We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of several length scales in problem geometry and material contrast. We discretize the partial differential equation model over the truncated domain using the finite element method and develop a multi-step contour integral eigensolver to compute the resonances. The eigensolver first locates eigenvalues using a spectral indicator and then computes eigenvalues by a subspace projection scheme. The proposed numerical method is robust and scalable, and does not require initial guess as the iteration methods. Numerical examples are presented to demonstrate its effectiveness.

翻译：本文研究具有色散介质和小狭缝孔的金属光栅结构共振的数值计算问题。由于问题几何结构存在多个长度尺度且材料具有对比性，底层特征值问题具有非线性特征，数学模型呈现多尺度特性。我们采用有限元法对截断域上的偏微分方程模型进行离散，并开发了多步等高线积分特征值求解器用于计算共振。该特征值求解器首先利用谱指示器定位特征值，随后通过子空间投影方案计算特征值。所提出的数值方法具有鲁棒性和可扩展性，且无需像迭代方法那样进行初始猜测。数值算例验证了该方法的有效性。