A subregion expansion method for Laplace's equation

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.