边界单元法及其在位势问题近似解法中的应用

本文研究了边界单元法的理论及其在解位势问题中的应用。边界单元法从控制微分方程和边界条件出发,利用加权剩余法,建立积分方程,对边界进行剖分,得到在结点处位势所满足的线性代数方程组。文中提出了二维位势问题的常数元和线性元解法。边界单元法降低了求解空间的维数,减少了离散线性方程组的阶数,输入数据比较少,而工作效率高。

The Boundary Element Method and Its Application to Approximate Solution in Potential Problems

In this paper, we establish the theory for boundary element method and its application in potential problems. The boundary element method starts from the control equation and boundary value conditions, sets boundary integral equations with weighte residual method, splits the boundary into elements and obtains the linear algebraic equations .In this paper, the boundary element method of constant and linear element for potential problems in 2-dimensional space is discussed. This method reduces the number of space dimension, makes the equation system lower order, less data input and higher efficiency .