中文摘要：

针对电磁场分析中有限元法适应能力强，但计算量大，效率低，而解析法计算量小，但适用范围窄的各自优缺点，将有限元方法与解析方法相结合，提出了一种分域展开的半解析方法用以求解工程电磁场问题。依据龙格定理，把复杂的求解场域分割为若干形状简单的子域，在每个子域内利用本征函数构造半解析展开式逼近方程的解，然后通过子域拼接得到整个场域的解。展开式系数用配点法确定。由于采用解析展开式，逼近效率高，减少了未知数个数；同时由于是局域逼近，具有解函数形式简单，计算量小，矩阵是稀疏的，条件数小，易于求解，实施方便等优点。以二维Laplace问题为研究对象，数值算例验证了方法的有效性，表明该方法花费时间短，计算精确度高。

英文摘要：

In order to calculate the engineering electromagnetic problems, a new semi-analytical method, sub-region expansion method （SEM） is presented, which takes advantages of both the analytical methods and numerical methods. The basic idea is： firstly, the entire solving domain is divided into simple shaped sub-regions, and in each sub-region a semi-analytical expansion is used to approximate the solution; then all these sub-region expansions are jointed together by the continuity conditions ; and finally the coefficients of all expansions are determined by using point-matching technique （PMT）. This scheme can overcome some shortcomings of the conventional semi-analytical methods based on the entire-domain-bases, and has a lot of important advantages： the expansion expression is simple and the calculation is reduced; the system matrix is sparse, with a smaller conditioning number, easily to be solved; and lastly the method is easily for implementation. Numerical examples are given to verify the validity of the method.