An Improved Jacobi-Davidson Method for the Computation of Selected Eigenmodes in Waveguide Cross Sections
An Improved Jacobi-Davidson Method for the Computation of Selected Eigenmodes in Waveguide Cross Sections
复制标题
计算波导横截面中选定本征模的改进雅可比-戴维森方法
DOI：
10.1109/tmag.2010.2046315
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发表时间：
2010
影响因子：
2.1
通讯作者：
R. Schuhmann
中科院分区：
文献类型：
--
作者：
B. Bandlow;D. Sievers;R. Schuhmann
开式结构的数值模拟需要截断计算区域和定义适当的边界条件。然而，在有限距离处的任何人工边界都会在波导的本征分析中引起额外的不需要的模式，这些模式必须从计算的频谱中排除。通过引入特殊的加权函数，我们提出了对Jacobi-Davidson方法的扩展，该函数能够可靠地抑制在求解过程中已经存在的不需要的本征模。此外，该方法还可以大大减少迭代步数和计算时间。通过对光子晶体光纤中本征模的有限积分离散化计算，证明了本征模计算效率的提高。
Numerical simulation of open structures requires the truncation of the computational domain and the definition of appropriate boundary conditions. However, any artificial boundary at finite distances causes additional undesired modes in the eigenanalysis of waveguides which must be excluded from the computed spectrum. We propose an extension of the Jacobi-Davidson method by introducing a special weighting function that enables a reliable suppression of undesired eigenmodes already during the solution process. Moreover, the number of iteration steps as well as the computation time can be drastically reduced by this process. We show the improvement of efficiency by means of an eigenmode computation in a photonic crystal fiber discretized by the finite integration technique.