雙層正交Arnoldi 方法 解三維Drude 色散金屬光子晶體

Abstract

本篇論文主要討論Drude 色散金屬光子晶體的能帶結構。首先我們 透過Yee 格式將該問題進行離散化成一個三次特徵值問題並利用線性 化技巧將其改寫成一個等價的標準特徵值問題。其次，由於多項式特 徵值線性化後的特殊矩陣結構, 我們採用了雙層正交Arnoldi 方法進行 求解，用以達到減少記憶體的消耗。此外，為了提升雙層正交Arnoldi 方法的計算效能, 我們利用快速傅立葉轉換進行矩陣向量乘法, 並提出 合適的預處理降低迭代次數。經過設定不同參數的分析過後，我們發 現阻尼頻率會影響聚集，而電漿頻率會影響收斂速度。

In this thesis, we study the band structure of the Drude Dispersive Metallic Photonic Crystals. First, we discretize the problem to a cubic polynomial eigenvalue problem by Yee’s scheme , and rewrite a equivalent standard eigenvalue problem by linearized techniques. Next, due to the special matrix structure of linearized polynomial eigenvalue problem, we use the two-level orthogonalization Arnoldi (TOAR) method for solving the problem to reduce memory. Moreover, in order to enhance the computational performance of TOAR, we use the Fast Fourier Transform to implement matrix-vector multiplication, and choose a suitable preconditioner to reduce the numbers of iteration. After the analysis of setting different parameter, we discover the phenomenon that the damping frequency effect cluster and the plasma frequency effect speed of convergence.