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.

中文翻译：

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计算亚波长孔金属光栅结构共振的有限元轮廓积分法


我们考虑具有色散介质和小狭缝孔的金属光栅结构的共振的数值计算。由于问题几何和材料对比中存在多个长度尺度，潜在的特征值问题是非线性的，并且数学模型是多尺度的。我们使用有限元方法在截断域上离散化偏微分方程模型，并开发了多步轮廓积分本征求解器来计算共振。特征求解器首先使用光谱指示器定位特征值，然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，并且不需要像迭代方法那样进行初始猜测。数值例子证明了其有效性。