2508.06302
Parallelized computation of quasi-periodic solutions for finite element problems: A Fourier series expansion-based shooting method
Junqing Wu, Ling Hong, Mingwu Li, Jun Jiang
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s derivation of the FSE‑Shooting NAEs from the coupling boundary condition uses the same Fourier basis rotation identity as the model’s solution, and the special case d=1 as well as the phase conditions PC_i are handled in essentially the same way. The model adds minor clarifications (two-way equivalence and an abstract monodromy view of the Jacobian) that are consistent with the paper’s formulas.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The derivations are sound and practically motivated. The explicit NAE formulation, combined with parallel trajectory computation and clear phase conditions, offers a compelling approach for high-dimensional quasi-periodic responses. Minor clarifications (explicit iff statements, monodromy intuition) would further strengthen readability, but the core mathematics appears correct and well-justified.