在傳統的工程問題上，求解邊界積分式時，會遇到源點與場點重合所產生的奇異性問題，而在方程式係數矩陣的對角線項產生誤差。一般要解決這個問題都必須用到複雜的方程式及數學推導，使得程式設計的過程非常繁瑣。
本文提出奇異項重建法， 在振動體內部任意取兩個簡單點聲源，以該聲源所產生的邊界上聲壓與速度的理論值，作為方程式的已知值，得到兩組聯立方程式，逆算產生方程式中對角線奇異項的係數，完成方程式的係數矩陣，用以計算所要分析的未知聲場。本文以二維聲波場的放射與散射為實例，邊界上使用三節點二次式等參元素，所得到的數值解與解析解相比較均極為準確，證實此方法用在聲學問題上，為一有效且可靠的數值方法。

The purpose of this study is to handle the well-known singularity problems of Boundary Integral Equation. This study presents the application of singularity-term reconstruction method. By using known vibrating boundary conditions, which are gotten by setting two simple point sources in the vibration body, we get the singularity-terms without using complicated formulations. The two-dimensional acoustic radiation and scattering problems were tested. The three-noded curvilinear elements were adopted. The numerical results are very accurate compared to analytical solutions. It is proved that this method is an efficient and reliable numerical method in handling the acoustic problems.

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