2009-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/698347摘要：在這個計劃中，我們將利用NFJD可以快速求解Maxwell算子之特徵值的特性，並結合等位面方法來研究光子晶體在三維立方晶格上的優化問題。先從一個初始的結構開始，介電材料的分布將由一個等位面函數決定，同時設定一個代表能隙的目標函數。我們提出一個變分方法，使目標函數能夠優化。一旦 NFJD找出某一材料結構的能隙，就可以利用這個使目標函數優化的變分公式，決定等位面函數的改變量。等位面函數改變之後，材料的幾何結構亦隨之改變，即可再利用NFJD算出新結構的能隙。如此迭代以找到具有更大能隙的材料結構。在此計劃中，我們將提出數值模擬的結果，以驗證我們所提的變分算法。<br> Abstract: We will use Null-space Free Jacobi-Davidson algorithm and the level set method to investigate the band-gap optimization problem of the 3D photonic crystal. The permittivity structure of the photonic crystal will be initilized by setting up a level set function, and the band-gap will be presented by an objective function. We propose a variational formula to maximize the objective function. After NFJD computing the band-gap of a given structure, the variation formula will determine a new distribution of the level set function, and hence, getting a new structure of the photonic crystal. Using this iteration process, one can optimize the band-gap of the 3D photonic crystal. We will exame this algorithm by practicing numerical simulation.光子晶體結構最佳化變分法快速特徵值算法Photonic crystalstructure optimizationvariational methodfast eigensolver