非理想导电光栅锥形衍射的有限元法与积分方程法
Finite element and integral equation methods to conical diffraction by imperfectly conducting gratings
AI总结：
针对非理想导电光栅的锥形衍射问题，研究变分法与积分方程法，证明了解的强椭圆性与唯一性，验证了带透明边界条件的有限元法收敛性，还讨论了边界积分方程法。
摘要：
本文研究了周期结构中由亥姆霍兹方程阻抗边值问题建模的非理想导电光栅锥形衍射问题的变分法与积分方程法。我们证明了对应变分公式的半双线性型的强椭圆性，并证明了任意频率下解的唯一性。验证了采用透明边界条件（Dirichlet-to-Neumann映射）的有限元法的收敛性，同时讨论了边界积分方程法。
英文摘要：
In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic structures. We justify the strong ellipticity of the sesquilinear form corresponding to the variational formulation and prove the uniqueness of solutions at any frequency. Convergence of the finite element method using the transparent boundary condition (Dirichlet-to-Neumann mapping) is verified. The boundary integral equation method is also discussed.
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