舰船静态电场微分递推换算法的泰勒展开优化

Taylor Expansion Optimization of Differential Recursive Algorithm for Static Electric Field of Ships

针对舰船静态电场的微分递推换算法在递推换算过程中误差不断积累这一问题,提出运用泰勒展开定理对其优化。推导出垂向二阶偏导数与水平二阶偏导数的关系,将其代入泰勒二阶展开后的递推公式,然后利用拉格朗日五点插值法,求得水平二阶偏导数,实现对递推公式的优化。对改进前与改进后的微分递推法的换算精度进行仿真比较,结果表明改进后的微分递推换算法的换算精度更高,说明了泰勒展开法对其进行精度优化可行。

In order to solve the problem of constant accumulation of errors in the recursive conversion algorithm for static electric field of ships,a Taylor expansion theorem was proposed to optimize the algorithm. The recursive formula of recursive conversion algorithm was put forward based on a second-order expansion of Taylor theorem,and the vertical second-order partial derivatives in the formula was converted to horizontal second-order partial derivatives which could be calculated by using the Lagrange five point interpolation method. In comparison of the improved recursive algorithm and the unimproved recursive algorithm,the simulation calculation was done,and result showed that the conversion accuracy of the improved recursive algorithm is higher than the unimproved one which showed the feasibility of the Taylor expansion method.