基於積分方程電磁場解答器的適應性網格生成和細分

Abstract

利用力差法（method of moments，簡稱MOM）解電場積分方程式（electric field integral equation，簡稱EFIE）時，取樣網格的分佈對解的準確性有極大的影響。網格的分佈往往需要先經過人為的調整，才可能得到較準確的解。有鑑於此，本論文提出一個適應性網格細分的演算法，結合將網格元素分解形成更小的單元（h-refinement）以及移動節點的位置（r-refinement）兩種網格細分的方法，使網格分佈能適應電場積分方程式的解。利用divid-and-conquer方法對欲模擬的結構產生均勻分佈的Delaunay三角形網格，並依據力差法解得的結構表面電流分佈細分網格，以上適應性網格細分的過程不斷重複進行，直到電流解收斂或達到使用者或程式預設的停止細分條件（如最小邊長或最大網格細分次數等）。為了加速網格細分的過程，此論文亦嘗試忽略力差法矩陣方程式中的遠交互作用來解力差法矩陣方程式。以上自動網格細分的方法亦應用在許多電磁模擬的分析的例子，如接近帶電流導線的導體平面，以及金屬導線散射平面波。

When the method of moments (MOM) is applied to solve the electric field integral equation (EFIE) for electromagnetic radiation and scattering problems, the accuracy of solutions greatly depends on a proper discretization of the simulated domain. Most of time, the grid distribution needs to be manually tuned for getting an accurate solution. In this thesis, we propose a mesh refinement algorithm that adapts meshes to EFIE solutions by splitting elements (h-refinement) and relocating nodes (r-refinement). Using a divide-and-conquer Delaunay triangulation, an initial mesh is generated with equally spaced seeds on the surfaces of the simulated structure. Then the mesh is iteratively refined according the current distribution on the surface. The refinement process automatically terminates when the current distribution converges or when preset criteria, such as the smallest edge length and the maximum pass of refinement, are met. In order to expedite the iterative refinement process, the current is calculated only by the near-interaction terms of the MOM impedance matrix. The adaptive mesh refinement algorithm is further applied to solve radiation and scattering from metallic structures.