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本文用数学中的无穷序列逼近方法(微扰理论)将变系数及非线性偏微分方程(地下水流控制方程)分解化为一系列常系数线性偏微分方程,这一系列方程与其相应的初边值条件构成的定解问题用边界元法很容易求得其解,最后通过这一系列解的回代合成即可求得原渗流问题的终解。此方法使传统的边界元法解非均质或无压地下水流问题有了新的进展。
In this paper, we use the infinite sequence approximation method (perturbation theory) in mathematics to decompose variable coefficients and nonlinear partial differential equations (groundwater flow control equations) into a series of constant coefficient linear partial differential equations. This series of equations and its corresponding primary edge The solution to the definite solution of the value condition is easily solved by the boundary element method. Finally, the final solution of the original seepage problem can be obtained through the synthesis of the series of solutions. This method has made new progress in solving the problem of non-homogeneous or non-pressure groundwater flow by the traditional boundary element method.