這篇論文中，我們使用邊界近似法去解決一個圓上徑向裂縫的問題。假設在一個單位圓上，直線裂缝從圓的邊緣裂向圓心。工程上利用電極的發射與接收，可以測出電極與裂縫的角度。我們寫出這個問題的數學模型，並且利用邊界近似法去計算這模型在各種不同的角度下的數值。最後再利用這些數值結果，反過來決定裂縫的位置。

This thesis uses the boundary approximation method to solve a crack problem. On a unit circle, assume there is a crack along the radial direction and extended to the edge. In engineering we can use current electrodes to detect the angle between the crack and electrodes. We first write down the mathematical model for this problem. Then use the boundary approximation method to compute its numerical solutions under different angles. Finally we try to use these different numerical results to probe the position of the crack.

1 Introduction . . . . . . . . . . . . . . . . . 2
2 Laplace Solutions . . . . . . . . . . . . . . .3
3 Crack Problem . . . . . . . . . . . . . . . . 6
4 Boundary ApproximationMethod . . .. . . . . . 13
5 Numerical Results . . . . . . . . . . . . . 19

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