2024/09/23 by Carmen Scalone, Lukas Einkemmer, Scalone, C. +5 · 2 citations
Engineering · Materials Science · Physics and Astronomy · #FOS: Mathematics #Nuclear Materials and Properties #Nuclear Physics and Applications #Nuclear reactor physics and engineering #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2409.14938
openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work of Kusch, Whewell, McClarren and Frank \citeKWMF showed that performing a low-rank approximation can be very effective in reducing the high memory requirement and computational cost of such problems. In this work, we propose a rank adaptive approach that changes the rank during the inverse power iteration. This allows us to progressively increase the rank (i.e. changing the fidelity of the model) as we get closer to convergence, thereby further reducing computational cost. We then exploit this multi-fidelity approach to optimize a simplified nuclear reactor. In this case the system is parameterized and the values of the parameters that give criticality are sought.