Eigenmode analysis of arbitrarily shaped two-dimensional cavities by the method of point-matching

In the proposed method, as in the boundary element method (BEM), a field problem is solved on its boundary along which nodes are distributed. The distinct feature of the proposed method is related to the fact that no interpolation functions between the nodes are required, so that the basic collocation method is employed to satisfy a given boundary condition. This approach reduces a large amount of numerical calculation induced due to the interpolation functions. Unlike the method of auxiliary sources (MAS), in the proposed method only the regular functions that have finite functional values everywhere including the origins are employed as basis functions. As a result, the proposed method does not need the auxiliary surface, the construction of which is a troublesome work because its form, dimension, shifting, etc. strongly influence the accuracy of the MAS. The eigenvalues calculated by the proposed method rapidly converge to the exact values thanks to the simplicity of the method. Moreover, the method gives mode shapes successfully without using the interpolation functions between the nodes. The efficiency and accuracy of the method are verified through several applications.