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油田区域性外加电流阴极保护系统可视作性定电流场，区域内的电位分布遵守Poisson方程．利用边界元素法求得Poisson方程及其边值条件的数值解，同时利用牛顿法和梯度法相结合的方法求解大型非线性方程组，在系统阳极位置的寻优过程中应用可变误差多面体算法解决了带约束条件的多元非线性隐含目标函数的寻优问题．本文对油田区域性外加电流阴极保护系统计算机辅助优化设计中的数学模型及其求解进行了探索性研究，并得到了实验验证．
The field impressed current cathodic protection system can be regarded as the constant current field, and the potential distribution in the area obeys the Poisson equation. The boundary element method is used to solve the Poisson equation and the numerical solution of its boundary conditions. At the same time, the method of combining Newton method with gradient method is used to solve large nonlinear equations. The variable error polyhedron algorithm is used in the optimization of the anode position of the system The Optimization Problem of Multivariate Nonlinear Implicit Objective Function with Constraints. In this paper, the mathematic model and its solution in the computer-aided optimization design of the regional impressed current cathodic protection system are explored and verified by experiments.