Multidimensional transfer function models

Transfer functions are a standard description of one-dimensional linear and time-invariant systems. They provide an alternative to the conventional representation by ordinary differential equations and are suitable for computer implementation. This article extends that concept to multidimensional (MD) systems, normally described by partial differential equations (PDEs). Transfer function modeling is presented for scalar and for vector PDEs. Vector PDEs contain multiple dependent output variables, e.g., a potential and a flux quantity. This facilitates the direct formulation of boundary and interface conditions in their physical context. It is shown how carefully constructed transformations for the space variable lead to transfer function models for scalar and vector PDEs. They are the starting point for the derivation of discrete models by standard methods for one-dimensional systems. The presented functional transformation approach is suitable for a number of technical applications, like electromagnetics, optics, acoustics and heat and mass transfer