麦克斯韦方程组的前向模微分
Forward-Mode Differentiation of Maxwell's Equations
摘要：
我们提出了一个以前未探索的麦克斯韦方程组的前向模式微分法，在灵敏度分析领域的应用。这种方法产生精确的梯度，是类似于流行的伴随变量方法，但提供了一个显着的改善，在内存和速度缩放的问题，涉及几个输出参数，因为我们分析的背景下，时域有限差分（FDTD）模拟。此外，它提供了一个精确的替代数值导数方法，基于有限差分近似。为了证明该方法的实用性，我们进行了两个问题的敏感性分析。首先，我们计算了散射体的空间近场强度分布随其介电常数的变化。然后，我们计算了表面光栅耦合器的光谱功率和耦合效率随其填充因子的变化。
英文摘要：
We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as we analyze in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical derivative methods, based on finite-difference approximations. To demonstrate the usefulness of the method, we perform sensitivity analysis of two problems. First we compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielectric constant. Then, we compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
