发表机构
Universidad de Guanajuato（瓜纳华托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种物理感知超降阶框架，利用算子对逆介电张量的仿射依赖，通过POD与事件驱动采样分别加速固定几何和移动边界扫描中的算子组装，使组装成本降低一个数量级以上。
AI 中文摘要
光子波导设计通常需要在波长和几何参数上反复进行全矢量麦克斯韦本征模求解，其中介电界面处所需的亚像素平滑使得算子组装成为成本的重要组成部分。我们提出了一种物理感知的超降阶框架来加速这一组装过程。该方法利用了离散算子对局部采样的逆介电常数张量的精确仿射依赖性，并根据参数对界面单元的作用方式来选择其策略。我们展示了两种情形。在固定几何的波长扫描中，张量值在一组固定的单元上变化，采用本征正交分解结合矩阵离散经验插值方法，可以从少量快照中重构算子。在移动边界扫描中，界面信息在网格上重新定位，事件驱动的动态局部采样仅更新几何步骤变化所影响的系数，从而精确地重构完整的算子。这些结果表明，在不近似移动边界的情况下，算子组装可以减少一个数量级以上，从而将光子模式扫描的成本转移到本征求解器上。
英文摘要
Photonic waveguide design often requires repeated full-vector Maxwell eigenmode solves over wavelength and geometry, where the subpixel smoothing needed at dielectric interfaces makes operator assembly a substantial part of the cost. We present a physics-aware hyper-reduction framework for accelerating this assembly. The method exploits an exact affine dependence of the discrete operators on the locally sampled inverse-permittivity tensor, and chooses its strategy from how a parameter acts on the interface cells. We demonstrate two regimes. In wavelength sweeps at fixed geometry, tensor values change on a fixed set of cells, and proper orthogonal decomposition with matrix discrete empirical interpolation reproduces the operators from few snapshots. In moving-boundary sweeps, interface information relocates across the grid, and event-driven dynamic local sampling updates only the coefficients a geometric step changes, reproducing full assembly exactly. These results show that operator assembly can be reduced by more than an order of magnitude without approximating the moving boundary, shifting the cost of a photonic mode sweep to the eigensolver.
