Solution of three-dimensional Laplace equation by multipole theory method

A new approach, the multipole theory (MT) method, is presented for calculating three-dimensional (3-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 presented. The MT method is tested for accuracy by comparing the numerically calculated the capacitances against those analytically obtained for various electrostatic systems associated with 3-D Laplace equation. The results obtained by the MT method are also compared with the exact data reported in the literature. It has been proven that the MT method is an effective approach for calculating 3-D Laplace equation boundary-value problems.