General transfer matrix method for the multi-material junction and wedge problems

Abstract

A general transfer matrix method (GTMM) is developed to derive the characteristic equation for the multi-material junction and wedge problems. Using complex variable techniques, the boundary conditions can be represented by a matrix equation. The matrix itself can be simplified to be a square matrix of order 4, for both the junction and wedge problems. In the case of a uniform temperature field, non-homogeneous terms occur on the interface of different kinds of materials. Including the logarithmic terms of potential for temperature, the GTMM can also be applied in this case. Since the derivation of the method involves only a matrix of order 4 or less, the GTMM is much more convenient in the implementation of computer programs.