Solution of three-dimensional Helmholtz equation by multipole theory method

A new approach, the multipole theory (MT) method, is presented for computat ion of three-dimensional (3-D) Helmholtz wave equations. By the mathematica l deduction, the generalized MT formula and its applied laws are derived. I n order to check the accuracy of this method, the new approach has been app lied to computation of two resonant cavities with analytical solutions. Fur thermore, the MT method is applied to analysis of the resonant frequency of the reentrant cylindrical cavity which is widely employed in the design of microwave oscillators. Excellent agreement with results obtained by experi ment is demonstrated. It has been shown that the MT method is an effective approach for computation of 3-D Helmholtz wave equations.