Solution of two-dimensional Laplace equation by multipole theory method

A new approach, the multipole theory (MT) method, is presented for calculating two-dimensional (2-D) Laplace equation boundary-value problem. By the mathematical deduction, the generalized MT series formula and its applied laws are derived. The numerical analysis procedure and application of the MT method in electromagnetic engineering have been discussed. In order to verify the accuracy of this method, the MT method is applied to calculate the characteristic impedances of transmission lines of various cross-section configurations. The results obtained by the MT method are compared with exact data reported in the literature. It has been proven that the MT method is an effective approach for calculating 2-D Laplace equation boundary-value problems.