邊界元素法在拉普拉斯方程反算問題之應用

Abstract

本研究係以「邊界元素法」來求解一給過定邊界條件之拉普拉斯方程問題。首先對於各種不同類型的邊界元素法，藉由影響係數矩陣中的條件數來了解在良態問題中矩陣之特性。進而推廣至拉普拉斯方程之反算問題，探討其影響係數矩陣的病態行為，且對於病態之反算問題提出結合「捨去奇異值分解法」及「L-曲線」之正規化方法來得到合理解。並以一數值算例來驗證本研究之正確性及可行性。In this paper, the Laplace problem with overspecified boundary conditions was investigated by using BEM. First, the condition numbers of the influence matrices for different BEMs were obtained. To understand the ill-posed behavior, the condition number of the influence matrices for the well-posed and ill-posed problems was examined for comparison. The reasonable solution of the inverse problem was obtained by employing the regularization technique of truncated SVD and L-curve. Numerical experiments for a circular case was performed.