An essentially different type of finite difference equation is presented in this work. This new FD equation, named the Measured Equation of Invariance (MEI), is not derived directly from Maxwell's differential equations, but is numerically derived from a set of known solutions. Since the MEI is not derived from any physical conditions, it can be used to terminate the computational domain at any point, even at the object boundary. By terminating the computational domain very close to the object of interest, the locality of the methods based on differential equations and the reduction in the number of unknown of the methods based on intergral equations are combined in a single method. This is especially useful in open boundary problems. For this type of problems, the MEI method uses a number of unknowns of the same order of magnitude as the Method of Moments, but with a computational time of order ;This method has been successfully applied to scattering by two-dimensional conducting and dielectric cylinders, scattering by 3-dimensional conducting objects, propagation of waves in transmission lines, waveguide discontinuities, and radiation problems. In all cases, it has been shown to be robust and achieves dramatic savings in computer time and memory.
展开▼
