arxiv.org/abs/2610.36266
AB  - We study Monte Carlo power iteration algorithms in the context of reactor criticality simulations. Under mild conditions on the underlying physical system and the algorithmic structure, we derive explicit error bounds, which are to the best of our knowledge the first rigorous results for such methods which are ubiquitous in nuclear engineering. This is done by exploiting connections to Sequential Monte Carlo algorithms, and extending recent developments about stochastic neutron transport. We demonstrate the applicability of our results by considering a concrete version of the Monte Carlo power iteration algorithm as well as variance reduction schemes.
ER  -