臺灣博碩士論文加值系統

在本論文中，我們將以Legendre 擬譜補償法( pseudospectral penalty formulation) 建立格式，來求解定義在直角坐標中的Poisson 微分方程式之數值解，並使得數值解的L2 誤差值為最小。我們將這樣的計算方式撰寫成程式，並做數值實驗。由實驗結果得知的確與理論分析吻合，並且比傳統上使用強制性邊界條件(strongly enforced boundary condition) 的方式更能得到精確的數值解。此外，我們也將此方法與使用Chebyshev 擬譜補償式建立格式的方法作比較。

In this thesis, we present a scheme based on Legendre pseudospectral penalty formulation for solving Poisson equation’s numerical solution, and make the numerical solution of L2 error be minimized. We conducted this calculation to be programs, and executive numerical experiments. The result of experiments tallies with the theoretical analysis, and it is better accuracy than the traditional strongly enforced boundary condition. Moreover, we compared this method with the format by Chebyshev pseudospectral penalty formulation.

誌謝辭................................................. i
中文摘要.............................................. ii
Abstract............................................. iii
目錄.................................................. iv
圖表目次................................................ v
壹、簡介................................................ 1
貳、Poisson 邊界值問題與擬譜補償函數式的模型.............. 3
一、Poisson 方程式與其邊界條件........................... 3
二、誤差值最小化........................................ 4
參、將解法推廣至多維度.................................. 11
一、二維空間的Poisson 方程式與其邊界條件................. 11
二、數值上的驗證....................................... 13
肆、結論.............................................. 15
參考文獻.............................................. 16
附錄：補償參數值τ±之推導過程............................ 18

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