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对二维位场的向上延拓问题,在第一类边界条件下,通过等比延伸,将远边界取为无穷远。为了适应起伏地形,使用三角网格剖分,采用双线性插值方式,使用有限单元法求解。探讨泛函方程的推导、单元分析和对方程的求解。对比起伏地形下理论值和使用有限元的延拓解,曲线形态和值的大小基本吻合,证明了方法的正确性。
In the case of the upward extension of two-dimensional field, under the first kind of boundary conditions, the far boundary is taken as infinity through the same ratio extension. In order to adapt to the ups and downs of the terrain, triangulation using triangulation, using bilinear interpolation, the use of finite element method to solve. Exploring the derivation of functional equations, unit analysis and solving equations. Comparing the theoretical value under undulating topography with the extension solution using finite element method, the shape of the curve and the value of the curve basically agree with each other, which proves the correctness of the method.