Laplace方程复位函数半解析方法

为高效快捷地求解电磁场问题，将复位函数方法与半解析方法相结合，求解了二维静电场问题。引入复位函数，对广义多极技术、多极理论和新型等效源方法等几种不同的半解析方法进行了统一描述，简化了半解析解的表述方式，降低了计算量，而且为直接从边值问题出发寻找复位函数解答建立了一条新途径，并进行了数值算例验证。研究表明，复位函数半解析方法思路直观简捷，实施方便，计算量小；在相同计算量情况下，计算精确度明显优于其他各种数值方法。

A semi-analytical complex potential method for solving Laplace's equation

The complex potential function method is combined with the semi-analytical method to solve 2D Laplace problems. The semi-analytical method takes advantage of both the high efficiency of analytical techniques and the fldxibility of numerical methods. The complex potential function method is an effective method for solving 2D electric and magnetic field. However, its implementation is limited due to the difficulty in finding the complex function from the boundary value problem. The combination of the two methods not only simplifies the formula and the calculation of the semi-analytical method, but also gives a new way for finding the complex functions. Numerical examples verified the validity of the method.