A FEM domain decomposition method for photonic and electromagnetic band gap structures
A FEM domain decomposition method for photonic and electromagnetic band gap structures
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DOI：
10.1109/tap.2005.863095
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发表时间：
2006-02
影响因子：
5.7
通讯作者：
M. Vouvakis;Zoltan Cendes;Jin-Fa Lee
中科院分区：
文献类型：
--
作者：
M. Vouvakis;Zoltan Cendes;Jin-Fa Lee
本文引入了一种有效的域分解算法，用于在三维，有限大小的光子带隙和电磁条带隙结构中产生的时间谐波电磁场的解决方案。该方法基于有限元近似和非重叠域分解方法。已明确引入了一组“水泥”界面界面上的“水泥”未知数，以实施适当的场连续性。这些额外的未知数的引入允许跨域的不合格/不匹配三角剖分，从而消除了对周期性网格的需求。为了确保和改善外迭代回路的收敛性，可使用罗宾传输条件来跨接口传达信息。通过快速算法求解所得的方程系统，该算法松散地类似于众所周知的有限元撕裂和互连算法。在此算法中，该方法在预处理步骤中为Robin Primal子域问题多次求解，一次激发一个双重未知。此步骤生成一个迭代矩阵，然后将其用于更新外环迭代中的双重未知数。对于几何重复的问题，例如光子和电磁带隙结构，目前的方法变得极为有效。
This paper introduces an efficient domain decomposition algorithm for the solution of time-harmonic electromagnetic fields arising in three dimensional, finite-size photonic band gap and electromagnetic band gap structures. The method is based on the finite element approximation and a nonoverlapping domain decomposition method. A set of "cement" unknowns on the inter-domain interfaces has been explicitly introduced to enforce the appropriate field continuities. The introduction of these extra unknowns allows for nonconforming/nonmatching triangulations across domain, eliminating the need for periodic mesh. To ensure and improve the convergence of the outer iteration loop, Robin transmission condition is used to communicate information across interfaces. The resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm. In this algorithm, the method solves, in the preprocessing step, for the Robin primal subdomain problems multiple times, by exciting one dual unknown at a time. This step generates an iteration matrix that is then used to update the dual unknowns in the outer-loop iteration. The present method becomes extremely efficient for problems with geometric repetitions, such as, photonic and electromagnetic band gap structures.