Finite Distributed Element Method for Fractal Element Analysis Based on Multilayer Resistive-Capacitive Media

Abstract

It is shown that the analysis of fractal elements realized on the basis of an inhomogeneous multilayer resistive-capacitive medium using the classical finite element method (FEM) gives unsatisfactory results for normalized frequencies ωRC > 10. A hybrid computational scheme of the FEM based on L-splines as finite elements (FEs), which at each FE are a solution to the differential equation of homogeneous RC-lines. It is proposed to replace one-dimensional and two-dimensional FEs of various shapes (three-, four-, etc., coal) with a corresponding physical equivalent circuit, where the sides of polygonal FEs are segments of a homogeneous RC-line, which we called a one-dimensional homogeneous RC-element with distribution parameters (OH RC-EDPs).Thus, the problem of determining the characteristics and parameters of the investigated fractal element is replaced by the problem of determining the impedance of the resulting electrical equivalent circuit based on the OH RC-EDP. We called this method of analysis the FDEM (finite distributed element method).