各向异性介质波导不连续问题的半解析谱单元法分析

Analysis of Waveguide Discontinuities with Anisotropic Dielectric by Semi-analytical Spectral Element Method

将谱单元法与精细积分法相结合求解各向异性介质的波导不连续问题.从矢量波动方程的单变量变分形式出发,采用基于Gauss-Lobatto-Legendre多项式零点作为插值结点的谱单元,对含有各向异性介质波导的横截面进行离散,然后将问题导入哈密顿体系利用精细积分法进行求解.由于采用了谱单元法,在单元网格数较少时,可获得高准确度的计算结果;又由于利用了精细积分法,结构的纵向长度可以任意设定,克服了当人工边界设置在离介质块较远处时,计算量不断增加的缺点.研究表明半解析谱单元法可有效地应用于各向异性介质的波导不连续问题,在提高准确度的同时可大量节省计算时间.

The spectral element combined with precise integration method was used to simulate and analyze the waveguide discontinuities with anisotropic dielectric.With the variational principle based on single variable corresponding to the vector wave equation,spectral elements,a special type of higher order finite element with sampling points defined as the Gauss-Lobatto-Legendre points,were employed to discretize the cross section of the waveguide structure,which contains anisotropic dielectric.Then the semidiscretized problem was cast into Hamilton system and sloved by the precision integration method.With adopting the spectral elements,high precision of calculation results can be obtained under the low number of unit grids;With the precise integration method,the longitudinal length of structure can be set arbitrarily.It can overcome the weakness of increasing computation amounts as lengthening the distance from artificial boundary to dielectric block.Results show that semi-analytical spectral element method can be used to effectively solve waveguide discontinuities problems,which contains anisotropic dielectric.The proposed methords is demanstrated to solve waveguide discontinuities problems with high computational accuracy and efficiency.