AI 中文总结
本文提出基于离散外微积分的计算框架，将非线性光传播模拟速度提升100倍以上，保持谱级精度，可缩短大规模多尺度光子器件模拟的计算时间，适用于基孤子等多种光学场景。
AI 中文摘要
复杂光子结构中非线性光传播的高效模拟仍是一项重大挑战，因为这些系统兼具复杂的横向几何结构与跨越多个衍射长度的传播距离。现有数值方法常需要计算密集型的均匀离散化，或难以准确表征复杂材料边界，限制了多尺度非线性光子器件的实际模拟。本文提出一种求解非线性薛定谔方程的计算框架，与传统方法相比，模拟速度提升两个数量级以上（超过100倍），同时保持谱级精度，将求解大规模多尺度问题的计算时间从数天缩短至数小时。该方法基于离散外微积分，可直接在非结构化网格上实现贴合几何的离散化，无需传统有限元方法所需的弱形式。与基于傅里叶的谱求解器不同，它避免了全局过采样，消除了材料界面处的吉布斯型振荡，自然融入了吸收边界条件，并保留了基础微分算子的拓扑结构。该框架的一个关键特性是，高阶传播算子可通过算法从低阶离散算子生成，为将模拟扩展至标准非线性薛定谔方程之外提供了系统路径。对基孤子、非对称光束和光学涡旋的基准测试证实了其谱级精度，同时展示了超过100倍的计算加速比。
英文摘要
Efficient simulation of nonlinear light propagation in complex photonic structures remains a major challenge because these systems combine intricate transverse geometries with propagation over distances spanning many diffraction lengths. Existing numerical methods often require computationally intensive uniform discretizations or struggle to accurately represent complex material boundaries, limiting the practical simulation of multiscale nonlinear photonic devices. Here we introduce a computational framework for solving the nonlinear Schrödinger equation that accelerates simulations by more than two orders of magnitude (over 100x) compared with conventional approaches while maintaining spectral-level accuracy, thereby reducing the computational time required to solve large-scale and multiscale problems from days to hours. The method is based on discrete exterior calculus, enabling geometry-conforming discretization directly on unstructured meshes without the weak formulations required by conventional finite-element methods. In contrast to Fourier-based spectral solvers, it avoids global oversampling, eliminates Gibbs-type oscillations at material interfaces, naturally incorporates absorbing boundary conditions, and preserves the topological structure of the underlying differential operators. A key feature of the framework is that higher-order propagation operators are generated algorithmically from lower-order discrete operators, providing a systematic route to extending simulations beyond the standard nonlinear Schrödinger equation. Benchmarks on fundamental solitons, asymmetric beams, and optical vortices confirm spectral-level accuracy while demonstrating computational speedups exceeding 100x.
